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TI Toolkit Tokens Wiki

Welcome to the tokens wiki! This project aims to collect and organize documentation for every token on the TI-83 series of calculators, sourced from both TI's official reference and community contributions. Each page corresponds to a single token, and includes the token's syntax, functionality, location, translations, error conditions, and other information.

While several documentation sites have emerged over the years, many are no longer actively maintained. The tokens wiki is intended to fill in these gaps, as well as provide documentation that is both human- and machine-readable.

You can view the pages either directly on GitHub or on GitHub Pages. Each token is indexed by its bytes (e.g. Ox14) and readable name (e.g. augment(), with some escaping to make the names web-safe. Our sources are listed here, with attributions found at the bottom of each page. Contributions welcome!

Data sources

And various community members who helped with testing, comparing translations, versions... Why not you? :)

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Ended: Categories

Tokens ↵

Property Value
Hex Value $40
Categories
Localizations
  • FR: et

and

Overview

Returns 1 (true) when both valueA and valueB are true. Otherwise, return is 0 (false).
valueA and valueB can be real numbers, expressions, or lists.
TI Connect™ Program Editor Tip:
Notice the token is "and" where "_" is a space.

Availability: Token available everywhere.

Syntax

valueA and valueB

Arguments

NameTypeOptional
valueAreal|expression|real[]
valueBreal|expression|real[]

Location

2nd, test, LOGIC, 1:and

Description

Examples

Explanation 1

code 1

Explanation 2

code 2

Error Conditions

Advanced Notes

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $95
Categories
Localizations
  • FR: Combinaison

nCr

Overview

Returns the number of combinations of valueA taken valueB at a time.

Availability: Token available everywhere.

Syntax

valueA nCr valueB

Arguments

NameTypeOptional
valueA
valueB

Location

math, PRB, 3:nCr

Overview

Returns a list of the combinations of value taken each element in list at a time.

Availability: Token available everywhere.

Syntax

value nCr list

Arguments

NameTypeOptional
value
listlist

Location

math, PRB, 3:nCr

Overview

Returns a list of the combinations of each element in list taken value at a time.

Availability: Token available everywhere.

Syntax

list nCr value

Arguments

NameTypeOptional
listlist
value

Location

math, PRB, 3:nCr

Overview

Returns a list of the combinations of each element in listA taken each element in listB at a time.

Availability: Token available everywhere.

Syntax

listA nCr listB

Arguments

NameTypeOptional
listAlist
listBlist

Location

math, PRB, 3:nCr

Description

Examples

Explanation 1

code 1

Explanation 2

code 2

Error Conditions

Advanced Notes

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $94
Categories
Localizations
  • FR: Arrangement

nPr

Overview

Returns the number of permutations of valueA taken valueB at a time.

Availability: Token available everywhere.

Syntax

valueA nPr valueB

Arguments

NameTypeOptional
valueA
valueB

Location

math, PRB, 2:nPr

Overview

Returns a list of the permutations of value taken each element in list at a time.

Availability: Token available everywhere.

Syntax

value nPr list

Arguments

NameTypeOptional
value
listlist

Location

math, PRB, 2:nPr

Overview

Returns a list of the permutations of each element in list taken value at a time.

Availability: Token available everywhere.

Syntax

list nPr value

Arguments

NameTypeOptional
listlist
value

Location

math, PRB, 2:nPr

Overview

Returns a list of the permutations of each element in listA taken each element in listB at a time.

Availability: Token available everywhere.

Syntax

listA nPr listB

Arguments

NameTypeOptional
listAlist
listBlist

Location

math, PRB, 2:nPr

Description

Examples

Explanation 1

code 1

Explanation 2

code 2

Error Conditions

Advanced Notes

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $3C
Categories
Localizations
  • FR: ou

or

Overview

Returns 1 if valueA or valueB is ≠ 0. valueA and valueB can be real numbers, expressions, or lists.

Availability: Token available everywhere.

Syntax

valueA or valueB

Arguments

NameTypeOptional
valueAreal|expression|real[]
valueBreal|expression|real[]

Location

2nd, test, LOGIC, 2:or

Description

Examples

Explanation 1

code 1

Explanation 2

code 2

Error Conditions

Advanced Notes

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $3D
Categories
Localizations
  • FR: ouExcl

xor

Overview

Returns 1 if only valueA or valueB = 0. valueA and valueB can be real numbers, expressions, or lists.

Availability: Token available everywhere.

Syntax

valueA xor valueB

Arguments

NameTypeOptional
valueAreal|expression|real[]
valueBreal|expression|real[]

Location

2nd, test, LOGIC, 3:xor

Description

Examples

Explanation 1

code 1

Explanation 2

code 2

Error Conditions

Advanced Notes

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $2D
Categories
Localizations
  • FR: !

!

Overview

Availability: Token available everywhere.

Syntax

!

Description

Examples

Explanation 1

code 1

Explanation 2

code 2

Error Conditions

Advanced Notes

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $6F
Categories
Localizations
  • FR: ≠

≠

Overview

Availability: Token available everywhere.

Syntax

≠

Description

Examples

Explanation 1

code 1

Explanation 2

code 2

Error Conditions

Advanced Notes

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $BB9E
Categories
Localizations
  • FR: ¡

¡

Overview

Availability: Token available everywhere.

Syntax

¡

Description

Examples

Explanation 1

code 1

Explanation 2

code 2

Error Conditions

Advanced Notes

History

Calculator OS Version Description
TI-83+ 1.03 Added
Property Value
Hex Value $BBD2
Categories
Localizations
  • FR: #

#

Overview

Availability: Token available everywhere.

Syntax

#

Description

Examples

Explanation 1

code 1

Explanation 2

code 2

Error Conditions

Advanced Notes

History

Calculator OS Version Description
TI-83+ 1.15 Added
Property Value
Hex Value $BBD3
Categories
Localizations
  • FR: $

$

Overview

Availability: Token available everywhere.

Syntax

$

Description

Examples

Explanation 1

code 1

Explanation 2

code 2

Error Conditions

Advanced Notes

History

Calculator OS Version Description
TI-83+ 1.15 Added
Property Value
Hex Value $BBDA
Categories
Localizations
  • FR: %

%

Overview

Availability: Token available everywhere.

Syntax

%

Description

Examples

Explanation 1

code 1

Explanation 2

code 2

Error Conditions

Advanced Notes

History

Calculator OS Version Description
TI-83+ 1.15 Added
Property Value
Hex Value $BBD4
Categories
Localizations
  • FR: &

&

Overview

Availability: Token available everywhere.

Syntax

&

Description

Examples

Explanation 1

code 1

Explanation 2

code 2

Error Conditions

Advanced Notes

History

Calculator OS Version Description
TI-83+ 1.15 Added
Property Value
Hex Value $10
Categories
Localizations
  • FR: (

(

Overview

Availability: Token available everywhere.

Syntax

(

Description

Examples

Explanation 1

code 1

Explanation 2

code 2

Error Conditions

Advanced Notes

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $BB9A
Categories
Localizations
  • FR: ´

´

Overview

Availability: Token available everywhere.

Syntax

´

Description

Examples

Explanation 1

code 1

Explanation 2

code 2

Error Conditions

Advanced Notes

History

Calculator OS Version Description
TI-83+ 1.03 Added
Property Value
Hex Value $AE
Categories
Localizations
  • FR: '

'

Overview

Availability: Token available everywhere.

Syntax

'

Description

Examples

Explanation 1

code 1

Explanation 2

code 2

Error Conditions

Advanced Notes

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $BBD0
Categories
Localizations
  • FR: '

'

Overview

Syntax

'

Description

Examples

Explanation 1

code 1

Explanation 2

code 2

Error Conditions

Advanced Notes

History

Calculator OS Version Description
Property Value
Hex Value $BB9A
Categories
Localizations
  • FR: ´

´

Overview

Availability: Token available everywhere.

Syntax

´

Description

Examples

Explanation 1

code 1

Explanation 2

code 2

Error Conditions

Advanced Notes

History

Calculator OS Version Description
TI-83+ 1.03 Added
Property Value
Hex Value $BB9C
Categories
Localizations
  • FR: ¨

¨

Overview

Availability: Token available everywhere.

Syntax

¨

Description

Examples

Explanation 1

code 1

Explanation 2

code 2

Error Conditions

Advanced Notes

History

Calculator OS Version Description
TI-83+ 1.03 Added
Property Value
Hex Value $BBD8
Categories
Localizations
  • FR: |

|

Overview

Syntax

|

Description

Examples

Explanation 1

code 1

Explanation 2

code 2

Error Conditions

Advanced Notes

History

Calculator OS Version Description
TI-83+ 1.15 Added
Property Value
Hex Value $B0
Categories
Localizations
  • FR: ⁻

⁻

Overview

Availability: Token available everywhere.

Syntax

⁻

Description

Examples

Explanation 1

code 1

Explanation 2

code 2

Error Conditions

Advanced Notes

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $BBCF
Categories
Localizations
  • FR: ~

~

Overview

Comment:CF-DA: 83+ 1.15 or later

Syntax

~

Description

Examples

Explanation 1

code 1

Explanation 2

code 2

Error Conditions

Advanced Notes

History

Calculator OS Version Description
TI-83+ 1.15 Added
Property Value
Hex Value $BBCF
Categories
Localizations
  • FR: ~

~

Overview

Comment:CF-DA: 83+ 1.15 or later

Syntax

~

Description

Examples

Explanation 1

code 1

Explanation 2

code 2

Error Conditions

Advanced Notes

History

Calculator OS Version Description
TI-83+ 1.15 Added
Property Value
Hex Value $BB9C
Categories
Localizations
  • FR: ¨

¨

Overview

Availability: Token available everywhere.

Syntax

¨

Description

Examples

Explanation 1

code 1

Explanation 2

code 2

Error Conditions

Advanced Notes

History

Calculator OS Version Description
TI-83+ 1.03 Added
Property Value
Hex Value $BBD9
Categories
Localizations
  • FR: _

_

Overview

Syntax

_

Description

Examples

Explanation 1

code 1

Explanation 2

code 2

Error Conditions

Advanced Notes

History

Calculator OS Version Description
TI-83+ 1.15 Added
Property Value
Hex Value $11
Categories
Localizations
  • FR: )

)

Overview

Availability: Token available everywhere.

Syntax

)

Description

Examples

Explanation 1

code 1

Explanation 2

code 2

Error Conditions

Advanced Notes

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $70
Categories
Localizations
  • FR: +

+

Overview

Availability: Token available everywhere.

Syntax

+

Description

Examples

Explanation 1

code 1

Explanation 2

code 2

Error Conditions

Advanced Notes

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $2B
Categories
Localizations
  • FR: ,

,

Overview

Availability: Token available everywhere.

Syntax

,

Description

Examples

Explanation 1

code 1

Explanation 2

code 2

Error Conditions

Advanced Notes

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $04
Categories
Localizations
  • FR: →

→

Overview

Stores value in variable.

Availability: Token available everywhere.

Syntax

Store: value→variable

Arguments

NameTypeOptional
Store:
value
variable

Location

sto→

Description

The → (store) command will store a number, variable, or expression to a variable, using the respective value(s) of the variable(s) at the time. When storing a value in a variable, you have the value on the left side of → and the variable that it will be stored to on the right side.

:1→X
           1

:{1.3,5.7,9.11→ABC
           {1.3 5.7 9.11}

:"HELLO WORLD→Str1
           "HELLO WORLD"

Advanced

It's not easy to put a → symbol into a string, since "→→Str1 would produce a syntax error (and in general, when the calculator 'sees' a → symbol, it assumes that the string is over, and interprets the symbol literally).

However, you can use Equ►String( (outside a program) to get the → or " symbols in a string:

  1. Type them on the home screen and press [ENTER]
  2. Select 1:Quit when the ERR:SYNTAX comes up.
  3. Press [Y=] to go to the equation editor.
  4. Press [2nd] [ENTRY] to recall the symbols to Y1
  5. Now, use Equ►String(Y1,Str1) to store the symbols to a string.

Optimization

You can remove closing parentheses, braces, brackets, and quotes that are before a → command.

Here are a series of examples of using the → command. The first line of each example uses more bytes than necessary. The line following strips out the unnecessary characters and uses less bytes.

Real Variables
1/(2*(3/4))→X
1/(2(3/4→X
Strings
"Hello"→Str1
"Hello→Str1
Lists
{1,2,3,2(X+1)}→L₁
{1,2,3,2(X+1→L₁

5→L₁(1)
5→L₁(1

{4,5,6}→ʟLISTX
{4,5,6→LISTX

Tip: You can remove the ʟ character when storing an entire list to a custom named list, but you must keep the ʟ character present when storing to a specific item, such as 3→ʟLISTX(1

Related Commands

Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, patriotsfan.

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $71
Categories
Localizations
  • FR: -

-

Overview

Availability: Token available everywhere.

Syntax

-

Description

Examples

Explanation 1

code 1

Explanation 2

code 2

Error Conditions

Advanced Notes

History

Calculator OS Version Description
TI-82 1.0 Added

Related Commands

Property Value
Hex Value $30
Categories
Localizations
  • FR: 0

0

Overview

Availability: Token available everywhere.

Syntax

0

Description

Examples

Explanation 1

code 1

Explanation 2

code 2

Error Conditions

Advanced Notes

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $00
Categories
Localizations
  • FR: ``

``

Overview

Syntax

``

Description

Examples

Explanation 1

code 1

Explanation 2

code 2

Error Conditions

Advanced Notes

History

Calculator OS Version Description
Property Value
Hex Value $01
Categories
Localizations
  • FR: ►DMS

►DMS

Overview

Displays value in DMS format.

Availability: Token available everywhere.

Syntax

value►DMS

Arguments

NameTypeOptional
value

Location

2nd, angle, ANGLE, 4:DMS

Description

The ►DMS command can be used when displaying a real number on the home screen, or with the Disp and Pause commands. It will then format the number as an angle with degree, minute, and second parts.

30►DMS
    30°0'0"
100/9°►DMS
    11°6'40"

It will also work when displaying a number by putting it on the last line of a program by itself. It does not work with Output(, Text(, or any other more complicated display commands.

Although ►DMS is meant as a way to format angles in Degree mode, it doesn't depend on the angle mode chosen, only on the number itself. Note that entering a number as degree°minute'second" will also work, in any mode, and it will not be converted to radians in Radian mode.

Rounding to Nearest Second

If you'd prefer to not have seconds with decimal places, you can round your answer to the nearest second with the following formula:

round(Ans*3600,0)/3600►DMS

Or a slightly shorter version:

round(Ans36,2)/36►DMS

Tip: If you find yourself needing this formula regularly, put it into a Y= graphing-function as:

Y1=round(X36,2)/36

And then you can call it from your home screen via:

Y1(123.45678►DMS

Error Conditions

  • ERR:SYNTAX is thrown if the command is used somewhere other than the allowed display commands.
  • ERR:DATA TYPE is thrown if the value is complex, or if given a list or matrix as argument.

Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583, thornahawk.

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $02
Categories
Localizations
  • FR: ►Dec

►Dec

Overview

Displays a real or complex number, expression, list, or matrix in decimal format.

Availability: Token available everywhere.

Syntax

value►Dec

Arguments

NameTypeOptional
value

Location

math, MATH, 2:Dec

Description

This command is generally useless. Its supposed use is to convert numbers into decimal form, but any typed fractions are displayed as decimals anyway.

1/3
     .3333333333
1/3►Dec
     .3333333333

In 2.53 MP or higher, typed fractions are displayed in fraction form. Therefore, the ►Dec command is useful in this case.

Source: parts of this page were written by the following TI|BD contributors: alexrudd, blue_bear_94, burr, CloudVariable, DarkerLine, GoVegan, Myles_Zadok, Timtech.

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $03
Categories
Localizations
  • FR: ►Frac

►Frac

Overview

Displays a real or complex number, expression, list, or matrix as a fraction simplified to its simplest terms.

Availability: Token available everywhere.

Syntax

value►Frac

Arguments

NameTypeOptional
value

Location

math, MATH, 1:Frac

Description

►Frac attempts to display the input in fraction form. It only works on the home screen outside a program, or with the Disp and Pause commands in a program. It takes up to 12 decimal places of a non-terminating decimal to find the corresponding fraction. The decimal input is returned if ►Frac fails to find the fraction form.

For a more versatile algorithm for finding fractions, see the Decimal to Fraction routine.

.333►Frac
        .333
.333333333333►Frac
         1/3

See Also

Source: parts of this page were written by the following TI|BD contributors: alexrudd, burr, CloudVariable, DarkerLine, GoVegan, kg583, Myles_Zadok.

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $04
Categories
Localizations
  • FR: →

→

Overview

Stores value in variable.

Availability: Token available everywhere.

Syntax

Store: value→variable

Arguments

NameTypeOptional
Store:
value
variable

Location

sto→

Description

The → (store) command will store a number, variable, or expression to a variable, using the respective value(s) of the variable(s) at the time. When storing a value in a variable, you have the value on the left side of → and the variable that it will be stored to on the right side.

:1→X
           1

:{1.3,5.7,9.11→ABC
           {1.3 5.7 9.11}

:"HELLO WORLD→Str1
           "HELLO WORLD"

Advanced

It's not easy to put a → symbol into a string, since "→→Str1 would produce a syntax error (and in general, when the calculator 'sees' a → symbol, it assumes that the string is over, and interprets the symbol literally).

However, you can use Equ►String( (outside a program) to get the → or " symbols in a string:

  1. Type them on the home screen and press [ENTER]
  2. Select 1:Quit when the ERR:SYNTAX comes up.
  3. Press [Y=] to go to the equation editor.
  4. Press [2nd] [ENTRY] to recall the symbols to Y1
  5. Now, use Equ►String(Y1,Str1) to store the symbols to a string.

Optimization

You can remove closing parentheses, braces, brackets, and quotes that are before a → command.

Here are a series of examples of using the → command. The first line of each example uses more bytes than necessary. The line following strips out the unnecessary characters and uses less bytes.

Real Variables
1/(2*(3/4))→X
1/(2(3/4→X
Strings
"Hello"→Str1
"Hello→Str1
Lists
{1,2,3,2(X+1)}→L₁
{1,2,3,2(X+1→L₁

5→L₁(1)
5→L₁(1

{4,5,6}→ʟLISTX
{4,5,6→LISTX

Tip: You can remove the ʟ character when storing an entire list to a custom named list, but you must keep the ʟ character present when storing to a specific item, such as 3→ʟLISTX(1

Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, patriotsfan.

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $05
Categories
Localizations
  • FR: Carré

Boxplot

Overview

Defines Plot# (1, 2, or 3) of type

Availability: Token only available from within the Basic editor.

Syntax

Boxplot Plot#(type,Xlist[,freqlist,color#])

Arguments

NameTypeOptional
type
Xlistlist
freqlistlistYes
color#colorNumYes

Location

2nd, stat plot

Description

The commands Plot1(, Plot2(, and Plot3(, which are identical except for which stat plot (1, 2, or 3) they affect, define their corresponding stat plot. When the stat plot is defined, it is also turned on so no PlotsOn command is necessary.

The first argument of the commands is always the type of plot, and is one of Scatter, xyLine, Histogram, Boxplot, ModBoxplot, and NormProbPlot - these types are found in the TYPE submenu of the stat plot menu. The other arguments vary. For all but Histogram and Boxplot, there is a mark argument - this is a dot, a cross, or a box, symbols that can be found in the MARK submenu of the stat plot menu. On color calculators, there is an optional final argument to specify the color of the plot.

Scatter plot

Plot#(Scatter, x-list, y-list, mark) defines a scatter plot. The points defined by x-list and y-list are plotted using mark on the graph screen.

x-list and y-list must be the same length.

xyLine plot

Plot#(xyLine, x-list, y-list, mark) defines an xyLine plot. Similarly to a scatter plot, the points defined by x-list and y-list are plotted using mark on the graph screen, but with an xyLine plot they are also connected by a line, in the order that they occur in the lists.

x-list and y-list must be the same length.

Histogram plot

Plot#(Histogram, x-list, freq list) defines a Histogram plot. The x-axis is divided into intervals that are Xscl wide. A bar is drawn in in each interval whose height corresponds to the number of points in the interval. Points that are not between Xmin and Xmax are not tallied.

Xscl must not be too small - it can divide the screen into no more than 47 different bars.

Box plot

Plot#(Boxplot, x-list, freq list) defines a box plot. A rectangular box is drawn whose left edge is Q1 (the first quartile) of the data, and whose right edge is Q3 (the third quartile). A vertical segment is drawn within the box at the median, and 'whiskers' are drawn from the box to the minimum and maximum data points.

The box plot ignores the Ymax and Ymin dimensions of the screen, and any plots that aren't box plots or modified box plots. Each box plot takes approximately 1/3 of the screen in height, and if more than one are plotted, they will take up different areas of the screen.

Modified box plot

Plot#(ModBoxplot, x-list, freq list, mark) defines a modified box plot. This is almost entirely like the normal box plot, except that it also draws outliers. Whiskers are only drawn to the furthers point within 1.5 times the interquartile range (Q3-Q1) of the box. Beyond this point, data points are drawn individually, using mark.

The box plot ignores the Ymax and Ymin dimensions of the screen, and any plots that aren't box plots or modified box plots. Each box plot takes approximately 1/3 of the screen in height, and if more than one are plotted, they will take up different areas of the screen.

Normal probability plot

Plot#(NormProbPlot, data list, data axis, mark) defines a normal probability plot. The mean and standard deviation of the data are calculated. Then for each point, the number of standard deviations it is from the mean is calculated, and the point is plotted against this number using mark. data axis can be either X or Y: it determines whether the value of a point determines it's x-coordinate or y-coordinate.

The point behind this rather convoluted process is to test the extent to which the data is normally distributed. If it follows the normal distribution closely, then the result will be close to a straight line - otherwise it will be curved.

Advanced Uses

After doing a regression, a scatter plot of ʟRESID against the x-list is a useful measure of the effectiveness of the regression. If the plot appears random, this is a good sign; if there is a pattern to the plot, this means it's likely that a better regression model exists.

Optimization

The ʟ symbol at the beginning of list names can be omitted everywhere in this command.

In addition, every element except the plot type and the data list or data lists are optional, and take on the following default values:

  • freq list is 1 by default, meaning that all frequencies are 1.
  • mark is the box by default.
  • data axis is X by default.

Error Conditions

  • ERR:DIM MISMATCH is thrown if the x and y lists, or the data and frequency lists, have different dimensions.
  • ERR:STAT is thrown if Xscl is too small in the case of a Histogram.

All errors are thrown when plotting the stat plot, as opposed to when the command is executed, and do not provide a 2:Goto option.

Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Myles_Zadok.

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $06
Categories
Localizations
  • FR: [

[

Overview

Syntax

[

Description

Examples

Explanation 1

code 1

Explanation 2

code 2

Error Conditions

Advanced Notes

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $07
Categories
Localizations
  • FR: ]

]

Overview

Syntax

]

Description

Examples

Explanation 1

code 1

Explanation 2

code 2

Error Conditions

Advanced Notes

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $08
Categories
Localizations
  • FR: {

{

Overview

Syntax

{

Description

Examples

Explanation 1

code 1

Explanation 2

code 2

Error Conditions

Advanced Notes

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $09
Categories
Localizations
  • FR: }

}

Overview

Syntax

}

Description

Examples

Explanation 1

code 1

Explanation 2

code 2

Error Conditions

Advanced Notes

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $0A
Categories
Localizations
  • FR: ʳ

ʳ

Overview

Availability: Token available everywhere.

Syntax

ʳ

Description

Normally, when the calculator is in degree mode, the trigonometric functions only return values calculated in degrees. With the r symbol you can have the angle evaluated as if in radian mode because it converts the angle into degrees.

One full rotation around a circle is 2π radians, which is equal to 360°. To convert an angle in radians to degrees you multiply by 180/π, and to convert from degrees to radians multiply by π/180.

In degree mode:

sin(π)        \\sine of Pi degrees
    .0548036651
sin(π^^r)
    0

In radian mode:

sin(π)
    0
sin(π^^r)
    0        \\There's no difference when in radians

Optimization

When you only call the trig function once in a program and want it calculated in radians, instead of changing the mode you can just use ° to save one-byte (the newline from using the command Radian)

:Radian
:sin(X)
can be
:sin(X^^r)
  • ° (degree symbol)

Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Myles_Zadok.

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $0B
Categories
Localizations
  • FR: °

°

Overview

Availability: Token available everywhere.

Syntax

°

Description

Normally, when the calculator is in radian mode, the trigonometric functions only return values calculated in radians. With the ° symbol you can have the angle evaluated as if in degree mode because it converts the angle into radians.

You can insert the degree symbol by pressing [2ND] [ANGLE] [ENTER].

One full rotation around a circle is 2π radians, which is equal to 360°. To convert an angle in radians to degrees you multiply by 180/π, and to convert from degrees to radians multiply by π/180.

In radian mode:

sin(45)        \\ actually calculating sin(2578.31)
    .8509035245
sin(45°)
    .7071067812

In degree mode:

sin(45)
    .7071067812
sin(45°)
    .7071067812    \\ There's no difference when in degrees

Converting Degrees, Minutes & Seconds

The degree symbol also allows you to convert degrees, minutes and seconds into decimal degrees. For example:

90°30'
       90.5
90°30'09"
       90.5025

The minute symbol is inserted by pressing [2ND] [ANGLE] [2]. The seconds symbol is inserted via [ALPHA] [+].

To convert back the other way (decimal to degrees-minutes-seconds) use the ►DMS command, accessed via [2ND] [ANGLE] [4]:

90.5025►DMS
       90°30'09"

Optimization

When you only call the trig function once in a program and want it calculated in degrees, instead of changing the mode you can just use ° to save one-byte (the newline from using the command Degree)

:Degree
:sin(X)
can be
:sin(X°)

Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, simplethinker.

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $0C
Categories
Localizations
  • FR: ⁻¹
⁻¹

Overview

Availability: Token available everywhere.

Syntax

⁻¹

Description

The ֿ¹ command returns the reciprocal of a number, equivalent to dividing 1 by the number (although reciprocals are sometimes more convenient to type). It also works for lists, by calculating the reciprocal of each element.

The ֿ¹ command can also be used on matrices, but it is the matrix inverse that is computed, not the reciprocal of each element. If [A] is an N by N (square) matrix, then [A]ֿ¹ is the N by N matrix such that [A][A]ֿ¹=[A]ֿ¹[A] is the identity matrix. ֿ¹ does not work on non-square matrices.

4ֿ¹
        .25
{1,2,3}ֿ¹
        {1 .5 .3333333333}
[[3,2][4,3]]ֿ¹
        [[3  -2]
         [-4 3 ]]

Much like the number 0 does not have a reciprocal, some square matrices do not have inverses (they are called singular matrices) and you'll get an error when you try to invert them.

Optimization

Writing Aֿ¹B instead of B/A is sometimes beneficial when B is a complicated expression, because it allows you to take off closing parentheses of B. For example:

:(P+√(P²-4Q))/2
can be
:2ֿ¹(P+√(P²-4Q

This may be slower than dividing. There are also situations in which this optimization might lose precision, especially when the number being divided is large:

7fPart(4292/7
        1
7fPart(7ֿ¹4292
        .9999999999

Error Conditions

Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, thornahawk, ztrumpet.

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $0D
Categories
Localizations
  • FR: ²

²

Overview

Availability: Token available everywhere.

Syntax

²

Description

Examples

Explanation 1

code 1

Explanation 2

code 2

Error Conditions

Advanced Notes

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $0E
Categories
Localizations
  • FR: ᵀ

ᵀ

Overview

Availability: Token available everywhere.

Syntax

ᵀ

Description

T.GIF

Command Summary

This command calculates the transpose of a matrix.

Command Syntax

matrixT

Menu Location

Press:

  1. MATRX (on the 83) or 2nd MATRX (83+ or higher) to access the Matrix menu.
  2. LEFT to access the MATH submenu
  3. 2 to select T, or use arrows

Calculator Compatibility

TI-83/84/+/SE

Token Size

1 byte

The T command is used to calculate the transpose of a matrix: it flips a matrix along its main diagonal. This means that the (i,j)th element becomes the (j,i)th element, and vice versa. As a result, the transpose of an M by N matrix is an N by M matrix.

[[1,2,3][4,5,6]]
………… [[1 2 3]
…………. [4 5 6]]
AnsT
………… [[1 4]
…………. [2 5]
…………. [3 6]]

Advanced Uses

In addition to its many uses in linear algebra, the T operation is useful to programmers: with operations such as Matr►list( and augment(, which normally deal with columns, T allows you to use rows instead. See the "Related Commands" section for the commands that this is useful for.

Source: parts of this page were written by the following TI|BD contributors: DarkerLine, Timothy Foster.

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $0F
Categories
Localizations
  • FR: ³

³

Overview

Availability: Token available everywhere.

Syntax

³

Description

Examples

Explanation 1

code 1

Explanation 2

code 2

Error Conditions

Advanced Notes

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $10
Categories
Localizations
  • FR: (

(

Overview

Availability: Token available everywhere.

Syntax

(

Description

Examples

Explanation 1

code 1

Explanation 2

code 2

Error Conditions

Advanced Notes

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $11
Categories
Localizations
  • FR: )

)

Overview

Availability: Token available everywhere.

Syntax

)

Description

Examples

Explanation 1

code 1

Explanation 2

code 2

Error Conditions

Advanced Notes

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $12
Categories
Localizations
  • FR: arrondi(

round(

Overview

Returns a number, expression, list, or matrix rounded to #decimals ( 9).

Availability: Token available everywhere.

Syntax

round(value[,#decimals])

Arguments

NameTypeOptional
value
#decimalsYes

Location

math, NUM, 2:round(

Description

round(value[,#decimals]) returns value rounded to #decimals decimal places. #decimals must be < 10. The default value for #decimals is 9. Also works on complex numbers, lists and matrices.

round(5.45,0)
     5
round(5.65,0)
     6
round(‾5.65,0)
     ‾6
round(π)-π
     4.102e-10
round(π,4)
     3.1416
round({1.5,2.4,3.8},0)
     {2,2,4}
round([[1.8,3.5,120.3][3,‾1,0.2]],0)
     [[2  4   120]
     [3  ‾1  0   ]]

Advanced Uses

Sometimes, round-off error will cause the result of an expression to be slightly off of the correct integer value — for example, a result may be 5.0000000013 instead of 5. If the error is small enough, it will not even be visible if you recall the variable on the home screen. However, this is enough to cause a ERR:DOMAIN error with commands such as sub( and Output(, which require their arguments to be integers.

The easiest way to fix this problem is by wrapping the different arguments in a round( instruction. For example, instead of:

Output(X,1,">")

Try:

Output(round(X,0),1,">")

The int( command will not work here because the round-off error may be negative, such as 4.9999999986 instead of 5, in which case the number will be rounded down to 4.

Error Conditions

  • ERR:DOMAIN if the number of places to round to is not an integer 0 through 9.

Source: parts of this page were written by the following TI|BD contributors: burr, CloudVariable, DarkerLine, GoVegan.

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $13
Categories
Localizations
  • FR: pxl-Test(

pxl-Test(

Overview

Returns 1 if pixel (row, column) is on, 0 if it is off;

Availability: Token available everywhere.

Syntax

pxl-Test(row,column)

Arguments

NameTypeOptional
row
column

Location

2nd, draw, POINTS, 7:pxl-Test(

Description

The pxl-Test( command is used to test a pixel at the given (Y,X) coordinates of the graph screen, to see whether it is on or off. One is returned if the pixel is on and zero is returned if the pixel is off. Please note that the coordinates are switched around so that the row comes first and then the column — it's (Y,X) instead of (X,Y). This command's coordinates are independent of the window settings.

You can store the result of pxl-Test( to a variable for later use, or use the command in a conditional or loop.

:Pxl-On(25,25
:If pxl-Test(25,25
:Disp "Pixel turned on!

Error Conditions

  • ERR:DOMAIN is triggered if the coordinates are not whole numbers or not in the right range ([0..62] for row, [0..94] for column). These bounds are also affected by split screen mode (Horiz)

Source: parts of this page were written by the following TI|BD contributors: Battlesquid, burr, DarkerLine, GoVegan.

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $14
Categories
Localizations
  • FR: chaîne(

augment(

Overview

Returns a matrix, which is matrixB appended to matrixA as new columns.

Availability: Token available everywhere.

Syntax

augment( matrixA ,matrixB )

Arguments

NameTypeOptional
matrixAmatrix
matrixBmatrix

Location

2nd, matrix, MATH, 7:augment(

Overview

Returns a list, which is listB concatenated to the end of listA.

Availability: Token available everywhere.

Syntax

augment(listA,listB)

Arguments

NameTypeOptional
listAlist
listBlist

Location

2nd, list, OPS, 9:augment(

Description

The augment( command is used to combine two lists or two matrices into one. For lists, this is done the obvious way: adding the elements of the second on to the elements of the first. For example:

augment({1,2,3,4},{5,6,7
    {1 2 3 4 5 6 7}

For matrices, the columns of the second matrix are added after the columns of the first matrix: an R by C matrix augmented with an R by D matrix will result in an R by (C+D) matrix. For example:

augment([[1][2]],[[3][4]
    [[1 3]
     [2 4]]

Advanced Uses

Use the T (transpose) command if you want to combine two matrices vertically, rather than horizontally. For example:

augment([[1,2]]T,[[3,4]]T)T
    [[1 2]
     [3 4]]

Optimization

You may be tempted to use augment( to add one element to the end of a list:

:augment(L1,{X→L1

However, the following way is faster and more memory-efficient while the program is running (although it increases the program's size):

:X→L1(1+dim(L1

Error Conditions

  • ERR:DATA TYPE is thrown if you try to augment a single number to a list, a common error — use {X instead of X.
  • ERR:DIM MISMATCH is thrown if you try to augment two matrices with a different number of rows.
  • ERR:INVALID DIM is thrown if one of the arguments is a list with dimension 0, or if the result would have dimension over 999 (for lists) or 99x99 (for matrices).
  • dim( – for retrieving the size of a list
  • seq( – for creating a list based on a formula, or to create a subset of an existing list
  • T – to transpose a 2D matrix

Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Myles_Zadok, Trenly.

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $15
Categories
Localizations
  • FR: permutLigne(

rowSwap(

Overview

Returns a matrix with rowA of matrix swapped with rowB.

Availability: Token available everywhere.

Syntax

rowSwap(matrix,rowA,rowB)

Arguments

NameTypeOptional
matrixmatrix
rowA
rowB

Location

2nd, matrix, MATH, C:rowSwap(

Description

The rowSwap( command swaps two rows of a matrix and returns the result. It is an elementary row operation used in Gaussian Elimination.

[[1,2][3,4]]
    [[1 2]
     [3 4]]
rowSwap(Ans,1,2)
    [[3 4]
     [1 2]]

Advanced Uses

You can swap columns instead of rows with the aid of the T (transpose) command.

Error Conditions

  • ERR:INVALID DIM is thrown if one of the row arguments isn't a valid row (larger than the matrix size, or otherwise bad)

Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan.

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $16
Categories
Localizations
  • FR: ligne+(

row+(

Overview

Returns a matrix with rowA of matrix added to rowB and stored in rowB.

Availability: Token available everywhere.

Syntax

row+(matrix,rowA,rowB)

Arguments

NameTypeOptional
matrixmatrix
rowA
rowB

Location

2nd, matrix, MATH, D:row+(

Description

The row+( command adds one row of a matrix to the second, and returns the result. It is an elementary row operation used in Gaussian Elimination.

[[1,2][3,4]]
    [[1 2]
     [3 4]]
row+(Ans,1,2)
    [[1 2]
     [4 6]]

Advanced Uses

You can add columns instead of rows with the aid of the T (transpose) command.

Error Conditions

  • ERR:INVALID DIM is thrown if one of the row arguments isn't a valid row (larger than the matrix size, or otherwise bad)

Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, jnesselr, Weregoose.

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $17
Categories
Localizations
  • FR: *ligne(

*row(

Overview

Returns a matrix with row of matrix multiplied by value and stored in row.

Availability: Token available everywhere.

Syntax

*row(value,matrix,row)

Arguments

NameTypeOptional
*
value
matrixmatrix
row

Location

2nd, matrix, MATH, E:row(

Description

Examples

Explanation 1

code 1

Explanation 2

code 2

Error Conditions

Advanced Notes

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $18
Categories
Localizations
  • FR: *ligne+(

*row+(

Overview

Returns a matrix with rowA of matrix multiplied by value, added to rowB, and stored in rowB.

Availability: Token available everywhere.

Syntax

*row+(value,matrix,rowA,rowB)

Arguments

NameTypeOptional
*
value
matrixmatrix
rowA
rowB

Location

2nd, matrix, MATH, F:row+(

Description

Examples

Explanation 1

code 1

Explanation 2

code 2

Error Conditions

Advanced Notes

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $19
Categories
Localizations
  • FR: max(

max(

Overview

Returns the larger of valueA and valueB.

Availability: Token available everywhere.

Syntax

max(valueA,valueB)

Arguments

NameTypeOptional
valueA
valueB

Location

math, NUM, 7:max(

Overview

Returns the larger of valueA and valueB.

Availability: Token available everywhere.

Syntax

max(list)

Arguments

NameTypeOptional
listlist

Location

math, NUM, 7:max(

Overview

Returns largest real or complex element in list.

Availability: Token available everywhere.

Syntax

max(list)

Arguments

NameTypeOptional
listlist

Location

2nd, list, MATH, 2:max(

Overview

Returns a real or complex list of the larger of each pair of elements in listA and listB.

Availability: Token available everywhere.

Syntax

max(listA,listB)

Arguments

NameTypeOptional
listAlist
listBlist

Location

2nd, list, MATH, 2:max(

Overview

Returns a real or complex list of the larger of value or each list element.

Availability: Token available everywhere.

Syntax

max(value,list)

Arguments

NameTypeOptional
value
listlist

Location

2nd, list, MATH, 2:max(

Description

max(X,Y) returns the largest of the two numbers X and Y. max(list) returns the largest element of list. max(list1,list2) returns the pairwise maxima of the two lists. max(list1,X) (equivalently, max(X,list1)) returns a list whose elements are the larger of X or the corresponding element of the original list.

max(2,3)
     3
max({2,3,4})
     4
max({1,3},{4,2})
     {4 3}
max({1,3},2)
     {2 3}

Unlike comparison operators such as < and >, max( can also compare complex numbers. To do this, both arguments must be complex — either complex numbers or complex lists: max(2,𝑖) will throw an error even though max(2+0𝑖,𝑖) won't. In the case of complex numbers, the number with the largest absolute value will be returned. When the two numbers have the same absolute value, the first one will be returned: max(𝑖,-𝑖) returns 𝑖 and max(-𝑖,𝑖) returns -𝑖.

Advanced Uses

max( can be used in Boolean comparisons to see if at least one of a list is 1 (true) — useful because commands like If or While only deal with numbers, and not lists, but comparisons like L₁=L₂ return a list of values. In general, the behavior you want varies, and you will use the min( function or the max( function accordingly.

Using max( will give you a lenient test — if any one element of the list is 1 (true), then the max( of the list is true — this is equivalent to putting an or in between every element. For example, this tests if K is equal to any of 24, 25, 26, or 34 (the getKey arrow key values):

:If max(K={24,25,26,34
:Disp "ARROW KEY

To get the element of a real list in Ans with the greatest absolute value, use imag(max(𝑖Ans)) or max(abs(Ans)).

max( can be also used along with min( to constrain a value between a lower and upper number:

:max(-1,min(1,100)) // returns 1 because 1 is between -1 & 100
:max(-1,min(1,0)) // returns 0 because 1 is not between -1 & 0

where the bounds for which the number 1 must fall between are first argument of max( and the second argument of min( in the above code.

Error Conditions

  • ERR:DATA TYPE is thrown when comparing a real and a complex number. This can be avoided by adding +0𝑖 to the real number (or i^4 right after it, for those who are familiar with complex numbers)
  • ERR:DIM MISMATCH is thrown, when using max( with two lists, if they have different dimensions.

Source: parts of this page were written by the following TI|BD contributors: burr, coltonj96, DarkerLine, GoVegan, kg583, lirtosiast, Mapar007, simplethinker.

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $1A
Categories
Localizations
  • FR: min(

min(

Overview

Returns smaller of valueA and valueB.

Availability: Token available everywhere.

Syntax

min(valueA,valueB)

Arguments

NameTypeOptional
valueA
valueB

Location

math, NUM, 6:min(

Overview

Returns smallest real or complex element in list.

Availability: Token available everywhere.

Syntax

min(list)

Arguments

NameTypeOptional
listlist

Location

2nd, list, MATH, 1:min(

Overview

Returns real or complex list of the smaller of each pair of elements in listA and listB.

Availability: Token available everywhere.

Syntax

min(listA,listB)

Arguments

NameTypeOptional
listAlist
listBlist

Location

2nd, list, MATH, 1:min(

Overview

Returns a real or complex list of the smaller of value or each list element.

Availability: Token available everywhere.

Syntax

min(value,list)

Arguments

NameTypeOptional
value
listlist

Location

2nd, list, MATH, 1:min(

Description

min(x,y) returns the smallest of the two numbers x and y. min(list) returns the smallest element of list. min(list1,list2) returns the pairwise minima of the two lists. min(list1,x) (equivalently, min(x,list1)) returns a list whose elements are the smaller of x or the corresponding element of the original list.

min(2,3)
     2
min({2,3,4})
     2
min({1,3},{4,2})
     {1 2}
min({1,3},2)
     {1 2}

Unlike relational operators, such as < and >, min( can also compare complex numbers. To do this, both arguments must be complex — either complex numbers or complex lists: min(2,𝑖) will throw a ERR:DATA TYPE error even though min(2+0𝑖,𝑖) won't. In the case of complex numbers, the number with the smallest absolute value will be returned. When the two numbers have the same absolute value, the second one will be returned: min(𝑖,-𝑖) returns -𝑖 and min(-𝑖,𝑖) returns 𝑖.

Advanced Uses

min( can be used in Boolean comparisons to see if every value of a list is 1 (true) — useful because commands like If or While only deal with numbers, and not lists, but comparisons like L1=L2 return a list of values. In general, the behavior you want varies, and you will use the min( or max( functions accordingly.

Using min( will give you a strict test — only if every single value of a list is true will min( return true. For example, the following code will test if two lists are identical — they have the same exact elements — and print EQUAL in that case:

:If dim(L1)=dim(L2
:Then
:If min(L1=L2
:Disp "EQUAL
:End

The first check, to see if the sizes are identical, is necessary because otherwise comparing the lists will return a ERR:DIM MISMATCH error.

Error Conditions

  • ERR:DATA TYPE is thrown when comparing a real and a complex number. This can be avoided by adding 0𝑖 to the real number.
  • ERR:DIM MISMATCH is thrown, when using min( with two lists, if they have different dimensions.

Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $1B
Categories
Localizations
  • FR: R►Pr(

R►Pr(

Overview

Returns R, given rectangular coordinates x and y or a list of rectangular coordinates.

Availability: Token available everywhere.

Syntax

R►Pr(x,y)

Arguments

NameTypeOptional
x
y

Location

2nd, angle, ANGLE, 5:R, Pr(

Description

R►Pr( (Rectangular to polar radius) takes the (x,y) (Cartesian) coordinates, and gives the radius coordinate r of the same point in (r,θ) (polar) mode. The identity used for this conversion is _r_² = _x_²+_y_²

R►Pr(3,4)
    5
√(3²+4²)
    5
R►Pr({6,5},{8,12})
    {10 13}

The function works even when the equivalent √(_x_²+_y_²) fails due to overflow:

R►Pr(3e99,4e99)
    5e99

Optimization

R►Pr( is the smallest way to implement the distance formula \(d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\). Just give the values x1-x2 and y1 - y2 as arguments:

:√((5-2)²+(4-0)²)
can be
:R►Pr(5-2,4-0)

Error Conditions

Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Myles_Zadok, thornahawk, Timothy Foster.

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $1C
Categories
Localizations
  • FR: R►Pθ(

R►Pθ(

Overview

Returns θ, given rectangular coordinates x and y or a list of rectangular coordinates.

Availability: Token available everywhere.

Syntax

R►Pθ(x,y)

Arguments

NameTypeOptional
θ
x
y

Location

2nd, angle, ANGLE

Description

R►Pθ( (Rectangular to polar θ) takes the (x,y) (Cartesian) coordinate, and returns the angle that the ray from (0,0) to (x,y) makes with the positive x-axis. This is the θ-coordinate of the same point in (r,θ) (polar) mode. The identity used for this conversion is tan(θ)=y__/x, with the correct inverse being chosen depending on the quadrant that the point is in. The range of the angle returned is -π<θ≤π. R►Pθ( can also be used on lists.

R►Pθ( is equivalent to the atan2() instruction seen in C/++ and FORTRAN.

R►Pθ(3,4)
    .927295218
tanֿ¹(4/3)
    .927295218
R►Pθ(0,{1,-1})
    {1.570796327, -1.57096327}

R►Pθ( is affected by Degree and Radian mode in its output, which is an angle measured in degrees or radians respectively.

Advanced Uses

If you want the result to always be a radian angle, regardless of mode settings, you can divide the result by 1ʳ:

R►Pθ(x,y)/1^^r

If you want the result to always be a degree angle, regardless of mode settings, you can divide the result by 1°:

R►Pθ(x,y)/1°

Error Conditions

Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, thornahawk.

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $1D
Categories
Localizations
  • FR: P►Rx(

P►Rx(

Overview

Returns X, given polar coordinates r and θ or a list of polar coordinates.

Availability: Token available everywhere.

Syntax

P►Rx(r,θ)

Arguments

NameTypeOptional
r
θ

Location

2nd, angle, ANGLE, 7:P, Rx(

Description

P►Rx( (polar►rectangular x-coordinate) calculates the x-coordinate of a polar point. Polar coordinates are of the form (r,θ), where θ is the counterclockwise angle made with the positive x-axis, and r is the distance away from the origin (the point (0,0)). The conversion identity x=r*cos(θ) is used to calculate P►Rx(.

The value returned depends on whether the calculator is in radian or degree mode. A full rotation around a circle is 2π radians, which is equal to 360°. The conversion from radians to degrees is angle180/π and from degrees to radians is angleπ/180. The P►Rx( command also accepts a list of points.

P►Rx(5,π/4)
    3.535533906
5*cos(π/4)
    3.535533906
P►Rx({1,2},{π/4,π/3})
    {.7071067812 1}

Advanced Uses

You can bypass the mode setting by using the ° (degree) and ʳ (radian) symbols. This next command will return the same values no matter if your calculator is in degrees or radians:

P►Rx(1,{π/4^^r,60°})
    {.7071067812 .5}

Optimization

In most cases P►Rx(r,θ) can be replaced by r*cos(θ) to save a byte:

:P►Rx(5,π/12)
can be
:5cos(π/12)

Conversely, complicated expressions multiplied by a cosine factor can be simplified by using P►Rx(r,θ) instead.

:(A+BX)cos(π/5)
can be
:P►Rx(A+BX,π/5)

Error Conditions

Source: parts of this page were written by the following TI|BD contributors: CloudVariable, DarkerLine, GoVegan, simplethinker, thornahawk.

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $1E
Categories
Localizations
  • FR: P►Ry(

P►Ry(

Overview

Returns Y, given polar coordinates r and θ or a list of polar coordinates.

Availability: Token available everywhere.

Syntax

P►Ry(r,θ)

Arguments

NameTypeOptional
r
θ

Location

2nd, angle, ANGLE, 8:P, Ry(

Description

P►Ry( (polar to rectangular y-coordinate) calculates the y-coordinate of a polar point. Polar coordinates are of the form (r,θ), where θ is the counterclockwise angle made with the positive x-axis, and r is the distance away from the origin (the point (0,0)). The conversion identity y=r*sin(θ) is used to calculate P►Ry(.

The value returned depends on whether the calculator is in radian or degree mode. A full rotation around a circle is 2π radians, which is equal to 360°. The conversion from radians to degrees is angle180/π and from degrees to radians is angleπ/180. The P►Ry( command also accepts a list of points.

P►Ry(5,π/4)
    3.535533906
5*sin(π/4)
    3.535533906
P►Ry({1,2},{π/4,π/3})
    {.7071067812 1.732050808}

Advanced Uses

You can bypass the mode setting by using the ° (degree) and ʳ (radian) symbols. This next command will return the same values no matter if your calculator is in degrees or radians:

P►Ry(1,{π/4^^r,60°})
    {.7071067812 .8660254038}

Optimization

In most cases P►Ry(r,θ) can be replaced by r*sin(θ) to save a byte:

:P►Ry(5,π/12)
can be
:5sin(π/12)

Conversely, complicated expressions multiplied by a sine factor can be simplified by using P►Ry(r,θ) instead.

:(A+BX)sin(π/5)
can be
:P►Ry(A+BX,π/5)

Error Conditions

Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, thornahawk.

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $1F
Categories
Localizations
  • FR: médianne

median(

Overview

Returns the median of list with frequency freqlist.

Availability: Token available everywhere.

Syntax

median(list[,freqlist])

Arguments

NameTypeOptional
listlist
freqlistlistYes

Location

2nd, list, MATH, 4:median(

Description

The median( command finds the median of a list. It takes a list of real numbers as a parameter. For example:

:Prompt L1
:Disp "MEDIAN OF L1",median(L1

That's not all, however. Awesome as the median( command is, it can also take a frequency list argument, for situations when your elements occur more than once. For example:

:Disp median({1,2,3},{5,4,4})

is short for

:median({1,1,1,1,1,2,2,2,2,3,3,3,3})

The frequency list {5,4,4} means that the first element, 1, occurs 5 times, the second element, 2, occurs 4 times, and the third element, 3, occurs 4 times.

Advanced Uses

Frequency lists don't need to be whole numbers. Amazing as that may sound, your calculator can handle being told that one element of the list occurs 1/3 of a time, and another occurs 22.7 times. It can even handle a frequency of 0 - it will just ignore that element, as though it weren't there. One caveat, though - if all of the elements occur 0 times, there's nothing to take the median of and your calculator will throw an error.

Error Conditions

  • ERR:DATA TYPE is thrown, among other cases, if the data list is complex, or if the frequencies are not all positive and real.
  • ERR:DIM MISMATCH is thrown if the frequency list and the data list have a different number of elements.
  • ERR:DIVIDE BY 0 is thrown if the frequency list's elements are all 0.

Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Mr Dino, Timothy Foster.

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $20
Categories
Localizations
  • FR: MatAléat(

randM(

Overview

Returns a random matrix of rows × columns.
Max rows x columns = 400 matrix elements.

Availability: Token available everywhere.

Syntax

randM(rows,columns)

Arguments

NameTypeOptional
rowsinteger
columnsinteger

Location

2nd, matrix, MATH, 6:randM(

Description

randM(M, N) generates an M by N matrix whose entries are pseudorandom integers between -9 and 9 inclusive.

seed→rand affects the output of randM(.

0→rand
    0
randM(3,3)
    [[9  -3 -9]
     [4  -2 0 ]
     [-7 8  8 ]]

If you actually cared about the bounds of the random numbers, this command would not be very useful, since it's hard to manipulate the matrix to yield uniformly spread random numbers in a different range.

Formulas

The entries of randM( are actually the outputs of successive calls to randInt(-9,9), filled in starting at the bottom right and moving left across each row from the last row to the first.

Error Conditions

  • ERR:INVALID DIM is thrown if the number of rows or columns of the matrix isn't an integer 1-99.

Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, MrTanookiMario.

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $21
Categories
Localizations
  • FR: moyenne(

mean(

Overview

Returns the mean of list with frequency freqlist.

Availability: Token available everywhere.

Syntax

mean(list[,freqlist])

Arguments

NameTypeOptional
listlist
freqlistlistYes

Location

2nd, list, MATH, 3:mean(

Description

The mean( command finds the mean, or the average, of a list. It's pretty elementary. It takes a list of real numbers as a parameter. For example:

:Prompt L1
:Disp "MEAN OF L1",mean(L1

That's not all, however. Awesome as the mean( command is, it can also take a frequency list argument, for situations when your elements occur more than once. For example:

:Disp mean({1,2,3},{5,4,4})

is short for

:mean({1,1,1,1,1,2,2,2,2,3,3,3,3})

The frequency list {5,4,4} means that the first element, 1, occurs 5 times, the second element, 2, occurs 4 times, and the third element, 3, occurs 4 times.

Advanced Uses

You can also use the frequency list version of mean( to calculate weighted averages. For example, suppose you're trying to average grades in a class where homework is worth 50%, quizzes 20%, and tests 30%. You have a 90% average on homework, 75% on quizzes (didn't study too well), but 95% average on tests. You can now calculate your grade with the mean( command:

:mean({90,75,95},{50,20,30

You should get a 88.5 if you did everything right.

Frequency lists don't need to be whole numbers. Amazing as that may sound, your calculator can handle being told that one element of the list occurs 1/3 of a time, and another occurs 22.7 times. It can even handle a frequency of 0 - it will just ignore that element, as though it weren't there. In particular, mean(L1,L2) is effectively equivalent to sum (L1*L2)/sum(L2).

One caveat, though - if all of the elements occur 0 times, there's nothing to take an average of and your calculator will throw an error.

Error Conditions

  • ERR:DATA TYPE is thrown, among other cases, if the data list is complex, or if the frequencies are not all positive and real.
  • ERR:DIM MISMATCH is thrown if the frequency list and the data list have a different number of elements.
  • ERR:DIVIDE BY 0 is thrown if the frequency list's elements are all 0.

Source: parts of this page were written by the following TI|BD contributors: alexrudd, burr, DarkerLine, GoVegan, Mr Dino, thornahawk.

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $22
Categories
Localizations
  • FR: résoudre(

solve(

Overview

Solves expression for variable, given an initial guess and lower and upper bounds within which the solution is sought.

Availability: Token only available from within the Basic editor.

Syntax

solve(expression,variable,guess,{lower,upper})

Arguments

NameTypeOptional
expressionexpression
variable
guess
lower
upper

Location

math, MATH, 0:solve(

Description

The solve( command attempts to iteratively find a real root of a given equation, given the variable to solve for, and an initial guess; i.e., given f(x), solve( will attempt to find a value of x such that f(x)=0. solve( can take a list {lower,upper} as an optional fourth argument, in which case it attempts to find a root between lower and upper inclusive (by default, lower and upper are taken to be -E99 and E99 respectively). Brent's method is used for finding the root.

Unfortunately, the solve( command (as with most iterative methods) is not perfect at solving equations. solve( will in general be unable to find "multiple roots", or can only find it to an accuracy less than the usual (an example would be the root x=1 of the equation (x-1)^n=0 for n greater than 1). solve( will only return one of many possible roots to your equation if your equation has many roots to begin with. The root returned, in general, depends on the value of the guess given. The root returned is usually the root closest to the guess given for well-behaved equations; bad choices of the guess can cause solve( to either return a faraway root or not converge at all to a root.

If possible, the equation should first be solved by hand - if there is a relatively simple formula for the root, that will (usually) be more efficient than using solve(. Otherwise, ensure that the solve( call actually works in all the expected cases during use.

The Solver… utility (located in the same menu in the same place) is usually much easier and more intuitive to use, and is recommended instead of directly using solve( whenever applicable (e.g. the home screen). The same limitations apply to its efficiency. If you are unable to find roots using the Solver, try graphing the function and scanning for roots manually, then using 2:zero in the 2nd:CALC menu to refine your guess.

Note: Solver… changes the value of the variable being solved for to the root found; solve(, on the other hand, finds the root, but does not modify the original value of the variable.

Advanced Uses

Reformulating an equation may be useful in certain instances. For example, the equations f(x)=0 and ef(x)=1 are equivalent. solve((X+1)2,X,0 returns ERR:NO SIGN CHG, while solve(e^((X+1)2)-1,X,0 returns -1.000000616 (pretty close to the root -1). Rearranging the equation may sometimes help as well.

Specifying bounds usually helps solve( to find roots more efficiently. If bounds are readily available, they should be supplied to solve(.

The error condition Bad Guess will occur if you use a string for the equation. There is a way around though. If you store the string into a function and use the function in place of the equation it will work.

Str1 → Y1
solve(Y1,X,0

Error Conditions

  • ERR:BAD GUESS will be thrown if guess wasn't within the lower and upper bound, or else the function is undefined at that point, or if a string is used for an equation.

Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, iPhoenixOnTIBD, Silver Phantom, thornahawk, Timothy Foster.

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $23
Categories
Localizations
  • FR: suite(

seq(

Overview

Returns list created by evaluating expression with regard to variable, from begin to end by increment.

Availability: Token available everywhere.

Syntax

seq(expression,variable,begin,end[,increment])

Arguments

NameTypeOptional
expressionexpression
variable
begin
end
incrementYes

Location

2nd, list, OPS, 5:seq(

Description

The seq( command is very powerful, as it is (almost) the only command that can create a whole list as output. This means that you will need make use of it almost every time that you use lists. The seq( command creates a list by evaluating a formula with one variable taking on a range of several values.

It is similar in this to the For( command, but unlike For(, instead of running a block of commands, it only evaluates a formula. Like the For( command, there is an optional "step" that you can use to get every 3rd, every 5th, etc. value in the range.

Some sample uses of the command:

:seq(I,I,3,7
  • evaluates the expression 'I' with I taking on the values 3..7
  • returns {3,4,5,6,7}
:seq(AX²,X,1,7
  • evaluates the expression AX² with X taking on the values 1..7
  • returns {A,4A,9A,16A,25A,36A,49A}, depending on the value of A
:seq(Y1(T),T,1,9,2
  • evaluates the expression Y₁(T) with T taking on every 2nd value 1..9
  • returns {Y₁(1),Y₁(3),Y₁(5),Y₁(7),Y₁(9)} depending on Y₁

Note: the value of the variable used in the expression does not change. If X has some value stored to it, and you do a seq( command using X, X will still hold that original value. However, if X was undefined before the command, after the command, it will be defined and have a value of 0.

Advanced Uses

The step argument supplied can be negative. If it is, and if the starting value is greater than the ending value, then the sequence will "go backward", evaluating the expression in the opposite order. For example:

:seq(I,I,1,7
    {1,2,3,4,5,6,7}
:seq(I,I,7,1,-1
    {7,6,5,4,3,2,1}

You can use seq( to get a "sublist", that is, to get a list that is only a section of another list. This is pretty much the only effective way to extract a sublist. For example, to get the 2nd through 10th elements of L₁, do the following:

:seq(L1(I),I,2,10

While using seq(, the calculator can still interpret keypresses and store them to getKey. One possible way you can use this feature is to make a password function that asks the user to enter in the correct password before time expires.

Optimizations

It's faster to do an operation on an entire list, than to do the same operation inside a seq( command. For example, take the following:

:seq(Y1(T),T,1,9
can be
:Y1(seq(T,T,1,9

However, not all commands that work for numbers will work for lists. A notable example is getting an element from a list: L₁({1,2,3 will not return the first, second, and third elements of L₁, so you will have to put the L₁ inside the seq( command.

For this same reason, you shouldn't use a seq( command when you're really performing an operation on each element of a list. For example, if L₁ has 10 elements:

:seq(L1(I)²,I,1,dim(L1
can be
:L1²

When generating a list of values incremented by a number i from i to a number N, seq( is not recommended as the amount of overhead on the command considerably slows the generation of the list.
In cases where such a list is to be generated, it is beneficial to generate a list of a specific length, fill that list with the incrementer, and cumulatively sum each value in the list. For example, if a list of all the numbers between 1 and 500 were desired:

:500→dim(L1
:Fill(1,L1
:cumSum(L1→L1

This operation can be sped up even more using binomcdf( or binompdf(.

A seq( command can replace a For( command, if all you're doing inside the For( command is storing to an element of a list. This will improve on both speed and size of your program. For example:

:For(I,1,10
:I²→L1(I
:End
can be
:seq(I²,I,1,10→L1

The seq( command itself can often be replaced with an unusual use of the binomcdf( or binompdf( commands, improving speed and sometimes size as well. However, this optimization is fairly advanced; read the pages for those commands to learn about it.

Error Conditions

  • ERR:ILLEGAL NEST is thrown if you try to use seq( inside of another seq( command.
  • ERR:DATA TYPE occurs when any of the inputted arguments are imaginary or complex.
  • ERR:INVALID DIM occurs when the generated list has a dimension larger than 999.

Source: parts of this page were written by the following TI|BD contributors: alexrudd, burr, DarkerLine, GoVegan, kg583, Timothy Foster, Timtech, Zenohm.

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $24
Categories
Localizations
  • FR: fnInt(

fnInt(

Overview

Returns the function integral of expression with respect to variable, between lower and upper, with specified tolerance.

Availability: Token available everywhere.

Syntax

fnInt(expression,variable,lower,upper[,tolerance])

Arguments

NameTypeOptional
expressionexpression
variable
lower
upper
toleranceYes

Location

math, MATH, 9:fnInt(

Description

fnInt(f(var),var,a,b[,tol]) computes an approximation to the definite integral of f with respect to var from a to b. tol controls the accuracy of the integral computed. The default value of tol is 10-5. fnInt( returns exact results for functions that are polynomials of small degree.

fnInt( only works for real numbers and expressions. The Gauss-Kronrod method is used for approximating the integral.

Tip: Sometimes, to get an answer of acceptable accuracy out of fnInt(, substitution of variables and analytic manipulation may be needed.

fnInt(1/X,X,1,2)
        .6931471806
fnInt(ln(X),X,0,1) <a difficult example>
        -.999998347
fnInt(ln(X),X,0,1,e-11)
        -1

Error Conditions

Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Myles_Zadok.

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $25
Categories
Localizations
  • FR: nDeriv(

nDeriv(

Overview

When command is used in Classic mode, returns approximate numerical derivative of expression with respect to variable at value, with specific tolerance ε.
In MathPrint mode, numeric derivative template pastes and uses default tolerance ε.

Availability: Token available everywhere.

Syntax

nDeriv(expression,variable,value[,ε])

Arguments

NameTypeOptional
expressionexpression
variable
value
εYes

Location

math, MATH, 8:nDeriv(

Description

nDeriv(f(var),var,value[,h]) computes an approximation to the value of the derivative of f(var) with respect to var at var=value. h is the step size used in the approximation of the derivative. The default value of h is 0.001.

nDeriv( only works for real numbers and expressions. nDeriv( can be used only once inside another instance of nDeriv(.

π→X
     3.141592654
nDeriv(sin(T),T,X)
     -.9999998333
nDeriv(sin(T),T,X,(abs(X)+E⁻6)E⁻6)
     -1.000000015
nDeriv(nDeriv(cos(U),U,T),T,X)
     .999999665

Advanced

If the default setting for h doesn't produce a good enough result, it can be difficult to choose a correct substitute. Although larger values of h naturally produce a larger margin of error, it's not always helpful to make h very small. If the difference between f(x+h) and f(x-h) is much smaller than the actual values of f(x+h) or f(x-h), then it will only be recorded in the last few significant digits, and therefore be imprecise.

A suitable compromise is to choose a tolerance h that's based on X. As suggested here, (abs(X)+]E⁻6)E⁻6 is a reasonably good value that often gives better results than the default.

Formula

The exact formula that the calculator uses to evaluate this function is:

(1) \(\begin{align} \texttt{nDeriv}(f(t),t,x,h)=\frac{f(x+h)-f(x-h)}{2h} \end{align}\)

This formula is known as the symmetric derivative, and using it generally increases the accuracy of the calculation. However, in a few instances it can give erroneous answers. One case where it gives false answers is with the function,

(2) \(\begin{align} f(x) = \dfrac{1}{x^2} \bigg\vert_{x=0} \end{align}\)

This derivative is undefined when calculated algebraically, but due to the method of calculation, the derivative given by nDeriv( is zero. These problems can be avoided by ensuring that a function's derivative is defined at the point of interest.

Error Conditions

  • ERR:DOMAIN is thrown if h is 0 (since this would yield division by 0 in the formula)
  • ERR:ILLEGAL NEST is thrown if nDeriv( commands are nested more than one level deep. Just having one nDeriv( command inside another is okay, though.

Source: parts of this page were written by the following TI|BD contributors: DarkerLine, Deoxal, GoVegan, kg583, Timothy Foster.

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $27
Categories
Localizations
  • FR: fMin(

fMin(

Overview

Returns the value of variable where the local minimum of expression occurs, between lower and upper, with specified tolerance.

Availability: Token available everywhere.

Syntax

fMin(expression,variable,lower,upper[,tolerance])

Arguments

NameTypeOptional
expressionexpression
variable
lower
upper
toleranceYes

Location

math, MATH, 6:fMin(

Description

fMin(f(var),var,lo,hi[,tol]) finds the value of var between lo and hi at which the minimum of f(var) occurs. tol controls the accuracy of the minimum value computed. The default value of tol is 10-5.

fMin( only works for real numbers and expressions. Brent's method for optimization is used for approximating the minimum value.

fMin(cos(sin(X)+Xcos(X)),X,0,2)
        1.076873875

Keep in mind that the result is the value of var, and not the value of f(var). In this example, 1.076873875 is not the lowest possible value of cos(sin(X)+Xcos(X)), but rather the X-value at which cos(sin(X)+Xcos(X)) is the lowest.

Advanced Uses

fMin( is sometimes useful in finding so-called "multiple roots" of a function. If the graph of your function appears "flat" near the root, fMin( might be able to find the value of the root more accurately than solve(.

Error Conditions

  • ERR:BOUND is thrown if the lower bound is greater than the upper bound.
  • ERR:DOMAIN is thrown if tol is 0.
  • ERR:TOL NOT MET is thrown if the tolerance is too small for this specific function.

Source: parts of this page were written by the following TI|BD contributors: alexrudd, burr, DarkerLine, GoVegan, kg583, thornahawk.

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $28
Categories
Localizations
  • FR: fMax(

fMax(

Overview

Returns the value of variable where the local maximum of expression occurs, between lower and upper,with specified tolerance.

Availability: Token available everywhere.

Syntax

fMax(expression,variable,lower,upper[,tolerance])

Arguments

NameTypeOptional
expressionexpression
variable
lower
upper
toleranceYes

Location

math, MATH, 7:fMax(

Description

fMax(f(var),var,lo,hi[,tol]) finds the value of var between lo and hi at which the maximum of f(var) occurs. tol controls the accuracy of the maximum value computed. The default value of tol is 10-5.

fMax( only works for real numbers and expressions. Brent's method for optimization is used for approximating the maximum value.

fMax(sin(X)cos(X),X,0,3)
        .7853995667

Keep in mind that the result is the value of var, and not the value of f(var). In this example, .7853995667 is not the highest possible value of sin(X)cos(X), but rather the X-value at which sin(X)cos(X) is the highest.

Error Conditions

  • ERR:BOUND is thrown if the lower bound is greater than the upper bound.
  • ERR:DOMAIN is thrown if tol is 0.
  • ERR:TOL NOT MET is thrown if the tolerance is too small for this specific function.

Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583, thornahawk.

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $29
Categories
Localizations
  • FR:

Overview

Syntax

Description

Examples

Explanation 1

code 1

Explanation 2

code 2

Error Conditions

Advanced Notes

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $2A
Categories
Localizations
  • FR: "

"

Overview

Availability: Token available everywhere.

Syntax

"

Description

Examples

Explanation 1

code 1

Explanation 2

code 2

Error Conditions

Advanced Notes

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $2B
Categories
Localizations
  • FR: ,

,

Overview

Availability: Token available everywhere.

Syntax

,

Description

Examples

Explanation 1

code 1

Explanation 2

code 2

Error Conditions

Advanced Notes

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $2C
Categories
Localizations
  • FR: 𝑖

𝑖

Overview

Returns the complex number i.

Comment:Complex i

Availability: Token available everywhere.

Syntax

i

Location

2nd, 𝑖

Description

The 𝑖 symbol is short for √(-1), and is used for complex numbers in algebra and complex analysis. On the calculator, entering 𝑖 will not cause an error, even in Real mode, but operations that result in a complex number (such as taking the square root of a negative number) will. If you're dealing with complex numbers, then, it's best to switch to a+b𝑖 or r𝑒^θ𝑖 mode.

Advanced Uses

By using 𝑖 in a calculation, the calculator switches to complex number mode to do it, even if in Real mode. So √(-1) will throw an ERR:NONREAL ANS, but √(0𝑖-1) will not (even though it's the same number). This can be used to force calculations to be done using complex numbers regardless of the mode setting — usually by adding or subtracting 0𝑖, although more clever ways can be found.

A good example of this technique is our Quadratic Formula routine.

See Also

Source: parts of this page were written by the following TI|BD contributors: burr, CloudVariable, DarkerLine, GoVegan.

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $2D
Categories
Localizations
  • FR: !

!

Overview

Availability: Token available everywhere.

Syntax

!

Description

Examples

Explanation 1

code 1

Explanation 2

code 2

Error Conditions

Advanced Notes

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $2E
Categories
Localizations
  • FR: RegCubique

CubicReg

Overview

Fits a cubic regression model to Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ.

Availability: Token available everywhere.

Syntax

CubicReg [Xlistname,Ylistname,freqlist,regequ]

Arguments

NameTypeOptional
XlistnamelistYes
YlistnamelistYes
freqlistlistYes
regequYes

Location

stat, CALC, 6:CubicReg

Description

The CubicReg command can calculate the best fit cubic function through a set of points. To use it, you must first store the points to two lists: one of the x-coordinates and one of the y-coordinates, ordered so that the nth element of one list matches up with the nth element of the other list. L₁ and L₂ are the default lists to use, and the List Editor (STAT > Edit…) is a useful window for entering the points. You must have at least 4 points because there are infinitely many cubics that can go through 3 points or less.

In its simplest form, CubicReg takes no arguments, and calculates a cubic through the points in L₁ and L₂:

:{9,13,21,30,31,31,34→L₁
:{260,320,420,530,560,550,590→L₂
:CubicReg

On the home screen, or as the last line of a program, this will display the equation of the quadratic: you'll be shown the format, y=ax³+bx²+cx+d, and the values of a, b, c, and d. It will also be stored in the RegEQ variable, but you won't be able to use this variable in a program — accessing it just pastes the equation wherever your cursor was. Finally, the statistical variables a, b, c, d, and R² will be set as well. This latter variable will be displayed only if "Diagnostic Mode" is turned on (see DiagnosticOn and DiagnosticOff).

You don't have to do the regression on L₁ and L₂, but if you don't you'll have to enter the names of the lists after the command. For example:

:{9,13,21,30,31,31,34→FAT
:{260,320,420,530,560,550,590→CALS
:CubicReg ʟFAT,ʟCALS

You can attach frequencies to points, for when a point occurs more than once, by supplying an additional argument — the frequency list. This list does not have to contain integer frequencies. If you add a frequency list, you must supply the names of the x-list and y-list as well, even when they're L₁ and L₂.

Finally, you can enter an equation variable (such as Y₁) after the command, so that the equation is stored in this variable automatically. This doesn't require you to supply the names of the lists, but if you do, the equation variable must come last. You can use polar, parametric, or sequential variables as well, but since the quadratic will be in terms of X anyway, this doesn't make much sense.

An example of CubicReg with all the optional arguments:

:{9,13,21,30,31,31,34→FAT
:{260,320,420,530,560,550,590→CALS
:{2,1,1,1,2,1,1→FREQ
:CubicReg ʟFAT,ʟCALS,ʟFREQ,Y₁

Advanced

Note that even if a relationship is actually linear or quadratic, since a cubic regression has all the freedom of a linear regression and more, it will produce a better R² value, especially if the number of points is small, and may lead you to (falsely) believe that a relationship is cubic when it actually isn't. Take the correlation constant with a grain of salt, and consider if the fit is really that much better at the expense of doubling the complexity and if there's any reason to believe the relationship between the variables may be cubic.

Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Myles_Zadok, thornahawk, Timothy Foster.

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $2F
Categories
Localizations
  • FR: RegQuatre

QuartReg

Overview

Fits a quartic regression model toXlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ.

Availability: Token available everywhere.

Syntax

QuartReg [Xlistname,Ylistname,freqlist,regequ]

Arguments

NameTypeOptional
XlistnamelistYes
YlistnamelistYes
freqlistlistYes
regequYes

Location

stat, CALC, 7:QuartReg

Description

The QuartReg command can calculate the best fit quartic equation through a set of points. To use it, you must first store the points to two lists: one of the x-coordinates and one of the y-coordinates, ordered so that the Nth element of one list matches up with the Nth element of the other list. L1 and L2 are the default lists to use, and the List Editor (STAT > Edit…) is a useful window for entering the points. You must have at least 5 points, because there's infinitely many quadratics that can go through 4 points or less

In its simplest form, QuartReg takes no arguments, and calculates a quartic through the points in L1 and L2:

:{9,13,21,30,31,31,34→L1
:{260,320,420,530,560,550,590→L2
:QuartReg

On the home screen, or as the last line of a program, this will display the equation of the quartic: you'll be shown the format, y=ax4+bx3+cx2+dx+e, and the values of a, b, c, d, and e. It will also be stored in the RegEQ variable, but you won't be able to use this variable in a program - accessing it just pastes the equation wherever your cursor was. Finally, the statistical variables a, b, c, d, e, and R2 will be set as well. This latter variable will be displayed only if "Diagnostic Mode" is turned on (see DiagnosticOn and DiagnosticOff).

You don't have to do the regression on L1 and L2, but if you don't you'll have to enter the names of the lists after the command. For example:

:{9,13,21,30,31,31,34→FAT
:{260,320,420,530,560,550,590→CALS
:QuartReg ʟFAT,ʟCALS

You can attach frequencies to points, for when a point occurs more than once, by supplying an additional argument - the frequency list. This list does not have to contain integer frequencies. If you add a frequency list, you must supply the names of the x-list and y-list as well, even when they're L1 and L2.

Finally, you can enter an equation variable (such as Y1) after the command, so that the quartic equation is stored to this variable automatically. This doesn't require you to supply the names of the lists, but if you do, the equation variable must come last. You can use polar, parametric, or sequential variables as well, but since the quadratic will be in terms of X anyway, this doesn't make much sense.

An example of QuartReg with all the optional arguments:

:{9,13,21,30,31,31,34→FAT
:{260,320,420,530,560,550,590→CALS
:{2,1,1,1,2,1,1→FREQ
:QuartReg ʟFAT,ʟCALS,ʟFREQ,Y1

Advanced

Note that even if a relationship is actually linear, since a quartic regression has all the freedom of a linear regression and much more, it will produce a better R2 value, especially if the number of points is small, and may lead you to (falsely) believe that a relationship is quartic when it actually isn't. An extreme example is the case of 5 points which are close to being on a line. The linear regression will be very good, but the quartic will seem even better - it will go through all 5 points and have an R2 value of 1. However, this doesn't make the 5 points special - any 5 (that don't have repeating x-values) will do! Take the correlation constant with a grain of salt, and consider if the fit is really that much better at the expense of much added complexity, and if there's any reason to believe the relationship between the variables may be quartic.

Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Timothy Foster.

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $30
Categories
Localizations
  • FR: 0

0

Overview

Availability: Token available everywhere.

Syntax

0

Description

Examples

Explanation 1

code 1

Explanation 2

code 2

Error Conditions

Advanced Notes

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $31
Categories
Localizations
  • FR: 1
1

Overview

Availability: Token available everywhere.

Syntax

1

Description

Examples

Explanation 1

code 1

Explanation 2

code 2

Error Conditions

Advanced Notes

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $32
Categories
Localizations
  • FR: 2

2

Overview

Availability: Token available everywhere.

Syntax

2

Description

Examples

Explanation 1

code 1

Explanation 2

code 2

Error Conditions

Advanced Notes

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $33
Categories
Localizations
  • FR: 3

3

Overview

Availability: Token available everywhere.

Syntax

3

Description

Examples

Explanation 1

code 1

Explanation 2

code 2

Error Conditions

Advanced Notes

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $34
Categories
Localizations
  • FR: 4

4

Overview

Availability: Token available everywhere.

Syntax

4

Description

Examples

Explanation 1

code 1

Explanation 2

code 2

Error Conditions

Advanced Notes

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $35
Categories
Localizations
  • FR: 5

5

Overview

Availability: Token available everywhere.

Syntax

5

Description

Examples

Explanation 1

code 1

Explanation 2

code 2

Error Conditions

Advanced Notes

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $36
Categories
Localizations
  • FR: 6

6

Overview

Availability: Token available everywhere.

Syntax

6

Description

Examples

Explanation 1

code 1

Explanation 2

code 2

Error Conditions

Advanced Notes

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $37
Categories
Localizations
  • FR: 7

7

Overview

Availability: Token available everywhere.

Syntax

7

Description

Examples

Explanation 1

code 1

Explanation 2

code 2

Error Conditions

Advanced Notes

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $38
Categories
Localizations
  • FR: 8

8

Overview

Availability: Token available everywhere.

Syntax

8

Description

Examples

Explanation 1

code 1

Explanation 2

code 2

Error Conditions

Advanced Notes

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $39
Categories
Localizations
  • FR: 9

9

Overview

Availability: Token available everywhere.

Syntax

9

Description

Examples

Explanation 1

code 1

Explanation 2

code 2

Error Conditions

Advanced Notes

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $3A
Categories
Localizations
  • FR: .

.

Overview

Availability: Token available everywhere.

Syntax

.

Description

Examples

Explanation 1

code 1

Explanation 2

code 2

Error Conditions

Advanced Notes

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $3B
Categories
Localizations
  • FR: ᴇ

ᴇ

Overview

Returns value times 10 to the exponent.

Availability: Token available everywhere.

Syntax

Exponent:valueᴇexponent

Arguments

NameTypeOptional
Exponent:
value
ᴇ
exponent

Location

2nd, ᴇᴇ

Overview

Returns list elements times 10 to the exponent.

Availability: Token available everywhere.

Syntax

Exponent:listᴇexponent

Arguments

NameTypeOptional
Exponent:
listlist
ᴇ
exponent

Location

2nd, ᴇᴇ

Overview

Returns matrix elements times 10 to the exponent.

Availability: Token available everywhere.

Syntax

Exponent:matrixᴇexponent

Arguments

NameTypeOptional
Exponent:
matrixmatrix
ᴇ
exponent

Location

2nd, ᴇᴇ

Description

Examples

Explanation 1

code 1

Explanation 2

code 2

Error Conditions

Advanced Notes

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $3C
Categories
Localizations
  • FR: ou

or

Overview

Returns 1 if valueA or valueB is ≠ 0. valueA and valueB can be real numbers, expressions, or lists.

Availability: Token available everywhere.

Syntax

valueA or valueB

Arguments

NameTypeOptional
valueAreal|expression|real[]
valueBreal|expression|real[]

Location

2nd, test, LOGIC, 2:or

Description

Examples

Explanation 1

code 1

Explanation 2

code 2

Error Conditions

Advanced Notes

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $3D
Categories
Localizations
  • FR: ouExcl

xor

Overview

Returns 1 if only valueA or valueB = 0. valueA and valueB can be real numbers, expressions, or lists.

Availability: Token available everywhere.

Syntax

valueA xor valueB

Arguments

NameTypeOptional
valueAreal|expression|real[]
valueBreal|expression|real[]

Location

2nd, test, LOGIC, 3:xor

Description

Examples

Explanation 1

code 1

Explanation 2

code 2

Error Conditions

Advanced Notes

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $3E
Categories
Localizations
  • FR: :

:

Overview

Availability: Token available everywhere.

Syntax

:

Description

Examples

Explanation 1

code 1

Explanation 2

code 2

Error Conditions

Advanced Notes

History

Calculator OS Version Description
TI-82 1.0 Added
Property Value
Hex Value $3F
Categories
Localizations

    ⏎ (newline)

    Overview

    Syntax

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $40
    Categories
    Localizations
    • FR: et

    and

    Overview

    Returns 1 (true) when both valueA and valueB are true. Otherwise, return is 0 (false).
    valueA and valueB can be real numbers, expressions, or lists.
    TI Connect™ Program Editor Tip:
    Notice the token is "and" where "_" is a space.

    Availability: Token available everywhere.

    Syntax

    valueA and valueB

    Arguments

    NameTypeOptional
    valueAreal|expression|real[]
    valueBreal|expression|real[]

    Location

    2nd, test, LOGIC, 1:and

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $41
    Categories
    Localizations
    • FR: A

    A

    Overview

    Availability: Token available everywhere.

    Syntax

    A

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $42
    Categories
    Localizations
    • FR: B

    B

    Overview

    Availability: Token available everywhere.

    Syntax

    B

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $43
    Categories
    Localizations
    • FR: C

    C

    Overview

    Availability: Token available everywhere.

    Syntax

    C

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $44
    Categories
    Localizations
    • FR: D

    D

    Overview

    Availability: Token available everywhere.

    Syntax

    D

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $45
    Categories
    Localizations
    • FR: E

    E

    Overview

    Availability: Token available everywhere.

    Syntax

    E

    Description

    The E symbol is used for entering numbers in scientific notation: it's short for *10^. This means that in many cases, its function is identical to that of the 10^( command (aside from the parenthesis). However, the exponent of E is limited to constant integer values ‾99 to 99.

    The E symbol is used in display by the calculator for large numbers, or when in Sci (scientific) or Eng (engineering) mode.

    Unlike the exponent of E, the mantissa (a special term for the A in A*10^B, in scientific notation) isn't limited in variable type: it can be a constant, a real or complex variable or expression, a list, a matrix, or even omitted entirely (and then it will be assumed to equal 1). The reason for this versatility is simple: internally, only the exponent is taken to be an actual argument for this command. The rest of the calculation is done through implied multiplication.

    5E3
    ………………5000
    E‾5
    ……………….00001

    Advanced Uses

    E99 and -E99 are often used for negative and positive infinity because the TI-83 series of calculators doesn't have an infinity symbol. Commands that often need to use infinity include solve(, fnInt(, normalcdf( (and the other distributions), and many others. The error introduced in this way is usually irrelevant, because it's less than the minimum calculator precision, anyway: E99 is mindbogglingly huge.

    Optimization

    Don't add the mantissa when it's 1:

    1E5
    should be
    E5

    In addition, E2 or E3 can be used as shorthand ways of writing 100 and 1000 respectively. This could be continued, in theory, for higher powers of 10, but those aren't necessary as often.

    Command Timings

    E is much faster than using the 10^( command or typing out 10^. The drawback, of course, is that it's limited to constant values.

    Source: parts of this page were written by the following TI|BD contributors: alexrudd, burr, DarkerLine, GoVegan, Myles_Zadok, simplethinker, Timothy Foster.

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $46
    Categories
    Localizations
    • FR: F

    F

    Overview

    Availability: Token available everywhere.

    Syntax

    F

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $47
    Categories
    Localizations
    • FR: G

    G

    Overview

    Availability: Token available everywhere.

    Syntax

    G

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $48
    Categories
    Localizations
    • FR: H
    H

    Overview

    Availability: Token available everywhere.

    Syntax

    H

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $49
    Categories
    Localizations
    • FR: I

    I

    Overview

    Availability: Token available everywhere.

    Syntax

    I

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $4A
    Categories
    Localizations
    • FR: J

    J

    Overview

    Availability: Token available everywhere.

    Syntax

    J

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $4B
    Categories
    Localizations
    • FR: K

    K

    Overview

    Availability: Token available everywhere.

    Syntax

    K

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $4C
    Categories
    Localizations
    • FR: L

    L

    Overview

    Availability: Token available everywhere.

    Syntax

    L

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $4D
    Categories
    Localizations
    • FR: M

    M

    Overview

    Availability: Token available everywhere.

    Syntax

    M

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $4E
    Categories
    Localizations
    • FR: N

    N

    Overview

    Availability: Token available everywhere.

    Syntax

    N

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $4F
    Categories
    Localizations
    • FR: O

    O

    Overview

    Availability: Token available everywhere.

    Syntax

    O

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $50
    Categories
    Localizations
    • FR: P

    P

    Overview

    Availability: Token available everywhere.

    Syntax

    P

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $51
    Categories
    Localizations
    • FR: Q

    Q

    Overview

    Availability: Token available everywhere.

    Syntax

    Q

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $52
    Categories
    Localizations
    • FR: R

    R

    Overview

    Availability: Token available everywhere.

    Syntax

    R

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $53
    Categories
    Localizations
    • FR: S

    S

    Overview

    Availability: Token available everywhere.

    Syntax

    S

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $54
    Categories
    Localizations
    • FR: T

    T

    Overview

    Availability: Token available everywhere.

    Syntax

    T

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $55
    Categories
    Localizations
    • FR: U

    U

    Overview

    Availability: Token available everywhere.

    Syntax

    U

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $56
    Categories
    Localizations
    • FR: V

    V

    Overview

    Availability: Token available everywhere.

    Syntax

    V

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $57
    Categories
    Localizations
    • FR: W

    W

    Overview

    Availability: Token available everywhere.

    Syntax

    W

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $58
    Categories
    Localizations
    • FR: X

    X

    Overview

    Availability: Token available everywhere.

    Syntax

    X

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $59
    Categories
    Localizations
    • FR: Y

    Y

    Overview

    Availability: Token available everywhere.

    Syntax

    Y

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $5A
    Categories
    Localizations
    • FR: Z

    Z

    Overview

    Availability: Token available everywhere.

    Syntax

    Z

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $5B
    Categories
    Localizations
    • FR: θ

    θ

    Overview

    Availability: Token available everywhere.

    Syntax

    θ

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $5C00
    Categories
    Localizations
    • FR: [A]

    [A]

    Overview

    Syntax

    [A]

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $5C01
    Categories
    Localizations
    • FR: [B]

    [B]

    Overview

    Syntax

    [B]

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $5C02
    Categories
    Localizations
    • FR: [C]

    [C]

    Overview

    Syntax

    [C]

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $5C03
    Categories
    Localizations
    • FR: [D]

    [D]

    Overview

    Syntax

    [D]

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $5C04
    Categories
    Localizations
    • FR: [E]

    [E]

    Overview

    Syntax

    [E]

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $5C05
    Categories
    Localizations
    • FR: [F]

    [F]

    Overview

    Syntax

    [F]

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-83 0.01013 Added
    Property Value
    Hex Value $5C06
    Categories
    Localizations
    • FR: [G]

    [G]

    Overview

    Syntax

    [G]

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-83 0.01013 Added
    Property Value
    Hex Value $5C07
    Categories
    Localizations
    • FR: [H]
    [H]

    Overview

    Syntax

    [H]

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-83 0.01013 Added
    Property Value
    Hex Value $5C08
    Categories
    Localizations
    • FR: [I]

    [I]

    Overview

    Syntax

    [I]

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-83 0.01013 Added
    Property Value
    Hex Value $5C09
    Categories
    Localizations
    • FR: [J]

    [J]

    Overview

    Syntax

    [J]

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-83 0.01013 Added
    Property Value
    Hex Value $5D00
    Categories
    Localizations
    • FR: L₁

    L₁

    Overview

    Availability: Token available everywhere.

    Syntax

    L₁

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $5D01
    Categories
    Localizations
    • FR: L₂

    L₂

    Overview

    Availability: Token available everywhere.

    Syntax

    L₂

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $5D02
    Categories
    Localizations
    • FR: L₃

    L₃

    Overview

    Availability: Token available everywhere.

    Syntax

    L₃

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $5D03
    Categories
    Localizations
    • FR: L₄

    L₄

    Overview

    Availability: Token available everywhere.

    Syntax

    L₄

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $5D04
    Categories
    Localizations
    • FR: L₅

    L₅

    Overview

    Availability: Token available everywhere.

    Syntax

    L₅

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $5D05
    Categories
    Localizations
    • FR: L₆

    L₆

    Overview

    Availability: Token available everywhere.

    Syntax

    L₆

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $5E10
    Categories
    Localizations
    • FR: Y₁

    Y₁

    Overview

    Syntax

    Y₁

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $5E11
    Categories
    Localizations
    • FR: Y₂

    Y₂

    Overview

    Syntax

    Y₂

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $5E12
    Categories
    Localizations
    • FR: Y₃

    Y₃

    Overview

    Syntax

    Y₃

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $5E13
    Categories
    Localizations
    • FR: Y₄

    Y₄

    Overview

    Syntax

    Y₄

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $5E14
    Categories
    Localizations
    • FR: Y₅

    Y₅

    Overview

    Syntax

    Y₅

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $5E15
    Categories
    Localizations
    • FR: Y₆

    Y₆

    Overview

    Syntax

    Y₆

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $5E16
    Categories
    Localizations
    • FR: Y₇

    Y₇

    Overview

    Syntax

    Y₇

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $5E17
    Categories
    Localizations
    • FR: Y₈

    Y₈

    Overview

    Syntax

    Y₈

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $5E18
    Categories
    Localizations
    • FR: Y₉

    Y₉

    Overview

    Syntax

    Y₉

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $5E19
    Categories
    Localizations
    • FR: Y₀

    Y₀

    Overview

    Syntax

    Y₀

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $5E20
    Categories
    Localizations
    • FR: X₁ᴛ

    X₁ᴛ

    Overview

    Syntax

    X₁ᴛ

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $5E21
    Categories
    Localizations
    • FR: Y₁ᴛ

    Y₁ᴛ

    Overview

    Syntax

    Y₁ᴛ

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $5E22
    Categories
    Localizations
    • FR: X₂ᴛ

    X₂ᴛ

    Overview

    Syntax

    X₂ᴛ

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $5E23
    Categories
    Localizations
    • FR: Y₂ᴛ

    Y₂ᴛ

    Overview

    Syntax

    Y₂ᴛ

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $5E24
    Categories
    Localizations
    • FR: X₃ᴛ

    X₃ᴛ

    Overview

    Syntax

    X₃ᴛ

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $5E25
    Categories
    Localizations
    • FR: Y₃ᴛ

    Y₃ᴛ

    Overview

    Syntax

    Y₃ᴛ

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $5E26
    Categories
    Localizations
    • FR: X₄ᴛ

    X₄ᴛ

    Overview

    Syntax

    X₄ᴛ

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $5E27
    Categories
    Localizations
    • FR: Y₄ᴛ

    Y₄ᴛ

    Overview

    Syntax

    Y₄ᴛ

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $5E28
    Categories
    Localizations
    • FR: X₅ᴛ

    X₅ᴛ

    Overview

    Syntax

    X₅ᴛ

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $5E29
    Categories
    Localizations
    • FR: Y₅ᴛ

    Y₅ᴛ

    Overview

    Syntax

    Y₅ᴛ

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $5E2A
    Categories
    Localizations
    • FR: X₆ᴛ

    X₆ᴛ

    Overview

    Syntax

    X₆ᴛ

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $5E2B
    Categories
    Localizations
    • FR: Y₆ᴛ

    Y₆ᴛ

    Overview

    Syntax

    Y₆ᴛ

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $5E40
    Categories
    Localizations
    • FR: r₁

    r₁

    Overview

    Syntax

    r₁

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $5E41
    Categories
    Localizations
    • FR: r₂

    r₂

    Overview

    Syntax

    r₂

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $5E42
    Categories
    Localizations
    • FR: r₃

    r₃

    Overview

    Syntax

    r₃

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $5E43
    Categories
    Localizations
    • FR: r₄

    r₄

    Overview

    Syntax

    r₄

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $5E44
    Categories
    Localizations
    • FR: r₅

    r₅

    Overview

    Syntax

    r₅

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $5E45
    Categories
    Localizations
    • FR: r₆

    r₆

    Overview

    Syntax

    r₆

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $5E80
    Categories
    Localizations
    • FR: |u

    |u

    Overview

    Availability: Token available everywhere.

    Syntax

    |u

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $5E81
    Categories
    Localizations
    • FR: |v

    |v

    Overview

    Availability: Token available everywhere.

    Syntax

    |v

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $5E82
    Categories
    Localizations
    • FR: |w

    |w

    Overview

    Availability: Token available everywhere.

    Syntax

    |w

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $5F
    Categories
    Localizations
    • FR: prgm

    prgm

    Overview

    Executes the program name.

    Availability: Token only available from within the Basic editor.

    Syntax

    prgmname

    Arguments

    NameTypeOptional
    name

    Location

    prgm, CTRL, D:prgm

    Description

    The prgm command is used to execute a program from inside another program (at any time while the program is running), with the secondary program acting as a subprogram for that program. Although they are listed in the program menu and can be executed independently like any other program, subprograms are primarily designed to do a particular task for the other program.

    You insert the prgm command into the program where you want the subprogram to run, and then type (with the alpha-lock on) the program name. You can also go to the program menu to choose a program, pressing ENTER to paste the program name into your program.

    PROGRAM:MYPROG
:ClrHome
:Output(3,3,"Hello
:prgmWHATEVER

    When the subprogram name is encountered during a program, the program will be put on hold and program execution will transfer to the subprogram. Once the subprogram is finished, program execution will go back to the program, continuing right after the subprogram name.

    Although subprograms can call themselves or other subprograms, this should be done sparingly because it can cause memory leaks if done too much or if the subprogram doesn't return to the parent program.

    Branching is local to each program, so you can’t use Goto in one program to jump to a Lbl in another program. In addition, all variables are global, so changing a variable in one program affects the variable everywhere else.

    Advanced Uses

    Each time you call a TI-Basic program, 16 bytes are used to save your place in the original program so you can return to it correctly. This is a small enough amount that you don't have to worry about it, unless you're low on RAM or use a lot of recursion.

    Error Conditions

    See Also

    Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Xphoenix.

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6000
    Categories
    Localizations
    • FR: Img1

    Pic1

    Overview

    Availability: Token available everywhere.

    Syntax

    Pic1

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6001
    Categories
    Localizations
    • FR: Img2

    Pic2

    Overview

    Availability: Token available everywhere.

    Syntax

    Pic2

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6002
    Categories
    Localizations
    • FR: Img3

    Pic3

    Overview

    Availability: Token available everywhere.

    Syntax

    Pic3

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6003
    Categories
    Localizations
    • FR: Img4

    Pic4

    Overview

    Availability: Token available everywhere.

    Syntax

    Pic4

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6004
    Categories
    Localizations
    • FR: Img5

    Pic5

    Overview

    Availability: Token available everywhere.

    Syntax

    Pic5

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6005
    Categories
    Localizations
    • FR: Img6

    Pic6

    Overview

    Availability: Token available everywhere.

    Syntax

    Pic6

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6006
    Categories
    Localizations
    • FR: Img7

    Pic7

    Overview

    Availability: Token available everywhere.

    Syntax

    Pic7

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-83 0.01013 Added
    Property Value
    Hex Value $6007
    Categories
    Localizations
    • FR: Img8

    Pic8

    Overview

    Availability: Token available everywhere.

    Syntax

    Pic8

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-83 0.01013 Added
    Property Value
    Hex Value $6008
    Categories
    Localizations
    • FR: Img9

    Pic9

    Overview

    Availability: Token available everywhere.

    Syntax

    Pic9

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-83 0.01013 Added
    Property Value
    Hex Value $6009
    Categories
    Localizations
    • FR: Img0

    Pic0

    Overview

    Availability: Token available everywhere.

    Syntax

    Pic0

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-83 0.01013 Added
    Property Value
    Hex Value $6100
    Categories
    Localizations
    • FR: BDG1

    GDB1

    Overview

    Availability: Token available everywhere.

    Syntax

    GDB1

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6101
    Categories
    Localizations
    • FR: BDG2

    GDB2

    Overview

    Availability: Token available everywhere.

    Syntax

    GDB2

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6102
    Categories
    Localizations
    • FR: BDG3

    GDB3

    Overview

    Availability: Token available everywhere.

    Syntax

    GDB3

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6103
    Categories
    Localizations
    • FR: BDG4

    GDB4

    Overview

    Availability: Token available everywhere.

    Syntax

    GDB4

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6104
    Categories
    Localizations
    • FR: BDG5

    GDB5

    Overview

    Availability: Token available everywhere.

    Syntax

    GDB5

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6105
    Categories
    Localizations
    • FR: BDG6

    GDB6

    Overview

    Availability: Token available everywhere.

    Syntax

    GDB6

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6106
    Categories
    Localizations
    • FR: BDG7

    GDB7

    Overview

    Availability: Token available everywhere.

    Syntax

    GDB7

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-83 0.01013 Added
    Property Value
    Hex Value $6107
    Categories
    Localizations
    • FR: BDG8

    GDB8

    Overview

    Availability: Token available everywhere.

    Syntax

    GDB8

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-83 0.01013 Added
    Property Value
    Hex Value $6108
    Categories
    Localizations
    • FR: BDG9

    GDB9

    Overview

    Availability: Token available everywhere.

    Syntax

    GDB9

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-83 0.01013 Added
    Property Value
    Hex Value $6109
    Categories
    Localizations
    • FR: BDG0

    GDB0

    Overview

    Availability: Token available everywhere.

    Syntax

    GDB0

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-83 0.01013 Added
    Property Value
    Hex Value $6201
    Categories
    Localizations
    • FR: RegEQ

    RegEQ

    Overview

    Availability: Token available everywhere.

    Syntax

    RegEQ

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6202
    Categories
    Localizations
    • FR: n

    n

    Overview

    Syntax

    n

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6203
    Categories
    Localizations
    • FR: x̄

    x̄

    Overview

    Syntax

    x̄

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6204
    Categories
    Localizations
    • FR: Σx

    Σx

    Overview

    Syntax

    Σx

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6205
    Categories
    Localizations
    • FR: Σx²

    Σx²

    Overview

    Syntax

    Σx²

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6206
    Categories
    Localizations
    • FR: [Sx]

    [Sx]

    Overview

    Syntax

    [Sx]

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6207
    Categories
    Localizations
    • FR: σx

    σx

    Overview

    Syntax

    σx

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6208
    Categories
    Localizations
    • FR: [minX]

    [minX]

    Overview

    Syntax

    [minX]

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6209
    Categories
    Localizations
    • FR: [maxX]

    [maxX]

    Overview

    Syntax

    [maxX]

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $620A
    Categories
    Localizations
    • FR: [minY]

    [minY]

    Overview

    Syntax

    [minY]

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $620B
    Categories
    Localizations
    • FR: [maxY]

    [maxY]

    Overview

    Syntax

    [maxY]

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $620C
    Categories
    Localizations
    • FR: ȳ

    ȳ

    Overview

    Syntax

    ȳ

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $620D
    Categories
    Localizations
    • FR: Σy

    Σy

    Overview

    Syntax

    Σy

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $620E
    Categories
    Localizations
    • FR: Σy²

    Σy²

    Overview

    Syntax

    Σy²

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $620F
    Categories
    Localizations
    • FR: [Sy]

    [Sy]

    Overview

    Syntax

    [Sy]

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6210
    Categories
    Localizations
    • FR: σy

    σy

    Overview

    Syntax

    σy

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6211
    Categories
    Localizations
    • FR: Σxy

    Σxy

    Overview

    Syntax

    Σxy

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6212
    Categories
    Localizations
    • FR: [r]

    [r]

    Overview

    Syntax

    [r]

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6213
    Categories
    Localizations
    • FR: [Med]

    [Med]

    Overview

    Availability: Token available everywhere.

    Syntax

    [Med]

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6214
    Categories
    Localizations
    • FR: Q₁

    Q₁

    Overview

    Syntax

    Q₁

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6215
    Categories
    Localizations
    • FR: Q₃

    Q₃

    Overview

    Syntax

    Q₃

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6216
    Categories
    Localizations
    • FR: [|a]

    [|a]

    Overview

    Syntax

    [|a]

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6217
    Categories
    Localizations
    • FR: [|b]

    [|b]

    Overview

    Syntax

    [|b]

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6218
    Categories
    Localizations
    • FR: [|c]

    [|c]

    Overview

    Syntax

    [|c]

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6219
    Categories
    Localizations
    • FR: [|d]

    [|d]

    Overview

    Syntax

    [|d]

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $621A
    Categories
    Localizations
    • FR: [|e]

    [|e]

    Overview

    Syntax

    [|e]

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $621B
    Categories
    Localizations
    • FR: x₁

    x₁

    Overview

    Syntax

    x₁

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $621C
    Categories
    Localizations
    • FR: x₂

    x₂

    Overview

    Syntax

    x₂

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $621D
    Categories
    Localizations
    • FR: x₃

    x₃

    Overview

    Syntax

    x₃

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $621E
    Categories
    Localizations
    • FR: y₁

    y₁

    Overview

    Syntax

    y₁

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $621F
    Categories
    Localizations
    • FR: y₂

    y₂

    Overview

    Syntax

    y₂

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6220
    Categories
    Localizations
    • FR: y₃

    y₃

    Overview

    Syntax

    y₃

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6221
    Categories
    Localizations
    • FR: 𝑛

    𝑛

    Overview

    Availability: Token available everywhere.

    Syntax

    𝑛

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6222
    Categories
    Localizations
    • FR: [p]

    [p]

    Overview

    Syntax

    [p]

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6223
    Categories
    Localizations
    • FR: [z]

    [z]

    Overview

    Syntax

    [z]

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6224
    Categories
    Localizations
    • FR: [t]

    [t]

    Overview

    Syntax

    [t]

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6225
    Categories
    Localizations
    • FR: χ²

    χ²

    Overview

    Syntax

    χ²

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6226
    Categories
    Localizations
    • FR: [|F]

    [|F]

    Overview

    Syntax

    [|F]

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6227
    Categories
    Localizations
    • FR: [df]

    [df]

    Overview

    Syntax

    [df]

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6228
    Categories
    Localizations
    • FR: p̂

    p̂

    Overview

    Syntax

    p̂

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6229
    Categories
    Localizations
    • FR: p̂₁

    p̂₁

    Overview

    Syntax

    p̂₁

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $622A
    Categories
    Localizations
    • FR: p̂₂

    p̂₂

    Overview

    Syntax

    p̂₂

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $622B
    Categories
    Localizations
    • FR: x̄₁

    x̄₁

    Overview

    Syntax

    x̄₁

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $622C
    Categories
    Localizations
    • FR: Éctypx₁

    Sx₁

    Overview

    Syntax

    Sx₁

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $622D
    Categories
    Localizations
    • FR: n₁

    n₁

    Overview

    Syntax

    n₁

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $622E
    Categories
    Localizations
    • FR: x̄₂

    x̄₂

    Overview

    Syntax

    x̄₂

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $622F
    Categories
    Localizations
    • FR: Éctypx₂

    Sx₂

    Overview

    Syntax

    Sx₂

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6230
    Categories
    Localizations
    • FR: n₂

    n₂

    Overview

    Syntax

    n₂

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6231
    Categories
    Localizations
    • FR: Éctypxp

    Sxp

    Overview

    Syntax

    Sxp

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6232
    Categories
    Localizations
    • FR: borninf

    lower

    Overview

    Availability: Token available everywhere.

    Syntax

    lower

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6233
    Categories
    Localizations
    • FR: bornsup

    upper

    Overview

    Syntax

    upper

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6234
    Categories
    Localizations
    • FR: [s]

    [s]

    Overview

    Syntax

    [s]

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6235
    Categories
    Localizations
    • FR: r²

    r²

    Overview

    Syntax

    r²

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6236
    Categories
    Localizations
    • FR: R²

    R²

    Overview

    Syntax

    R²

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6237
    Categories
    Localizations
    • FR: [factordf]

    [factordf]

    Overview

    Syntax

    [factordf]

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6238
    Categories
    Localizations
    • FR: [factorSS]

    [factorSS]

    Overview

    Syntax

    [factorSS]

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6239
    Categories
    Localizations
    • FR: [factorMS]

    [factorMS]

    Overview

    Syntax

    [factorMS]

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $623A
    Categories
    Localizations
    • FR: [errordf]

    [errordf]

    Overview

    Syntax

    [errordf]

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $623B
    Categories
    Localizations
    • FR: [errorSS]

    [errorSS]

    Overview

    Syntax

    [errorSS]

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $623C
    Categories
    Localizations
    • FR: [errorMS]

    [errorMS]

    Overview

    Syntax

    [errorMS]

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6300
    Categories
    Localizations
    • FR: ZXscl

    ZXscl

    Overview

    Availability: Token available everywhere.

    Syntax

    ZXscl

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6301
    Categories
    Localizations
    • FR: ZYscl

    ZYscl

    Overview

    Availability: Token available everywhere.

    Syntax

    ZYscl

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6302
    Categories
    Localizations
    • FR: Xscl

    Xscl

    Overview

    Availability: Token available everywhere.

    Syntax

    Xscl

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6303
    Categories
    Localizations
    • FR: Yscl

    Yscl

    Overview

    Availability: Token available everywhere.

    Syntax

    Yscl

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6304
    Categories
    Localizations
    • FR: u(𝑛Min)

    u(𝑛Min)

    Overview

    Availability: Token available everywhere.

    Syntax

    u(𝑛Min)

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 UnStart added
    TI-83 0.01013 Renamed UnStart to u(𝑛Min)
    Property Value
    Hex Value $6305
    Categories
    Localizations
    • FR: v(𝑛Min)

    v(𝑛Min)

    Overview

    Availability: Token available everywhere.

    Syntax

    v(𝑛Min)

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 VnStart added
    TI-83 0.01013 Renamed VnStart to v(𝑛Min)
    Property Value
    Hex Value $6306
    Categories
    Localizations
    • FR: U𝑛-₁

    U𝑛-₁

    Overview

    Syntax

    U𝑛-₁

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 U𝑛-₁ added
    TI-83 0.01013 U𝑛-₁ removed
    TI-83 1.010 U𝑛-₁ added
    Property Value
    Hex Value $6307
    Categories
    Localizations
    • FR: V𝑛-₁

    V𝑛-₁

    Overview

    Syntax

    V𝑛-₁

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 V𝑛-₁ added
    TI-83 0.01013 V𝑛-₁ removed
    TI-83 1.010 V𝑛-₁ added
    Property Value
    Hex Value $6308
    Categories
    Localizations
    • FR: Zu(𝑛Min)

    Zu(𝑛Min)

    Overview

    Syntax

    Zu(𝑛Min)

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 ZUnStart added
    TI-83 0.01013 Renamed ZUnStart to Zu(𝑛Min)
    Property Value
    Hex Value $6309
    Categories
    Localizations
    • FR: Zv(𝑛Min)

    Zv(𝑛Min)

    Overview

    Syntax

    Zv(𝑛Min)

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 ZVnStart added
    TI-83 0.01013 Renamed ZVnStart to Zv(𝑛Min)
    Property Value
    Hex Value $630A
    Categories
    Localizations
    • FR: Xmin

    Xmin

    Overview

    Availability: Token available everywhere.

    Syntax

    Xmin

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $630B
    Categories
    Localizations
    • FR: Xmax

    Xmax

    Overview

    Availability: Token available everywhere.

    Syntax

    Xmax

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $630C
    Categories
    Localizations
    • FR: Ymin

    Ymin

    Overview

    Availability: Token available everywhere.

    Syntax

    Ymin

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $630D
    Categories
    Localizations
    • FR: Ymax

    Ymax

    Overview

    Availability: Token available everywhere.

    Syntax

    Ymax

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $630E
    Categories
    Localizations
    • FR: Tmin

    Tmin

    Overview

    Availability: Token available everywhere.

    Syntax

    Tmin

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $630F
    Categories
    Localizations
    • FR: Tmax

    Tmax

    Overview

    Availability: Token available everywhere.

    Syntax

    Tmax

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6310
    Categories
    Localizations
    • FR: θMin

    θMin

    Overview

    Availability: Token available everywhere.

    Syntax

    θMin

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6311
    Categories
    Localizations
    • FR: θMax

    θMax

    Overview

    Availability: Token available everywhere.

    Syntax

    θMax

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6312
    Categories
    Localizations
    • FR: ZXmin

    ZXmin

    Overview

    Availability: Token available everywhere.

    Syntax

    ZXmin

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6313
    Categories
    Localizations
    • FR: ZXmax

    ZXmax

    Overview

    Availability: Token available everywhere.

    Syntax

    ZXmax

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6314
    Categories
    Localizations
    • FR: ZYmin

    ZYmin

    Overview

    Availability: Token available everywhere.

    Syntax

    ZYmin

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6315
    Categories
    Localizations
    • FR: ZYmax

    ZYmax

    Overview

    Availability: Token available everywhere.

    Syntax

    ZYmax

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6316
    Categories
    Localizations
    • FR: Zθmin

    Zθmin

    Overview

    Syntax

    Zθmin

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6317
    Categories
    Localizations
    • FR: Zθmax

    Zθmax

    Overview

    Syntax

    Zθmax

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6318
    Categories
    Localizations
    • FR: ZTmin

    ZTmin

    Overview

    Availability: Token available everywhere.

    Syntax

    ZTmin

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6319
    Categories
    Localizations
    • FR: ZTmax

    ZTmax

    Overview

    Availability: Token available everywhere.

    Syntax

    ZTmax

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $631A
    Categories
    Localizations
    • FR: TblStart

    TblStart

    Overview

    Availability: Token available everywhere.

    Syntax

    TblStart

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $631B
    Categories
    Localizations
    • FR: PlotStart

    PlotStart

    Overview

    Availability: Token available everywhere.

    Syntax

    PlotStart

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 𝑛Min added
    TI-83 0.01013 Renamed 𝑛Min to PlotStart
    Property Value
    Hex Value $631C
    Categories
    Localizations
    • FR: ZPlotStart

    ZPlotStart

    Overview

    Syntax

    ZPlotStart

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $631D
    Categories
    Localizations
    • FR: 𝑛Max

    𝑛Max

    Overview

    Availability: Token available everywhere.

    Syntax

    𝑛Max

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $631E
    Categories
    Localizations
    • FR: Z𝑛Max

    Z𝑛Max

    Overview

    Syntax

    Z𝑛Max

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $631F
    Categories
    Localizations
    • FR: 𝑛Min

    𝑛Min

    Overview

    Availability: Token available everywhere.

    Syntax

    𝑛Min

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 𝑛Start added
    TI-83 0.01013 Renamed 𝑛Start to 𝑛Min
    Property Value
    Hex Value $6320
    Categories
    Localizations
    • FR: Z𝑛Min

    Z𝑛Min

    Overview

    Syntax

    Z𝑛Min

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6321
    Categories
    Localizations
    • FR: ∆Tbl

    ∆Tbl

    Overview

    Availability: Token available everywhere.

    Syntax

    ∆Tbl

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6322
    Categories
    Localizations
    • FR: Tstep

    Tstep

    Overview

    Availability: Token available everywhere.

    Syntax

    Tstep

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6323
    Categories
    Localizations
    • FR: θstep

    θstep

    Overview

    Availability: Token available everywhere.

    Syntax

    θstep

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6324
    Categories
    Localizations
    • FR: ZTstep

    ZTstep

    Overview

    Availability: Token available everywhere.

    Syntax

    ZTstep

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6325
    Categories
    Localizations
    • FR: Zθstep

    Zθstep

    Overview

    Syntax

    Zθstep

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6326
    Categories
    Localizations
    • FR: ∆X

    ∆X

    Overview

    Availability: Token available everywhere.

    Syntax

    ∆X

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6327
    Categories
    Localizations
    • FR: ∆Y

    ∆Y

    Overview

    Availability: Token available everywhere.

    Syntax

    ∆Y

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6328
    Categories
    Localizations
    • FR: XFact

    XFact

    Overview

    Syntax

    XFact

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6329
    Categories
    Localizations
    • FR: YFact

    YFact

    Overview

    Syntax

    YFact

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $632A
    Categories
    Localizations
    • FR: TblInput

    TblInput

    Overview

    Availability: Token available everywhere.

    Syntax

    TblInput

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $632B
    Categories
    Localizations
    • FR: 𝗡

    𝗡

    Overview

    Syntax

    𝗡

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-83 0.01013 Added
    Property Value
    Hex Value $632C
    Categories
    Localizations
    • FR: I%

    I%

    Overview

    Syntax

    I%

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-83 0.01013 Added
    Property Value
    Hex Value $632D
    Categories
    Localizations
    • FR: VA

    PV

    Overview

    Syntax

    PV

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-83 0.01013 Added
    Property Value
    Hex Value $632E
    Categories
    Localizations
    • FR: PMT

    PMT

    Overview

    Syntax

    PMT

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-83 0.01013 Added
    Property Value
    Hex Value $632F
    Categories
    Localizations
    • FR: VAC

    FV

    Overview

    Syntax

    FV

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-83 0.01013 Added
    Property Value
    Hex Value $6330
    Categories
    Localizations
    • FR: |P/Y

    |P/Y

    Overview

    Syntax

    |P/Y

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-83 0.01013 Added
    Property Value
    Hex Value $6331
    Categories
    Localizations
    • FR: |C/Y

    |C/Y

    Overview

    Syntax

    |C/Y

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-83 0.01013 Added
    Property Value
    Hex Value $6332
    Categories
    Localizations
    • FR: w(𝑛Min)

    w(𝑛Min)

    Overview

    Availability: Token available everywhere.

    Syntax

    w(𝑛Min)

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-83 0.01013 Added
    Property Value
    Hex Value $6333
    Categories
    Localizations
    • FR: Zw(𝑛Min)

    Zw(𝑛Min)

    Overview

    Syntax

    Zw(𝑛Min)

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-83 0.01013 Added
    Property Value
    Hex Value $6334
    Categories
    Localizations
    • FR: GraphPas

    PlotStep

    Overview

    Availability: Token available everywhere.

    Syntax

    PlotStep

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-83 0.01013 Added
    Property Value
    Hex Value $6335
    Categories
    Localizations
    • FR: ZGraphPas

    ZPlotStep

    Overview

    Syntax

    ZPlotStep

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-83 0.01013 Added
    Property Value
    Hex Value $6336
    Categories
    Localizations
    • FR: Xres

    Xres

    Overview

    Syntax

    Xres

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-83 0.01013 Added
    Property Value
    Hex Value $6337
    Categories
    Localizations
    • FR: ZXres

    ZXres

    Overview

    Availability: Token available everywhere.

    Syntax

    ZXres

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-83 0.01013 Added
    Property Value
    Hex Value $6338
    Categories
    Localizations
    • FR: TracePas

    TraceStep

    Overview

    Syntax

    TraceStep

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-84+CSE 4.0 Added
    Property Value
    Hex Value $64
    Categories
    Localizations
    • FR: Radian

    Radian

    Overview

    Sets radian angle mode.

    Availability: Token only available from within the Basic editor.

    Syntax

    Radian

    Location

    mode, Radian

    Description

    The Radian command puts the calculator into Radian mode, where the inputs and/or outputs to trig functions are assumed to be radian angles.

    Angles measured in radians range from 0 to 2π. They are defined as the arc length of the arc, on a unit circle (circle with radius 1), that corresponds to the angle when it is placed in the center. This definition actually only differs from degree measurements by a constant factor.

    To convert from a degree angle to a radian angle, multiply by 180/π. To go the other way, and get a radian angle from a degree angle, multiply by π/180.

    The following commands are affected by whether the calculator is in Radian or Degree mode:

    The input is differently interpreted:

    The output is differently expressed:

    However, some commands are notably unaffected by angle mode, even though they involve angles, and this may cause confusion. This happens with the SinReg command, which assumes that the calculator is in Radian mode even when it's not. As a result, the regression model it generates will graph incorrectly in Degree mode.

    Also, complex numbers in polar form are an endless source of confusion. The angle( command, as well as the polar display format, are affected by angle mode. However, complex exponentials (see the e^( command), defined as \(e^{i\theta}=\cos\theta+i\sin\theta\), are evaluated as though in Radian mode, regardless of the angle mode. This gives mysterious results like the following:

    Degree:r𝑒^θ𝑖
        Done
𝑒^(πi)
        1𝑒^(180i)
Ans=𝑒^(180𝑖)
        0 (false)

    Overall, it's better to put your calculator in Radian mode when dealing with polar form of complex numbers, especially since no mathematician would ever use degrees for the purpose anyway.

    Optimization

    It's sometimes beneficial to use the ʳ command instead of switching to Radian mode. The r symbol will make sure a number is interpreted as a radian angle, even in degree mode, so that, for example:

    Degree
    ………………Done
    sin(π)
    ……………….0548036651
    sin(πr)
    ………………0

    This is smaller when only one trig calculation needs to be done. Also, it doesn't change the user's settings, which are good to preserve whenever possible.

    Source: parts of this page were written by the following TI|BD contributors: burr, CloudVariable, DarkerLine, GoVegan, Timothy Foster, Trenly.

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $65
    Categories
    Localizations
    • FR: Degré

    Degree

    Overview

    Sets degree angle mode.

    Availability: Token only available from within the Basic editor.

    Syntax

    Degree

    Location

    mode, Degree

    Description

    The Degree command puts the calculator into Degree mode, where the inputs and/or outputs to trig functions are assumed to be degree angles.

    Angles measured in degrees range from 0 to 360, with 0 being an empty angle, 90 being a right angle, 180 being a straight angle, and 360 being a full angle all the way around a circle.

    To convert from a radian angle to a degree angle, multiply by 180/π. To go the other way, and get a radian angle from a degree angle, multiply by π/180.

    The following commands are affected by whether the calculator is in Radian or Degree mode:

    The input is differently interpreted:

    The output is differently expressed:

    However, some commands are notably unaffected by angle mode, even though they involve angles, and this may cause confusion. This happens with the SinReg command, which assumes that the calculator is in Radian mode even when it's not. As a result, the regression model it generates will graph incorrectly in Degree mode.

    Also, complex numbers in polar form are an endless source of confusion. The angle( command, as well as the polar display format, are affected by angle mode. However, complex exponentials (see the e^( command), defined as \(e^{i\theta}=\cos\theta+i\sin\theta\), are evaluated as though in Radian mode, regardless of the angle mode. This gives mysterious results like the following:

    Degree:r𝑒^θ𝑖
        Done
𝑒^(πi)
        1𝑒^(180i)
Ans=𝑒^(180𝑖)
        0 (false)

    Overall, it's better to put your calculator in Radian mode when dealing with polar form of complex numbers, especially since no mathematician would ever use degrees for the purpose anyway.

    Optimization

    It's sometimes beneficial to use the ° symbol instead of switching to Degree mode. The ° symbol will make sure a number is interpreted as a degree angle, even in Radian mode, so that, for example:

    Radian
        Done
sin(90)
        -.8011526357
sin(90°)
        1

    This is smaller when only one trig calculation needs to be done. Also, it doesn't change the user's settings, which are good to preserve whenever possible.

    Source: parts of this page were written by the following TI|BD contributors: Adriweb, burr, DarkerLine, GoVegan, kg583, pandather.

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $66
    Categories
    Localizations
    • FR: Normal

    Normal

    Overview

    Sets normal display mode.

    Availability: Token only available from within the Basic editor.

    Syntax

    Normal

    Location

    mode, Normal

    Description

    The Normal command puts the calculator in normal number mode, in which it only uses scientific notation for large enough numbers (10 000 000 000 or higher), negative numbers large enough in absolute value (-10 000 000 000 or lower), or numbers close enough to 0 (less than .001 and greater than -.001)

    The other possible settings are Sci (which always uses scientific notation), or Eng (which uses a specific form of scientific notation based on powers of 1000)

    Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan.

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $67
    Categories
    Localizations
    • FR: Sci

    Sci

    Overview

    Sets scientific notation display mode.

    Availability: Token only available from within the Basic editor.

    Syntax

    Sci

    Location

    mode, Sci

    Description

    The Sci command puts the calculator in scientific notation mode, so that all results are displayed in scientific notation: as a (possibly fractional) number between 1 and 10 (not including 10) multiplied by a power of 10.

    Sci
        Done
1000
        1e3
{1,2,3}
        {1e0 2e0 3e0}

    Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan.

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $68
    Categories
    Localizations
    • FR: Ing

    Eng

    Overview

    Sets engineering display mode.

    Availability: Token only available from within the Basic editor.

    Syntax

    Eng

    Location

    mode, Eng

    Description

    The Eng command puts the calculator in engineering notation mode. This is a variation on scientific notation in which the exponent is restricted to be a multiple of 3 (and the mantissa can range between 1 and 1000, not including 1000 itself)

    Eng
        Done
12345
        12.345e3
{1,2,3}
        {1e0 2e0 3e0}

    Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Myles_Zadok.

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $69
    Categories
    Localizations
    • FR: Flottant

    Float

    Overview

    Sets floating decimal mode.

    Availability: Token only available from within the Basic editor.

    Syntax

    Float

    Location

    mode, Float

    Description

    The Float command makes the calculator display numbers with a "floating decimal point" — only as many digits after the decimal as needed are displayed (so whole numbers, for example, are shown without any decimal points). This is the default mode, and usually the most useful.

    A technicality of displaying real numbers on the calculator: A maximum of 14 significant digits are stored in a number, but only 10 of them are actually displayed (or used for comparisons) — the rest are used for additional precision. This means that if a number is displayed as a whole number, it isn't necessarily whole. For example, 1234567890.7 will be displayed as 1234567891 (rounded to 10 significant digits), and 1.0000000003 will be displayed as 1.

    This makes sense from many perspectives: if you get a result of 1.0000000003 after a calculation, odds are that this should be 1, and isn't just because of a precision error. Because the extra digits are there, though, even if they're not displayed, such a number will still be invalid for functions such as Pxl-On( or sub( that want integer arguments, and this sort of error is hard to track down.

    Finally, note that the Float and Fix commands only change the way numbers are displayed: they are saved in the same way in each case. Even if you're in Fix 0 mode, the calculations are not done using integers, and in general the calculations are still done using floating-point numbers no matter the number mode. The one exception is with regressions: if you store a regression to an equation in Fix N mode, it will truncate the numbers involved before storing them to the equation, and as a result, the equation will be different.

    Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583.

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6A
    Categories
    Localizations
    • FR: =

    =

    Overview

    Availability: Token available everywhere.

    Syntax

    =

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6B
    Categories
    Localizations
    • FR: <

    <

    Overview

    Availability: Token available everywhere.

    Syntax

    <

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6C
    Categories
    Localizations
    • FR: >

    >

    Overview

    Availability: Token available everywhere.

    Syntax

    >

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6D
    Categories
    Localizations
    • FR: ≤

    ≤

    Overview

    Availability: Token available everywhere.

    Syntax

    ≤

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6E
    Categories
    Localizations
    • FR: ≥

    ≥

    Overview

    Availability: Token available everywhere.

    Syntax

    ≥

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $6F
    Categories
    Localizations
    • FR: ≠

    ≠

    Overview

    Availability: Token available everywhere.

    Syntax

    ≠

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $70
    Categories
    Localizations
    • FR: +

    +

    Overview

    Availability: Token available everywhere.

    Syntax

    +

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $71
    Categories
    Localizations
    • FR: -

    -

    Overview

    Availability: Token available everywhere.

    Syntax

    -

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $72
    Categories
    Localizations
    • FR: Rep

    Ans

    Overview

    Returns the last answer.

    Availability: Token available everywhere.

    Syntax

    Ans

    Location

    2nd, ans

    Description

    The Ans variable holds the last answer that was stored in the calculator. Because Ans is stored in a special storage area built-in to the calculator, and it is extensively used by the calculator, you cannot delete it. Ans is also useful; it can make your programs both smaller and faster:

    • Unlike other variables which have a value type hard-coded in (i.e., a string can only hold text, and lists and matrices can only hold numbers), Ans can take on whatever value you want: a real or complex, list, matrix, or string are all acceptable.

    • Along with the finance variables, Ans is faster than the real, complex, list, matrix, and string variables; and subsequently, you should try to use it as much as possible.

    One of the most common places to use Ans is in place of storing a value to a variable. Just paste the Ans variable to the location where the variable was called, and then when the expression is evaluated, the calculator will use the current value of Ans. Using the Ans variable allows you to eliminate the variable, which helps save a little or a lot of memory (depending on the type of variable and its size).

    Instead of:

    30+5A→B
Disp 25A,B

    A shorter version would be:

    30+5A
Disp 25A,Ans

    (Since the Ans token is only 1 byte, you've just saved two bytes. In longer programs the savings can add up!)

    The one major drawback to using Ans is that its current value is only temporary.

    What commands modify Ans?

    Whenever you:

    • Store a value to a variable, such as 1→X

    • Place an expression or string on a line by itself, such as 1+2 or "Hello"

    • Use the optional argument of the Pause command such as Pause X. Ans will be updated to the new value.

    If you're performing multiple calculations across multiple variables, you might be better off storing each in a separate variable.

    What commands do NOT modify Ans?

    There are several cases in which changing the value of a variable does not modify Ans, thus preserving its current value for later use:

    • Asking a user for input via Prompt X or Input "X:",X

    • Storing to an equation variable such as "X+1"→Y₁

    • Using DelVar to delete a variable (i.e. set its value to zero, if it's a real variable)

    • For( loops

    • Changing the value with IS>( or DS<(

    Also most other commands that do not modify variables will preserve Ans, including:

    • ClrHome
    • If … Then … Else … End
    • Disp
    • Output()
    • Repeat
    • While
    • Lbl
    • Goto
    • Menu()
    • Pause (when there's no parameter following it, otherwise the parameter will be stored in Ans!)

    Knowing these cases can be very useful, allowing you to make efficient use of Ans to store a result and re-use it in later lines rather than create a temporary variable for it.

    Using Ans with Lists

    Ans can be used to store lists and access individual items. Take the following example:

    10→A
{11,22,33}
Disp Ans(1),Ans(2)

    In this example, the calculator is smart enough to know that Ans is currently holding a list, and so will interpret the (1) and (2) as accessing items from the list. As such it will display 11 and 22. Trying to access Ans(4) will display an error.

    However if we removed line 2 from the code above, Ans would instead be holding the value 10, and as such Ans would be multiplied by 1 and 2, resulting in 10 and 20.

    The augment() function can also be used with Ans to add additional items to your list, for example:

    {1,2}
augment(Ans,{3,4})
Disp Ans

    This will display {1 2 3 4}

    Timing

    Storing a real value into Ans takes approximately 1.0 ms. This does not include the time needed to compute or retrieve the value, which may be significant.

    Source: parts of this page were written by the following TI|BD contributors: alexrudd, burr, DarkerLine, GoVegan, kg583, lirtosiast, Myles_Zadok, rileyp, Timothy Foster, Trenly.

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $73
    Categories
    Localizations
    • FR: Fixe

    Fix

    Overview

    Sets fixed-decimal mode for # of decimal places.

    Availability: Token only available from within the Basic editor.

    Syntax

    Fix #

    Arguments

    NameTypeOptional
    #

    Location

    mode, 0123456789

    Description

    The Fix command puts the calculator in fixed-point display mode: all numbers will be displayed with a fixed number of digits (0-9) after the decimal, depending on the argument of Fix. This could be useful if you're trying to display potentially fractional numbers in a limited amount of space.

    A note on more technical aspects: first, if more digits are available than are displayed, the calculator will round off the displayed number (but not its stored value), so 3.97 will be displayed as 4 in Fix 1 mode. Second, the Fix command can't force more than 10 significant digits to be displayed, so something like 123456789.1 will only display one decimal digit even in Fix 9 mode.

    Finally, note that the Float and Fix commands only change the way numbers are displayed: they are saved in the same way in each case. Even if you're in Fix 0 mode, the calculations are not done using integers, and in general, the calculations are still done using floating-point numbers no matter the number mode. The one exception is with regressions: if you store a regression to an equation in Fix N mode, it will truncate the numbers involved before storing them to the equation, and as a result, the equation will be different.

    Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Myles_Zadok.

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $74
    Categories
    Localizations
    • FR: Horiz

    Horiz

    Overview

    Sets horizontal split-screen mode.

    Availability: Token only available from within the Basic editor.

    Syntax

    Horiz

    Location

    mode, Horiz

    Description

    Horiz is usually at the beginning of a program. It is used at the beginning to ensure that the screen mode is Horiz, for programs such as Hangman that want to use Input but also have the graph screen shown. Note that if you use pixels, the y-coordinate can be no larger than 30, since that is the maximum pixel's range.

    :Horiz

    Source: parts of this page were written by the following TI|BD contributors: alexrudd, Battlesquid, burr, DarkerLine, GoVegan, kg583, Xphoenix.

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $75
    Categories
    Localizations
    • FR: PleinEcr

    Full

    Overview

    Sets full screen mode.

    Availability: Token only available from within the Basic editor.

    Syntax

    Full

    Location

    mode, Full

    Description

    The Full command cancels the effects of either Horiz or G-T.

    Full is usually used either at the beginning and/or ending of a program. It is used at the beginning to ensure that the screen mode is Full, the standard setting. It is used at the end if the screen mode was changed in the middle of the program (as clean up).

    :Full

    Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583, Timothy Foster, Xphoenix, ztrumpet.

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $76
    Categories
    Localizations
    • FR: Fonct

    Func

    Overview

    Sets function graphing mode.

    Availability: Token only available from within the Basic editor.

    Syntax

    Func

    Location

    mode, Func

    Description

    The Func command enables the default function graphing mode. This command is usually unnecessary in a program, but if you want to graph a Y= equation, you'd want to make sure the calculator is in function mode first.

    In function mode, you can graph equations where y (the vertical coordinate) is a function of x (the horizontal coordinate). This mode is most commonly discussed in algebra and single-variable calculus courses. Many curves, such as a parabola, have simple expressions when written in the form y=f(x).

    However, in function mode, many expressions cannot be graphed at all. For example, a circle can't be easily graphed in function mode, since for some x-values, there are two y-values. Using two functions, you can achieve a circle, but it will still require a friendly graphing window to display perfectly.

    Many calculator features are specifically targeted at function mode graphing. For example, two graphing styles (see GraphStyle() can be only used with function mode. The DrawF and DrawInv commands draw functions as if in graphing mode.

    Advanced Uses

    The window variables that apply to function mode are:

    • Xmin — Determines the minimum X-value shown on the screen.
    • Xmax — Determines the maximum X-value shown on the screen.
    • Xscl — Determines the horizontal space between marks on the X-axis in AxesOn mode or dots in GridOn mode.
    • Ymin — Determines the minimum Y-value shown on the screen.
    • Ymax — Determines the maximum Y-value shown on the screen.
    • Yscl — Determines the vertical space between marks on the Y-axis in AxesOn mode or dots in GridOn mode.
    • Xres — Determines the pixel distance between points used for graphing. This is a value 1-8: 1 for best quality, 8 for best speed.

    Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583.

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $77
    Categories
    Localizations
    • FR: Param

    Param

    Overview

    Sets parametric graphing mode.

    Availability: Token only available from within the Basic editor.

    Syntax

    Param

    Location

    mode, Par

    Description

    The Param command enables parametric graphing mode.

    Parametric mode is in many ways a generalization of function mode. Instead of writing y as a function of x, both x and y are written as a function of a parameter t (hence the name, parametric mode). You can easily see that equations in function mode are just a special case of equations in parametric mode: if you set x equal to t, then writing y=f(t) is equivalent to writing y=f(x). Of course, graphing a function this way on a calculator will be slightly slower than doing it in function mode directly, because of the overhead.

    Parametric mode allows you the greatest freedom of all the possible graphing modes - nearly every curve you could encounter can be expressed in parametric form.

    In mathematics, the parameter t is commonly allowed to take on all values from negative to positive infinity. However, this would be impossible to do on a calculator, since the equation would never stop graphing (unlike function mode, there's no easy way to check for which values of t the equation will go off the screen and there's no need to graph it). Instead, the calculator has window variables Tmin, Tmax, and Tstep: it will evaluate the parameter at every value from Tmin to Tmax, increasing by Tstep each time, and 'connect the dots'.

    Polar mode, which you'll read about in the next section, is also a special case of parametric mode: To graph r=f(θ), you can instead graph x=f(t)cos(t) and y=f(t)sin(t), with t graphed over the same interval as θ.

    Advanced Uses

    The window variables that apply to parametric mode are:

    • Tmin — Determines the minimum T-value graphed for equations.
    • Tmax — Determines the maximum T-value graphed for equations.
    • Tstep — Determines the difference between consecutive T-values.
    • Xmin — Determines the minimum X-value shown on the screen.
    • Xmax — Determines the maximum X-value shown on the screen.
    • Xscl — Determines the horizontal space between marks on the X-axis in AxesOn mode or dots in GridOn mode.
    • Ymin — Determines the minimum Y-value shown on the screen.
    • Ymax — Determines the maximum Y-value shown on the screen.
    • Yscl — Determines the vertical space between marks on the Y-axis in AxesOn mode or dots in GridOn mode.

    Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan.

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $78
    Categories
    Localizations
    • FR: Polaire

    Polar

    Overview

    Sets polar graphing mode.

    Availability: Token only available from within the Basic editor.

    Syntax

    Polar

    Location

    mode, Polar

    Description

    The Polar command enables the polar graphing mode.

    Unlike the previous modes, polar mode doesn't use the more common (x,y) coordinates. Instead, the coordinates (r,θ) are used, where θ is the counterclockwise angle made with the positive x-axis, and r is the distance away from the origin (the point (0,0)). Although it's possible to translate from one system to the other, polar coordinates are more useful for some expressions (and, of course, less useful for others).

    In particular, they're very good at graphing anything circle-related. The equation for a circle in polar mode is just r=1 (or any other number, for a circle of different radius).

    Like in parametric mode, the parameter θ uses the window variables θmin, θmax, and θstep to determine which points are graphed. A common situation is θmin=0, θmax=2π: in Radian mode, this corresponds to going all the way around the circle. Of course, you could use Degree mode and set θmax to be 360, but this is uncommon in mathematics.

    Advanced Uses

    The window variables that apply to polar mode are:

    • θmin — Determines the minimum θ-value graphed for equations.
    • θmax — Determines the maximum θ-value graphed for equations.
    • θstep — Determines the difference between consecutive θ-values.
    • Xmin — Determines the minimum X-value shown on the screen.
    • Xmax — Determines the maximum X-value shown on the screen.
    • Xscl — Determines the horizontal space between marks on the X-axis in AxesOn mode or dots in GridOn mode.
    • Ymin — Determines the minimum Y-value shown on the screen.
    • Ymax — Determines the maximum Y-value shown on the screen.
    • Yscl — Determines the vertical space between marks on the Y-axis in AxesOn mode or dots in GridOn mode.

    Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $79
    Categories
    Localizations
    • FR: Suite

    Seq

    Overview

    Sets sequence graphing mode.

    Availability: Token only available from within the Basic editor.

    Syntax

    Seq

    Location

    mode, Seq

    Description

    The Seq command enables sequence graphing mode.

    Sequential mode is used for graphing sequences, which can be thought of as functions from the positive (or non-negative) integers. The TI-83 calculators let n be the independent variable in this situation, and the three sequences, instead of using subscripts, use the letters u, v, and w.

    One of the main advantages of sequential mode is that it allows recursive definitions: u(n) can be defined in terms of u(n-1) and u(n-2). For recursive definitions to work, an initial case must be defined: this is done using the variables u(_n_Min), v(_n_Min), and w(_n_Min). The constant _n_Min is the initial case, for which the calculator will use a specific value rather than the formula.

    For example, say a bunny population starts out at 100 and doubles each year. We can describe this situation using the recursive definition u(n)=2u(n-1) (this just says that the _n_th year population is twice the population of the previous year); then we set u(_n_Min)=100. Note that without u(_n_Min), the equation would be meaningless - without the initial population, we have no way to calculate any other population.

    When you're using more than one previous value — both u(n-1) and u(n-2)) — you need more than one initial value, and then u(_n_Min) becomes a list.

    Advanced Uses

    Sequence graphing mode has several submodes that can be selected from the 2nd FORMAT screen. They are Time, Web, uvAxes, uwAxes, and vwAxes. Sequences are still defined in the same way, but these modes control the way that they're graphed.

    The window variables that apply to sequence mode are:

    • _n_Min — Determines the minimum n-value calculated for equations.
    • _n_Max — Determines the maximum n-value calculated for equations.
    • PlotStart — Determines the first value of n that is actually graphed.
    • PlotStep — Determines the difference between consecutive graphed values of n.
    • Xmin — Determines the minimum X-value shown on the screen.
    • Xmax — Determines the maximum X-value shown on the screen.
    • Xscl — Determines the horizontal space between marks on the X-axis in AxesOn mode or dots in GridOn mode.
    • Ymin — Determines the minimum Y-value shown on the screen.
    • Ymax — Determines the maximum Y-value shown on the screen.
    • Yscl — Determines the vertical space between marks on the Y-axis in AxesOn mode or dots in GridOn mode.

    Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $7A
    Categories
    Localizations
    • FR: ValeursAuto

    IndpntAuto

    Overview

    Sets table to generate independent-variable values automatically.

    Availability: Token only available from within the Basic editor.

    Syntax

    IndpntAuto

    Location

    2nd, tblset, Indpnt: Auto

    Description

    The IndpntAuto setting sets the independent variable (X, T, θ, or n depending on graphing mode) to be filled in automatically in the table (which is accessible by pressing 2nd TABLE, or from a program with the DispTable command).

    The values which will be filled in start at the value TblStart and increment by ΔTbl(which can be negative, but not 0). They will also be stored in the list TblInput. All these variables can be accessed through the VARS|6:Table… menu; TblStart and ΔTbl can also be edited in the [2ND][TBLSET] menu.

    The other possibility for this setting is IndpntAsk - if that setting is turned on, you must scroll to the corresponding row in the independent variable column, and enter a value.

    Error Conditions

    Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, kg583.

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $7B
    Categories
    Localizations
    • FR: ValeursDem

    IndpntAsk

    Overview

    Sets table to ask for independent-variable values.

    Availability: Token only available from within the Basic editor.

    Syntax

    IndpntAsk

    Location

    2nd, tblset, Indpnt: Ask

    Description

    With the IndpntAsk setting, the independent variable (X, T, θ, or n depending on graphing mode) will not be calculated automatically in the table. Instead, when looking at the table, you must select an entry in the independent variable column, press ENTER, and enter a value. The values entered will also be stored to the TblInput list.

    (To access the table, press [2ND][TABLE], or use the DispTable command in a program)

    The alternative, IndpntAuto, fills in several values starting at TblStart and increasing by ΔTbl, and makes the table scrollable (up and down).

    Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, kg583.

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $7C
    Categories
    Localizations
    • FR: CalculsAuto

    DependAuto

    Overview

    Sets table to generate dependent-variable values automatically.

    Availability: Token only available from within the Basic editor.

    Syntax

    DependAuto

    Location

    2nd, tblset, Depend: Auto

    Description

    When the DependAuto setting (opposed to the DependAsk setting) is turned on, values in the table are automatically calculated. With IndpntAuto, that means the table is automatically filled out completely; with IndpntAsk, that means that as soon as you enter a value for the independent variable, all the values of the dependent variables are calculated. This is usually the setting you want to use.

    Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Myles_Zadok.

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $7D
    Categories
    Localizations
    • FR: CalculsDem

    DependAsk

    Overview

    Sets table to ask for dependent-variable values.

    Availability: Token only available from within the Basic editor.

    Syntax

    DependAsk

    Location

    2nd, tblset, Depend: Ask

    Description

    When the DependAsk setting (opposed to the DependAuto setting) is turned on, values in the table are not automatically calculated. To calculate the value of an equation, you have to select the column corresponding to that equation in the row corresponding to the value at which to calculate it, and press ENTER. For example, to calculate Y1 at X=0, select the X=0 column, scroll right to Y1, and press ENTER.

    The DependAsk setting might be useful when dealing with a difficult-to-calculate function, for which you wouldn't want to have to calculate values that aren't really necessary.

    Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Myles_Zadok.

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $7E
    Categories
    Localizations
    • FR: Graph Format

    Graph Format

    Overview

    Syntax

    Graph Format

    Description

    Examples

    Explanation 1

    code 1

    Explanation 2

    code 2

    Error Conditions

    Advanced Notes

    History

    Calculator OS Version Description
    Property Value
    Hex Value $7E00
    Categories
    Localizations
    • FR: Séquentiel

    Sequential

    Overview

    Sets mode to graph functions sequentially.

    Availability: Token only available from within the Basic editor.

    Syntax

    Sequential

    Location

    mode, Sequential

    Description

    Puts the calculator into sequential graphing mode (the default). When multiple equations are enabled at the same time, sequential graphing mode means that they will be graphed one after the other (as opposed to Simul mode, in which they will be graphed simultaneously)

    If you use a list in an equation, as with Y1={1,2,3}X, this will graph several equations that will always graph separately, regardless of this setting, which only affects multiple functions in different equation variables.

    Make sure not to confuse this with Seq mode, which is referred to in this guide as sequence graphing mode.

    Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $7E01
    Categories
    Localizations
    • FR: Simul

    Simul

    Overview

    Sets mode to graph functions simultaneously.

    Availability: Token only available from within the Basic editor.

    Syntax

    Simul

    Location

    mode, Simul

    Description

    Simul puts the calculator into simultaneous graphing mode. When multiple equations are enabled at the same time, simultaneous graphing mode graphs them at the same time (as opposed to Sequential mode, in which they will be graphed one after the other)

    If you use a list in an equation, as with Y1={1,2,3}X, this will graph several equations that will always graph separately, regardless of this setting, which only affects multiple functions in different equation variables.

    Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Myles_Zadok.

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $7E02
    Categories
    Localizations
    • FR: CoordPol

    PolarGC

    Overview

    Sets polar graphing coordinates format.

    Availability: Token only available from within the Basic editor.

    Syntax

    PolarGC

    Location

    2nd, format, PolarGC

    Description

    The PolarGC ("Polar Grid Coordinates") command (like its opposite, the RectGC) command, affects how the coordinates of a point on the graph screen are displayed. When PolarGC is enabled, the coordinates of a point are displayed as (R,θ).

    The polar coordinates of a point can be interpreted as the distance R it is away from the origin (0,0), and the direction θ. θ is the angle that a ray to the point would make with the positive X-axis (so polar coordinates are affected by Degree/Radian mode). An angle of 0 means the point is to the left of the origin; an angle of 90° (π/2 radians) means it's up from the origin, and so on. So, for example, the point with R=2 and θ=270° (3π/2 radians) would be two units down from the origin.

    Of course, coordinates are only displayed with the CoordOn setting; however, with CoordOff, RectGC and PolarGC are still useful, because in a variety of cases, the coordinates of a point are also stored to variables. PolarGC doesn't change the fact that they're stored to X and Y, as with RectGC; however, with PolarGC, they are also stored to R and θ.

    Although the PolarGC command naturally goes with Polar graphing mode, the two settings are independent; you can use both PolarGC and RectGC with any graphing mode.

    Advanced

    The following situations involve storing coordinates of a point to variables:

    • Graphing an equation
    • Tracing an equation or plot
    • Moving the cursor on the graph screen
    • Using the interactive mode of one of the 2nd DRAW commands
    • Using one of DrawF, DrawInv, or Tangent(
    • Anything in the 2nd CALC menu.

    Naturally, any command like Input or Select( which involves the above, will also store coordinates of a point.

    Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan.

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $7E03
    Categories
    Localizations
    • FR: CoordRect

    RectGC

    Overview

    Sets rectangular graphing coordinates format.

    Availability: Token only available from within the Basic editor.

    Syntax

    RectGC

    Location

    2nd, format, RectGC

    Description

    The RectGC ("Rectangular Grid Coordinates") command (like its opposite, the PolarGC) command, affects how the coordinates of a point on the graph screen are displayed. When RectGC is enabled, the coordinates of a point are displayed as (X,Y).

    The X and Y coordinates of a point are interpreted as the horizontal and vertical distance from the origin (the point (0,0)) Up and right are positive directions, while down and left are negative. For example, the point (1,-2) — that is, the point with x-coordinate 1 and y-coordinate -2 — is one horizontal unit right and two horizontal units down from (0,0).

    Of course, coordinates are only displayed with the CoordOn setting; however, with CoordOff, RectGC and PolarGC are still useful, because in a variety of cases, the coordinates of a point are also stored to variables. With RectGC enabled, they are stored to X and Y.

    Advanced

    The following situations involve storing coordinates of a point to variables:

    • Graphing an equation
    • Tracing an equation or plot
    • Moving the cursor on the graph screen
    • Using the interactive mode of one of the 2nd DRAW commands
    • Using one of DrawF, DrawInv, or Tangent(
    • Anything in the 2nd CALC menu.

    Naturally, any command like Input or Select( which involves the above, will also store coordinates of a point.

    Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan.

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $7E04
    Categories
    Localizations
    • FR: CoordAff

    CoordOn

    Overview

    Turns on cursor coordinate value display.

    Availability: Token only available from within the Basic editor.

    Syntax

    CoordOn

    Location

    2nd, format, CoordOn

    Description

    When moving a cursor on a screen, it's possible for the calculator to display the coordinates of the current point (either polar or rectangular coordinates, depending on which of RectGC or PolarGC is set). The CoordOn command turns on this option (to disable it, use the CoordOff command).

    The coordinates are displayed in practically every situation when you're moving a cursor on the graph screen, even including the Trace, Input or Select( commands in a program. The interactive mode of Text( and the Pen tool are the exceptions — this is because these two situations involve a pixel coordinate, and not a point.

    Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Myles_Zadok.

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $7E05
    Categories
    Localizations
    • FR: CoordNAff

    CoordOff

    Overview

    Turns off cursor coordinate value display.

    Availability: Token only available from within the Basic editor.

    Syntax

    CoordOff

    Location

    2nd, format, CoordOff

    Description

    When moving a cursor on a screen, it's possible for the calculator to display the coordinates of the current point (either polar or rectangular coordinates, depending on which of RectGC or PolarGC is set). The CoordOff command turns off this option.

    To turn it on, use the CoordOn command.

    Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, iPhoenixOnTIBD, Myles_Zadok.

    History

    Calculator OS Version Description
    TI-82 1.0 Added
    Property Value
    Hex Value $7E06
    Categories
      Localizations
      • FR: Thick

      Thick

      Overview

      Resets all Y=editor line-style settings to Thick.

      Availability: Token only available from within the Basic editor.

      Syntax

      Thick

      Location

      zT, Thick

      Description

      The Thick command converts all lines in the current function type to be drawn using a 2-3 pixel wide line (hence "Thick"). This mode is the default line drawing mode. It can be called on the homescreen or in a program.

      :AxesOff
:GridOff
:Thick

      Error Conditions

      • ERR:SYNTAX is thrown if any character is included in the same line as the Thick command.

      Source: parts of this page were written by the following TI|BD contributors: Battlesquid, jonbush, kg583, MrWompWomp.

      History

      Calculator OS Version Description
      TI-82 1.0 Connected added
      TI-84+CSE 4.0 Renamed Connected to Thick
      Property Value
      Hex Value $7E07
      Categories
        Localizations
        • FR: Dot-Thick

        Dot-Thick

        Overview

        Sets dot plotting mode; resets all Y=editor graph-style settings to Dot-Thick.

        Availability: Token only available from within the Basic editor.

        Syntax

        Dot-Thick

        Location

        mode, Dot-Thick

        Description

        The Dot-Thick command sets all lines in the current function type to be drawn using a series of thick points, about the size of a point drawn using Pt-On(, at each interval of the TraceStep. This command can be called on the homescreen or within a program.

        :AxesOff
:RectGC
:Dot-Thick

        Error Conditions

        • ERR:SYNTAX is thrown if any additional arguments are used with the command

        Source: parts of this page were written by the following TI|BD contributors: Battlesquid, kg583, MrWompWomp.

        History

        Calculator OS Version Description
        TI-82 1.0 Dot added
        TI-84+CSE 4.0 Renamed Dot to Dot-Thick
        Property Value
        Hex Value $7E08
        Categories
        Localizations
        • FR: AxesAff

        AxesOn

        Overview

        Turns on the graph axes with color. The coloroption allows the color of the axes to be specified.
        Color#: 10 - 24 or color name pasted from [vars] COLOR..

        Availability: Token only available from within the Basic editor.

        Syntax

        AxesOn[color#]

        Arguments

        NameTypeOptional
        color#colorNumYes

        Location

        2nd, format, AxesOn

        Description

        The AxesOn command enables the X and Y axes on the graph screen, so that they are drawn. They can be disabled with the AxesOff command.

        (the y=x line that is drawn when both Seq and Web modes are enabled is also controlled by this command)

        Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Myles_Zadok, Trenly.

        History

        Calculator OS Version Description
        TI-82 1.0 AxesOn added
        TI-84+CSE 4.0 Renamed AxesOn to AxesOn
        Property Value
        Hex Value $7E09
        Categories
        Localizations
        • FR: AxesNAff

        AxesOff

        Overview

        Turns off the graph axes.

        Availability: Token only available from within the Basic editor.

        Syntax

        AxesOff

        Location

        2nd, format, AxesOff

        Description

        The AxesOff command disables the X and Y axes on the graph screen, so that they aren't drawn. They can be enabled again with the AxesOn command.

        (the y=x line that is drawn when both Seq and Web modes are enabled is also controlled by this command)

        Generally, the AxesOff command should be used at the beginning of the program to disable the axes if the program is going to use the graph screen, since the axes get in the way. However, you should consider using StoreGDB and RecallGDB to save this setting if that's the case.

        Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Myles_Zadok, Trenly.

        History

        Calculator OS Version Description
        TI-82 1.0 Added
        Property Value
        Hex Value $7E0A
        Categories
          Localizations
          • FR: GridDot

          GridDot

          Overview

          Turns on grid dots in the graph area in the specified color.
          Color#: 10 - 24 or color name pasted from [vars] COLOR.

          Availability: Token only available from within the Basic editor.

          Syntax

          GridDot [color#]

          Arguments

          NameTypeOptional
          color#colorNumYes

          Location

          2nd, format, GridDot

          Description

          Examples

          Explanation 1

          code 1

          Explanation 2

          code 2

          Error Conditions

          Advanced Notes

          History

          Calculator OS Version Description
          TI-82 1.0 GridOn added
          TI-84+CSE 4.0 Renamed GridOn to GridDot
          Property Value
          Hex Value $7E0B
          Categories
          Localizations
          • FR: QuadNAff

          GridOff

          Overview

          Turns off grid format.

          Availability: Token only available from within the Basic editor.

          Syntax

          GridOff

          Location

          2nd, format, GridOff

          Description

          The GridOff command disables the grid on the graph screen. This is the default setting. Use GridOn to enable the grid.

          Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, kg583.

          History

          Calculator OS Version Description
          TI-82 1.0 Added
          Property Value
          Hex Value $7E0C
          Categories
          Localizations
          • FR: EtiqAff

          LabelOn

          Overview

          Turns on axes labels.

          Availability: Token only available from within the Basic editor.

          Syntax

          LabelOn

          Location

          2nd, format, LabelOn

          Description

          The LabelOn setting enables labels on the X and Y coordinate axes. If both LabelOnand AxesOn are set, the axes will be displayed with an X next to the X (horizontal) axis, and a Y next to the Y (vertical) axis. To disable these labels, use the LabelOff setting.

          LabelOn and LabelOff have no effect if the coordinate axes aren't displayed; there's nothing to label.

          A somewhat quirky behavior of the X and Y labels is that they aren't saved by StorePic. If you save a picture of the graph screen, it records every detail of the way it looks, including equations, drawn elements, axes, grid, everything — but not the labels.

          One final comment: okay, so by the way the command works we know it was once intended to label the axes. However, the command doesn't actually check where the axes are. It puts an "x" slightly above the bottom right corner, and a "y" slightly below the top left. Most of the time, including the default graphing window, that doesn't help you to distinguish the axes in the slightest. And in split-screen mode, as shown in the screenshot, they both seem to label the x-axis. Weird.

          Source: parts of this page were written by the following TI|BD contributors: Battlesquid, burr, DarkerLine, GoVegan, kg583, Myles_Zadok.

          History

          Calculator OS Version Description
          TI-82 1.0 Added
          Property Value
          Hex Value $7E0D
          Categories
          Localizations
          • FR: EtiqNAff

          LabelOff

          Overview

          Turns off axes labels.

          Availability: Token only available from within the Basic editor.

          Syntax

          LabelOff

          Location

          2nd, format, LabelOff

          Description

          The LabelOff setting disables labels on the X and Y coordinate axes. This is unnecessary if you've disabled the axes themselves, since the labels are only displayed when the axes are. To enable the labels, use the reverse setting LabelOn.

          Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan.

          History

          Calculator OS Version Description
          TI-82 1.0 Added
          Property Value
          Hex Value $7E0E
          Categories
          Localizations
          • FR: Toile

          Web

          Overview

          Sets sequence graphs to trace as webs.

          Availability: Token only available from within the Basic editor.

          Syntax

          Web

          Location

          2nd, format, Web

          Description

          In Web mode, sequence equations are graphed as web diagrams. This is a way of visualizing iterations of a function (that is, the sequence n, f(n), f(f(n)), f(f(f(n))), … for some function f and starting value n). For this mode to properly work, each sequence equation should be in terms of its previous value only: u(n) should be a function of u(n-1). Referencing other sequence equations, or u(n-2), will yield ERR:INVALID; referencing the value n is allowed by the calculator, but makes the result meaningless so you should avoid it.

          When you go to the graph screen, the associated function y=f(x) will be graphed. That is, if you define u(n) = cos(u(n-1)), the function y=cos(x) will be graphed. If you have AxesOn enabled, the line y=x will also be graphed. It's easy to see that the intersection points of the graphs y=f(x) and the line y=x represent the fixed points (points such that f(x)=x) of the function.

          The web diagram itself will be drawn if you press TRACE or use the Trace command. First you will choose the equation (u, v, or w) to trace; then, by pressing RIGHT repeatedly, the web will be drawn, starting from the initial value _n_Min. In a web diagram, a point (n, f(n)) on the graph of y=f(x) is connected by a horizontal segment to the point (f(n), f(n)) on the graph of y=x, and then by a vertical segment to the point (f(n), f(f(n))) on the graph of y=f(x) again; this process is repeated. Each pair of a horizontal and vertical segment represents an added iteration of.

          Web diagrams can be used to look at the attracting behavior of fixed points. For example:

          1. Graph the equation u(n)=cos(u(n-1)), u(_n_Min)=1 in Web mode, with Xmin=0, Xmax=1, Ymin=0, Ymax=1 in the WINDOW menu. You'll see that it has a single fixed point. If you TRACE the graph, the line segments will spiral around into the fixed point, so appears to be attractive.

          2. Graph the equation u(n)=π/2cos(u(n-1)), u(_n_Min)=1 in Web mode, with Xmin=0, Xmax=π/2, Ymin=0, Ymax=π/2 in the WINDOW menu. This equation looks a lot like the previous one, and also has a single fixed point. However, if you TRACE the graph, the line segments (which start out quite close to the fixed point) will spiral away from it. This intuitively shows that the fixed point of f(x)=π/2cos(x) is not attractive.

          See "Related Commands" for other possibilities of graphing sequences.

          Error Conditions

          • ERR:INVALID is thrown if an equation being graphed references other sequence equations or the n-2 term.

          Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

          History

          Calculator OS Version Description
          TI-82 1.0 Added
          Property Value
          Hex Value $7E0F
          Categories
          Localizations
          • FR: f(n)

          Time

          Overview

          Sets sequence graphs to plot with respect to time.

          Availability: Token only available from within the Basic editor.

          Syntax

          Time

          Location

          2nd, format, Time

          Description

          NOTE: This article is about the Time setting for sequence graphing. If you're looking for the clock commands on the TI-84 Plus and TI-84 Plus SE, see Time and Date Commands.

          The Time command sets equations in sequence mode to graph as the points (n, u(n)) (for the u equation; (n, v(n)) and (n, w(n)) for the other two) - the default setting. In dot mode, only the points themselves will be plotted, but if you change the graphing style to connected line or thick line, the points will be connected.

          Essentially, this mode makes sequence graphs a limited version of function graphs, but with the possibility of recursion.

          See "Related Commands" for other possibilities of graphing sequences.

          Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

          History

          Calculator OS Version Description
          TI-82 1.0 Added
          Property Value
          Hex Value $7E10
          Categories
          Localizations
          • FR: uvAxes

          uvAxes

          Overview

          Sets sequence graphs to plot u(n``) on the x-axis and v(``n``) on the y-axis.

          Availability: Token only available from within the Basic editor.

          Syntax

          uvAxes

          Location

          2nd, format, uv

          Description

          When uvAxes is enabled, and the calculator is in Seq mode, the equations u and v will be graphed against each other (that is, the points (u(n),v(n)) are graphed for the values of n between n_Min and _n_Max). With this setting, sequence mode graphs are a bit like parametric mode, except the parameter _n is always an integer, and recursive definitions are possible.

          The equation w is ignored when in uvAxes mode.

          See "Related Commands" for other possibilities of graphing sequences.

          Error Conditions

          Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

          History

          Calculator OS Version Description
          TI-82 1.0 Added
          Property Value
          Hex Value $7E11
          Categories
          Localizations
          • FR: vwAxes

          vwAxes

          Overview

          Sets sequence graphs to plot v(n``) on the x-axis and w(``n``) on the y-axis.

          Availability: Token only available from within the Basic editor.

          Syntax

          vwAxes

          Location

          2nd, format, vw

          Description

          When vwAxes is enabled, and the calculator is in Seq mode, the equations v and w will be graphed against each other (that is, the points (v(n),w(n)) are graphed for the values of n between n_Min and _n_Max). With this setting, sequence mode graphs are a bit like parametric mode, except the parameter _n is always an integer, and recursive definitions are possible.

          The equation u is ignored when in vwAxes mode.

          See "Related Commands" for other possibilities of graphing sequences.

          Error Conditions

          Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

          History

          Calculator OS Version Description
          TI-82 1.0 Added
          Property Value
          Hex Value $7E12
          Categories
          Localizations
          • FR: uwAxes

          uwAxes

          Overview

          Sets sequence graphs to plot u(n``) on the x-axis and w(``n``) on the y-axis.

          Availability: Token only available from within the Basic editor.

          Syntax

          uwAxes

          Location

          2nd, format, uw

          Description

          When uwAxes is enabled, and the calculator is in Seq mode, the equations u and w will be graphed against each other (that is, the points (u(n),w(n)) are graphed for the values of n between n_Min and _n_Max). With this setting, sequence mode graphs are a bit like parametric mode, except the parameter _n is always an integer, and recursive definitions are possible.

          The equation v is ignored when in uwAxes mode.

          See "Related Commands" for other possibilities of graphing sequences.

          Error Conditions

          Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

          History

          Calculator OS Version Description
          TI-82 1.0 Added
          Property Value
          Hex Value $7F
          Categories
          Localizations
          • FR: □

          □

          Overview

          Availability: Token available everywhere.

          Syntax

          □

          Description

          Examples

          Explanation 1

          code 1

          Explanation 2

          code 2

          Error Conditions

          Advanced Notes

          History

          Calculator OS Version Description
          TI-82 1.0 Added
          Property Value
          Hex Value $80
          Categories
          Localizations
          • FR: ﹢

          ﹢

          Overview

          Availability: Token available everywhere.

          Syntax

          ﹢

          Description

          Examples

          Explanation 1

          code 1

          Explanation 2

          code 2

          Error Conditions

          Advanced Notes

          History

          Calculator OS Version Description
          TI-82 1.0 Added
          Property Value
          Hex Value $81
          Categories
          Localizations
          • FR: ·

          ·

          Overview

          Availability: Token available everywhere.

          Syntax

          ·

          Description

          Examples

          Explanation 1

          code 1

          Explanation 2

          code 2

          Error Conditions

          Advanced Notes

          History

          Calculator OS Version Description
          TI-82 1.0 Added
          Property Value
          Hex Value $82
          Categories
          Localizations
          • FR: *

          *

          Overview

          Availability: Token available everywhere.

          Syntax

          *

          Description

          Examples

          Explanation 1

          code 1

          Explanation 2

          code 2

          Error Conditions

          Advanced Notes

          History

          Calculator OS Version Description
          TI-82 1.0 Added
          Property Value
          Hex Value $83
          Categories
          Localizations
          • FR: /

          /

          Overview

          Availability: Token available everywhere.

          Syntax

          /

          Description

          Examples

          Explanation 1

          code 1

          Explanation 2

          code 2

          Error Conditions

          Advanced Notes

          History

          Calculator OS Version Description
          TI-82 1.0 Added
          Property Value
          Hex Value $84
          Categories
          Localizations
          • FR: Trace

          Trace

          Overview

          Displays the graph and enters TRACE mode.

          Availability: Token available everywhere.

          Syntax

          Trace

          Location

          trace

          Description

          The Trace command displays the graph screen, and allows the user to trace any graphed equations or plots. It works in almost exactly the same way as pressing TRACE does outside a program. When the user presses ENTER, control returns to the program.

          When tracing, ExprOn and ExprOff affect how the currently-traced equation is displayed, and CoordOn and CoordOff affect whether the coordinates of the cursor are displayed (RectGC and PolarGC determine the type of coordinates).

          Since the ENTER key is already used for exiting, the Trace command lacks some of the functionality of pressing TRACE outside a program, where you can use ENTER to center the graphing window on the cursor. The independent variables X, T, θ, and n cannot by directly typed in, either - they can only be selected with the arrow buttons.

          Advanced Uses

          As a side effect, the coordinates of the last point traced are stored to X and Y (as well as R and θ, if you're in PolarGC mode, and T, θ and n depending on the graphing mode). Also, the window bounds may change if the user traces an equation past the edge of the screen.

          Error Conditions

          • ERR:INVALID is thrown if this command is used outside a program.

          Source: parts of this page were written by the following TI|BD contributors: b2jammer, DarkerLine, GoVegan.

          History

          Calculator OS Version Description
          TI-82 1.0 Added
          Property Value
          Hex Value $85
          Categories
          Localizations
          • FR: EffDessin

          ClrDraw

          Overview

          Clears all drawn elements from a graph or drawing.

          Availability: Token available everywhere.

          Syntax

          ClrDraw

          Location

          2nd, draw, DRAW, 1:ClrDraw

          Description

          The ClrDraw command is useful clearing away something drawn on the graph screen; in particular, you want to do this at the beginning of a program that uses the graph screen, to get rid of anything that might be on it initially. If there are functions, plots, axes, labels, or grid enabled, these will be redrawn even after you ClrDraw. If you don't want these, you should turn them off before the ClrDraw command.

          Like many other drawing commands, if you're outside a program and on the graph screen, you can use this command directly, without going to the home screen. Just select ClrDraw from the menu, and the screen will be cleared immediately.

          Advanced Uses

          Unless the final state of the graph screen is the intended effect of the program, you want to use ClrDraw at the end of the program so that the user doesn't have to deal with it.

          Caution: if the graph screen is displayed even before you execute ClrDraw, the user variable Y will be reset to 0. This might be useful as a side effect, but it's more likely to turn out to be a nuisance if you were relying on Y to store something useful. Also, such a wacky effect might get removed in later OS versions1, so it's a gamble relying on it to work for all users.

          The RecallPic command does not erase what is previously on the graph screen when recalling a picture. Unless this is what you intend, use ClrDraw to erase the graph screen's old contents before recalling a picture.

          Optimization

          The ClrDraw command is not the only way to clear the screen. If something changes about the state of the functions or plots plotted on the graph, about the window dimensions, or the axes, grid, and labels, the graph screen will be marked as 'dirty' by the calculator, and will be cleared the next time you display it.

          Don't be too confident about relying on this however. For example, if you cleared Y1 before displaying the graph, and Y1 previously contained something, the graph will be redrawn. However, if Y1 never existed, then you haven't changed anything, and the graph will remain.

          A lot of people choose their preferred window settings using the following two commands, which sets the window to X= -47..47, Y= -31..31:

          ZStandard:ZInteger

          Since this actually switches two window settings, at least one will be different from the previous settings, so the next time the graph screen is shown, it will be cleared without a ClrDraw command. There are other friendly window settings that you can use as well.

          See Also

          Footnotes

          1. Fixed on the TI-84+CSE

          Source: parts of this page were written by the following TI|BD contributors: Austin 332000, burr, DarkerLine, GoVegan, kg583.

          History

          Calculator OS Version Description
          TI-82 1.0 Added
          Property Value
          Hex Value $86
          Categories
          Localizations
          • FR: ZStandard

          ZStandard

          Overview

          Replots the functions immediately, updating the window variables to the default values.

          Availability: Token only available from within the Basic editor.

          Syntax

          ZStandard

          Location

          zoom, ZOOM, 6:ZStandard

          Description

          The ZStandard command resets all window variables found in the Window screen to their default values. This means that, unlike the other zoom commands, ZStandard can affect variables other than Xmin, Xmax, Ymin, and Ymax. However, it will only affect variables that have a purpose in the current graphing mode. Here are the default values set by ZStandard:

          In all modes:

          • Xmin=-10
          • Xmax=10
          • Xscl=1
          • Ymin=-10
          • Ymax=10
          • Yscl=1

          Only in Func mode:

          • Xres=1

          Only in Param mode:

          • Tmin=0
          • Tmax=2π (in Radian mode) or 360 (in Degree mode)
          • Tstep=π/24 (in Radian mode) or 7.5 (in Degree mode)

          Only in Polar mode:

          • θmin=0
          • θmax=2π (in Radian mode) or 360 (in Degree mode)
          • θstep=π/24 (in Radian mode) or 7.5 (in Degree mode)

          Only in Seq mode:

          • _n_Min=1
          • _n_Max=10
          • PlotStart=1
          • PlotStep=1

          These settings are often useful as a "lowest common denominator" that will work fairly well for all graphs.

          Advanced Uses

          ZStandard is often used before commands such as ZSquare or ZInteger in programs. This serves two purposes: it makes sure that the center of the screen for ZSquare and ZInteger is (0,0), and it ensures that the graph screen is cleared without having to resort to ClrDraw (because with two different zooms in a row, the window settings have to change at least once, which means the graph will have to be regraphed)

          Error Conditions

          • ERR:INVALID occurs if this command is used outside a program.

          Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan.

          History

          Calculator OS Version Description
          TI-82 1.0 Added
          Property Value
          Hex Value $87
          Categories
          Localizations
          • FR: ZTrig

          ZTrig

          Overview

          Replots the functions immediately, updating the window variables to preset values for plotting trig functions.

          Availability: Token only available from within the Basic editor.

          Syntax

          ZTrig

          Location

          zoom, ZOOM, 7:ZTrig

          Description

          The ZTrig command sets the screen to a special friendly window useful for trigonometric calculations. Unlike the ZDecimal and ZInteger commands, for which the distance between two pixels is a short decimal or integer, ZTrig sets the horizontal distance between two pixels to be π/24 (in Radian mode) or 7.5 (in Degree mode) . The specific changes ZTrig makes are:

          • Xmin=-352.5° or -47/24πʳ
          • Xmax=352.5° or 47/24πr
          • Xscl=90° or π/2r
          • Ymin=-4
          • Ymax=4
          • Yscl=1

          Although this window is not quite square (and therefore, distances in the X and Y direction are not exactly equally proportioned), it is quite close, when in Radian mode. In a square window (such as the output of ZSquare), Ymax would have to be 31/24π, which is approximately 4.05789. As you can see, the value of 4 that ZTrig uses is not too far off.

          Advanced Uses

          In theory, ZTrig should be quite useful in graphing trigonometric functions, since the calculated points would fall exactly on important angles; for example, it would graph the asymptotes of Y=tan(X) correctly. This is actually only true when in Degree mode. In Radian mode, due to round-off error, the pixels far away from the origin do not exactly correspond to rational multiples of π. For example, the pixel which was supposed to correspond to π/2 actually has a value of .5000000001*π, which is enough to make this command mostly useless.

          However, in G-T mode, the size that the graph takes up on the screen is different, and ZTrig uses the same values, unlike ZDecimal.

          Error Conditions

          • ERR:INVALID occurs if this command is used outside a program (but not if the menu option is used, of course).

          See Also

          Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Myles_Zadok.

          History

          Calculator OS Version Description
          TI-82 1.0 Added
          Property Value
          Hex Value $88
          Categories
          Localizations
          • FR: Zboîte

          ZBox

          Overview

          Displays a graph, lets you draw a box that defines a new viewing window, and updates the window.

          Availability: Token only available from within the Basic editor.

          Syntax

          ZBox

          Location

          zoom, ZOOM, 1:ZBox

          Description

          The ZBox command allows the user to select a smaller window within the current graphing window to zoom in to. To select the window, use the arrow keys and ENTER to select one corner of the window; then as you use the arrow keys and ENTER to select the other corner, a rectangle of the window's dimensions will be shown.

          It's not recommended to use this in most programs, because entering an empty window (with no width or no height) will cause an error and exit the program without letting it clean up.

          Error Conditions

          • ERR:INVALID occurs if this command is used outside a program.
          • ERR:ZOOM is thrown if an empty window is selected (with no width or no height)

          Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan.

          History

          Calculator OS Version Description
          TI-82 1.0 Added
          Property Value
          Hex Value $89
          Categories
          Localizations
          • FR: Zoom +

          Zoom In

          Overview

          Magnifies the part of the graph that surrounds the cursor location.

          Availability: Token only available from within the Basic editor.

          Syntax

          Zoom In

          Location

          zoom, ZOOM, 2:Zoom In

          Description

          Outside a program, the Zoom In tool allows you to pick a point on the graph screen and change the graphing window to a smaller one centered at that point. The Zoom In command, used in a program, also changes the graphing window to a smaller one, but doesn't let you pick a point — it uses the center of the screen.

          The variables XFact and YFact are used to determine how much the graphing window changes: the total width of the screen, Xmax-Xmin, is divided by XFact, and the total height, Ymax-Ymin, is divided by YFact. Because you can't store a value less than 1 to either of these variables, the screen is guaranteed to get no larger.

          Aside from Xmin, Xmax, Ymin, and Ymax, no window variables are modified by this command (although ΔX and ΔY change as they are defined).

          Error Conditions

          • ERR:INVALID occurs if this command is used outside a program.
          • ERR:WINDOW RANGE is thrown if the window is zoomed in beyond the level of the calculator's precision.

          Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan.

          History

          Calculator OS Version Description
          TI-82 1.0 Added
          Property Value
          Hex Value $8A
          Categories
          Localizations
          • FR: Zoom -

          Zoom Out

          Overview

          Displays a greater portion of the graph, centered on the cursor location.

          Availability: Token only available from within the Basic editor.

          Syntax

          Zoom Out

          Location

          zoom, ZOOM, 3:Zoom Out

          Description

          Outside a program, the Zoom Out tool allows you to pick a point on the graph screen and change the graphing window to a larger one centered at that point. The Zoom Out command, used in a program, also changes the graphing window to a larger one, but doesn't let you pick a point — it uses the center of the screen.

          The variables XFact and YFact are used to determine how much the graphing window changes: the total width of the screen, Xmax-Xmin, is multiplied by XFact, and the total height, Ymax-Ymin, is multiplied by YFact. Because you can't store a value less than 1 to either of these variables, the screen is guaranteed to get no smaller.

          Aside from Xmin, Xmax, Ymin, and Ymax, no window variables are modified by this command (although ΔX and ΔY change as they are defined).

          Error Conditions

          • ERR:INVALID occurs if this command is used outside a program.
          • ERR:ZOOM is thrown if an overflow occurs calculating the new window dimensions (the window is too big)

          Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan.

          History

          Calculator OS Version Description
          TI-82 1.0 Added
          Property Value
          Hex Value $8B
          Categories
          Localizations
          • FR: Zorthonormal

          ZSquare

          Overview

          Adjusts the X or Y window settings so that each pixel represents an equal width and height in the coordinate system, and updates the viewing window.

          Availability: Token only available from within the Basic editor.

          Syntax

          ZSquare

          Location

          zoom, ZOOM, 5:ZSquare

          Description

          The ZSquare command changes the window variables Xmin and Xmax, or Ymin and Ymax, so that ΔX=ΔY, preserving all other settings and the coordinate of the center of the screen. This ensures that a numerical distance on the graphscreen has the same physical length on the calculator display, no matter if it's vertical, horizontal, or diagonal. Probably the most obvious effect of this change is that circles (whether graphed with an equation or drawn with the Circle( command) are actually circles and not ovals.

          When determining which of Xmin and Xmax or Ymin and Ymax to change, the command picks the ones that would be increased, and not decreased. This way, the window can never get smaller.

          Note that ZDecimal, ZInteger, and to an extent ZTrig already have the same proportions, and don't require a ZSquare command to follow them.

          Advanced Uses

          ZSquare can be useful in setting up a friendly window.

          Error Conditions

          • ERR:INVALID occurs if this command is used outside a program.

          See Also

          Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, HJTP.

          History

          Calculator OS Version Description
          TI-82 1.0 Added
          Property Value
          Hex Value $8C
          Categories
          Localizations
          • FR: ZintConf

          ZInteger

          Overview

          Redefines the viewing window using the following dimensions: TraceStep=1,ΔX=0.5, Xscl=10,ΔY=1, Yscl=10.

          Availability: Token only available from within the Basic editor.

          Syntax

          ZInteger

          Location

          zoom, ZOOM, 8:ZInteger

          Description

          When ZInteger is chosen as a menu option outside a program, it asks for a point on the graph screen. This point's coordinates are rounded to the nearest integer point. Then the window variables are changed so the window is centered at this point, and so that the coordinates of every pixel are integers. ΔX and ΔY, the distances between two pixels next to each other, are both 1.

          The above process modifies Xmin, Xmax, Ymin, and Ymax. Xscl and Yscl are also modified: both are set to 10. No other variables are modified (unless you count ΔX and ΔY, which are affected as they are defined).

          The ZInteger command (usable in a program only) has a slightly different effect: instead of allowing you to choose a point, it automatically uses the point that is the current center.

          Advanced Uses

          A graph window commonly used in programming can be created by using the ZStandard and ZInteger commands:

          :ZStandard
:ZInteger

          Error Conditions

          • ERR:INVALID occurs if this command is used outside a program.

          See Also

          Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, seb83.

          History

          Calculator OS Version Description
          TI-82 1.0 Added
          Property Value
          Hex Value $8D
          Categories
          Localizations
          • FR: Zprécédent

          ZPrevious

          Overview

          Replots the graph using the window variables of the graph that was displayed before you executed the last ZOOM instruction.

          Availability: Token only available from within the Basic editor.

          Syntax

          ZPrevious

          Location

          zoom, MEMORY, 1:ZPrevious

          Description

          The ZPrevious command (and menu option) restore the window variables Xmin, Xmax, Xscl, Ymin, Ymax, and Yscl to the values they had before the last zoom command. This means, of course, that using ZPrevious a second time will cancel its effects.

          Since no variables that are specific to the current graphing mode are changed, ZPrevious doesn't always achieve the effect of reversing the previous zoom command. For example, in Polar graphing mode, ZStandard will set θmin and θmax to 0 and 2π respectively. However, even if they were different before ZStandard, ZPrevious will not restore these settings. Also, ZPrevious doesn't notice if you change the window settings directly (by storing to the window variables).

          Unlike ZoomSto and ZoomRcl, the values that ZPrevious uses aren't made available in any sort of variable.

          Optimization

          Using StoreGDB and RecallGDB is an excellent way to back up graph settings so a program doesn't modify them. However, if all you're doing is changing the window variables with one Zoom command, you can simply use ZPrevious at the end of the program instead.

          Error Conditions

          • ERR:INVALID occurs if this command is used outside a program (but not if the menu option is used, of course).

          Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, HJTP.

          History

          Calculator OS Version Description
          TI-82 1.0 Added
          Property Value
          Hex Value $8E
          Categories
          Localizations
          • FR: Zdécimal

          ZDecimal

          Overview

          Adjusts the viewing window so that TraceStep=0.1, ΔX=0.5 and ΔY=0.5, and displays the graph screen with the origin centered on the screen.

          Availability: Token only available from within the Basic editor.

          Syntax

          ZDecimal

          Location

          zoom, ZOOM, 4:ZDecimal

          Description

          The ZDecimal command makes the following changes to the window variables:

          • Xmin=-4.7
          • Xmax=4.7
          • Xscl=1
          • Ymin=-3.1
          • Ymax=3.1
          • Yscl=1

          If using a TI-84+CSE or CE, the window variables become:

          • Xmin=-6.6
          • Xmax=6.6
          • Xscl=1
          • Ymin=-4.1
          • Ymax=4.1
          • Yscl=1

          Because of the dimensions of the graph screen, this has the useful effect that every pixel has round X- and Y-coordinates with at most one decimal digit. Also, the screen has correct proportions: a specific distance in the X direction is the same number of pixels in length as the same distance in the Y direction. This makes the window dimensions created by ZDecimal a friendly window (the ZInteger and ZSquare commands also have this effect, but in slightly different ways)

          Advanced Uses

          Using the ZDecimal command prevents gaps in certain graphs, and makes sure vertical asymptotes with integer coordinates are graphed correctly. Also, circles will be drawn as actual circles with this graphing window(unlike other windows, with which they might appear stretched).

          The values given for Xmin, Xmax, etc. above are only correct for the Full mode setting (which is the default, and the most common setting). In Horiz and G-T modes, the values will be different, preserving the property that two pixels next to each other differ in coordinates by 0.1:

          • Ymin= -1.5 and Ymax= 1.5 in Horiz mode (Xmin and Xmax are the same)
          • Ymin= -2.5 and Ymax= 2.5 in G-T mode, while Xmin= -2.3 and Xmax= 2.3

          Error Conditions

          • ERR:INVALID occurs if this command is used outside a program.

          See Also

          Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, kg583.

          History

          Calculator OS Version Description
          TI-82 1.0 Added
          Property Value
          Hex Value $8F
          Categories
          Localizations
          • FR: ZoomStat

          ZoomStat

          Overview

          Redefines the viewing window so that all statistical data points are displayed.

          Availability: Token only available from within the Basic editor.

          Syntax

          ZoomStat

          Location

          zoom, ZOOM, 9:ZoomStat

          Description

          The ZoomStat command command zooms to a graphing window that accurately represents all the currently defined stat plots (see the PlotN( commands). You can think of it as ZoomFit, but for plots rather than equations.

          The specific function of the command is as follows: first, the minimum and maximum X and Y coordinates that stat plots will be using are calculated. Xmin, Xmax, Ymin, and Ymax are calculated to fit all these coordinates plus a padding on either side. The padding is 10% of the unpadded range on the left and right (for Xmin and Xmax), and 17% of the unpadded range on the top and bottom (for Ymin and Ymax).

          Of course, the exact function varies slightly with the type of plot defined. For example, Ymin and Ymax will not be affected by Boxplot and Modboxplot plots, since they ignore Y-coordinates when graphing. Also, Histogram fitting is a bit trickier than others. Xscl and Yscl also are changed for histograms, though not for the other plots.

          For all plots except Histogram, ZoomStat will create a window with Xmin=Xmax (or Ymin=Ymax) if the X range (or Y range) of the data is 0. This will throw an ERR:WINDOW RANGE. If a Histogram causes this error, though, ERR:STAT is thrown, and then when you access the graphscreen ERR:WINDOW RANGE will occur.

          Error Conditions

          • ERR:INVALID is thrown if this command is using outside a program (although the menu option, of course, is fine).
          • ERR:STAT is thrown when trying to ZoomFit to a Histogram with only one distinct number in the data list.
          • ERR:WINDOW RANGE is thrown when the window ends up being empty.

          Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, seb83, Zaphod Beeblebrox.

          History

          Calculator OS Version Description
          TI-82 1.0 Added
          Property Value
          Hex Value $90
          Categories
          Localizations
          • FR: ZoomRpl

          ZoomRcl

          Overview

          Graphs the selected functions in a user-defined viewing window.

          Availability: Token only available from within the Basic editor.

          Syntax

          ZoomRcl

          Location

          zoom, MEMORY, 3:ZoomRcl

          Description

          The ZoomRcl command restores a backup of the window settings previously saved by ZoomSto — this backup is stored in special variables found in the VARS>Zoom… menu, which are distinguished by a Z in front of their name. For example, Xmin is restored from ZXmin, PlotStart is restored from ZPlotStart, etc.

          Only those settings are restored that apply to the current graphing mode (that is, those that you can see in the window screen). And if no backup had been made, then the default settings are restored to (see ZStandard).

          One source of confusion with this command can be the fact that ZoomSto and ZoomRcl only deal with the current graphing mode (and don't touch settings from other graphing modes), but some window variables are shared by graphing modes. So some saved zoom variables only applicable to one mode, such as ZTmin, can be from older saves than those applicable to all modes, such as ZXmin.

          Error Conditions

          • ERR:INVALID occurs if this command is used outside a program (but not if the menu option is used, of course).

          Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Kydapoot.

          History

          Calculator OS Version Description
          TI-82 1.0 Added
          Property Value
          Hex Value $91
          Categories
          Localizations
          • FR: PrintScreen

          PrintScreen

          Overview

          Comment:Not available (only token)

          Syntax

          PrintScreen

          Description

          Examples

          Explanation 1

          code 1

          Explanation 2

          code 2

          Error Conditions

          Advanced Notes

          History

          Calculator OS Version Description
          TI-82 1.0 Added
          Property Value
          Hex Value $92
          Categories
          Localizations
          • FR: SauveFen

          ZoomSto

          Overview

          Immediately stores the current viewing window.

          Availability: Token only available from within the Basic editor.

          Syntax

          ZoomSto

          Location

          zoom, MEMORY, 2:ZoomSto

          Description

          The ZoomSto command backs up all window settings applicable to the current graphing mode (those that are shown in the WINDOW menu) to backup variables used specifically for this command. These backup variables are found in the VARS>Zoom… menu, and are distinguished by a Z in front of their name. For example, Xmin is backed up to ZXmin, PlotStart is backed up to ZPlotStart, etc.

          Using ZoomRcl, these backup variables can be used to overwrite the current window settings, recalling the saved window.

          One source of confusion with this command can be the fact that ZoomSto and ZoomRcl only deal with the current graphing mode (and don't touch settings from other graphing modes), but some window variables are shared by graphing modes. So some saved zoom variables only applicable to one mode, such as ZTmin, can be from older saves than those applicable to all modes, such as ZXmin.

          Error Conditions

          • ERR:INVALID occurs if this command is used outside a program (but not if the menu option is used, of course).

          Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Kydapoot.

          History

          Calculator OS Version Description
          TI-82 1.0 Added
          Property Value
          Hex Value $93
          Categories
          Localizations
          • FR: Texte(

          Text(

          Overview

          Writes text on graph beginning at pixel (row,column), where 0 ≤ row ≤ 164 and 0 ≤ column ≤ 264.
          Full mode, row must be <=148; column must be 256
          Horiz mode, row must be row<=66 and column must be <=256
          G-T mode, row must be row <=126; column must be 176

          Availability: Token available everywhere.

          Syntax

          Text(row,column,text1,text2,...,text n)

          Arguments

          NameTypeOptional
          row
          column
          text1string
          text2string
          ...
          text nstring

          Location

          2nd, draw, DRAW, 0:Text(

          Description

          The Text( command allows you to display text on the graph screen, using the small font. It takes three arguments: the row, which can range from 0 to the number of pixels tall the screen is (62 on grayscale, 164 on color) at which you want to display something, the column, which can range from 0 to the number of pixels wide the screen is (94 on grayscale, 264 on color), and whatever it is you want to display. Like the Output( command, it is limited to numbers and strings. If part of what you want to display goes off the screen, it will not be displayed - the calculator will cut you off at the most characters that will fit on the screen entirely.

          Unlike the large text used on the home screen, the small font this command uses varies in width from 2 pixels to as many as 6 (counting the blank space at the end of each character, which is 1 pixel). All characters are 6 pixels tall, but the top row of pixels is used very rarely (only in international characters such as ä). On the TI-84+/SE/CSE/CE, the Text( command may also erase a single row of pixels underneath the text: whether this occurs or not depends on whether it was the menu screen or the table that was visited last, of the two.
          Without storing them to a special string, the Text( command cannot be used to display quotation marks (") and the STO (→) command. However, you can mimic these respectively by using two apostrophes (' ' ), and two subtract signs and a greater than sign (—>).

          Like many other drawing commands, if you're outside a program and on the graph screen, you can use this command directly, without going to the home screen. Just select Text( from the draw menu, and you will be able to type text at a cursor you control with arrow keys; press CLEAR or ENTER (among other things) to exit this mode.

          Advanced Uses

          On the TI-83/84/+/SE/CSE/CE, Text( has an alternate syntax: put a -1 before the row and column to display the text using the large font instead of the small font. With this syntax, Text( becomes like an Output( for the graph screen, but with more features: you don't have to display text exactly aligned to one of the home screen's rows and columns, and you can display more than one string or number at a time. Also, text still won't wrap like Output('s does.

          This feature may be helpful in making programs more appealing, but remember that it does not work on the regular TI-83. If you want to maintain compatibility, don't use this syntax, or make an alternate version of your program without it.

          The Text( command is also critical to the sprite technique known as text sprites. Although they have limitations, they allow pure Basic programs to have high-quality graphics without taking up lots of space. This effect is not as good on the color calculators.

          On the TI-84+ and TI-84+ SE, another compatibility issue occurs with Text(. On certain occasions, using Text( to display small text on the graph screen will erase a 1-pixel margin below the text itself. The cause is a system option which is turned on when accessing the new MODE menu, and turned off when accessing the table, matrix editor, or list editor. The 1-pixel margin may not seem like a big deal, but it's enough to stop certain games (such as Bryan Thomas's Contra) from working on the TI-84+/SE.

          The situation can be detected quite easily: turn on a pixel, display text 6 rows above it, and test if the pixel is still turned on. Fixing the situation is slightly more difficult:

          • The hex code AsmPrgmFDCB058EC9 will disable the option (but it requires having an additional subprogram).
          • DispTable will also do the trick, but of course it will display the table as well.
          • Switch the program to G-T while it's on the graphscreen. Before doing this it's useful to have a FnOff.
            • The above two don't work in resetting the flag on OSes 2.53 MP or higher, the hex code is required.
          • There's the option of telling users to access a certain screen before playing…

          You can also try to get around the situation by storing and recalling pictures, to prevent anything from being erased when you don't want it to be.

          Error Conditions

          • ERR:DOMAIN is thrown if the coordinates of Text( are not integers or are out of range. A few comments:
            • ERR:DATA TYPE can sometimes occur instead on the TI-83+ or higher because of confusion with the alternate syntax
            • Similarly, Text(-1,0,0) will cause no error and display nothing whatsoever on the TI-83+ or higher.
            • With Text(-1,… the upper bound on the row is one less of what it would be normally.
            • In Horiz mode the upper bound on the row is 25 rather than 57. In G-T mode the upper bound on the column is 46.
          • ERR:ARGUMENT is thrown if the number of arguments given to Text( is 256 or more or if one of the arguments contains an imaginary part. The latter restriction can be bypassed with clever programming. One such method is displayed here: <complex number>:Text(x,y,real(Ans),sub(“+-“,1+(imag(Ans)<0)),imag(Ans),”i

          Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, Edward H, GoVegan, iPhoenixOnTIBD, Ivoah, kg583, mattyjraps, Myles_Zadok, Timothy Foster, ztrumpet.

          History

          Calculator OS Version Description
          TI-82 1.0 Added
          Property Value
          Hex Value $94
          Categories
          Localizations
          • FR: Arrangement

          nPr

          Overview

          Returns the number of permutations of valueA taken valueB at a time.

          Availability: Token available everywhere.

          Syntax

          valueA nPr valueB

          Arguments

          NameTypeOptional
          valueA
          valueB

          Location

          math, PRB, 2:nPr

          Overview

          Returns a list of the permutations of value taken each element in list at a time.

          Availability: Token available everywhere.

          Syntax

          value nPr list

          Arguments

          NameTypeOptional
          value
          listlist

          Location

          math, PRB, 2:nPr

          Overview

          Returns a list of the permutations of each element in list taken value at a time.

          Availability: Token available everywhere.

          Syntax

          list nPr value

          Arguments

          NameTypeOptional
          listlist
          value

          Location

          math, PRB, 2:nPr

          Overview

          Returns a list of the permutations of each element in listA taken each element in listB at a time.

          Availability: Token available everywhere.

          Syntax

          listA nPr listB

          Arguments

          NameTypeOptional
          listAlist
          listBlist

          Location

          math, PRB, 2:nPr

          Description

          Examples

          Explanation 1

          code 1

          Explanation 2

          code 2

          Error Conditions

          Advanced Notes

          History

          Calculator OS Version Description
          TI-82 1.0 Added
          Property Value
          Hex Value $95
          Categories
          Localizations
          • FR: Combinaison

          nCr

          Overview

          Returns the number of combinations of valueA taken valueB at a time.

          Availability: Token available everywhere.

          Syntax

          valueA nCr valueB

          Arguments

          NameTypeOptional
          valueA
          valueB

          Location

          math, PRB, 3:nCr

          Overview

          Returns a list of the combinations of value taken each element in list at a time.

          Availability: Token available everywhere.

          Syntax

          value nCr list

          Arguments

          NameTypeOptional
          value
          listlist

          Location

          math, PRB, 3:nCr

          Overview

          Returns a list of the combinations of each element in list taken value at a time.

          Availability: Token available everywhere.

          Syntax

          list nCr value

          Arguments

          NameTypeOptional
          listlist
          value

          Location

          math, PRB, 3:nCr

          Overview

          Returns a list of the combinations of each element in listA taken each element in listB at a time.

          Availability: Token available everywhere.

          Syntax

          listA nCr listB

          Arguments

          NameTypeOptional
          listAlist
          listBlist

          Location

          math, PRB, 3:nCr

          Description

          Examples

          Explanation 1

          code 1

          Explanation 2

          code 2

          Error Conditions

          Advanced Notes

          History

          Calculator OS Version Description
          TI-82 1.0 Added
          Property Value
          Hex Value $96
          Categories
          Localizations
          • FR: FonctAff

          FnOn

          Overview

          Selects all Y= functions or specified Y= functions.

          Availability: Token available everywhere.

          Syntax

          FnOn [function#,function#,...,function n]

          Arguments

          NameTypeOptional
          function#Yes
          function#Yes
          function nYes

          Location

          vars, Y-VARS, 4:On/Off1:FnOn

          Description

          The FnOn command is used to turn on equations in the current graphing mode. When you define an equation, it's turned on by default, but the FnOff command can turn an equation off (in which case, it's still defined, but isn't graphed). To turn functions on and off manually, put your cursor over the = symbol in the equation editor, and press enter.

          When FnOn is used by itself, it will turn on all defined equations in the current graphing mode. You can also specify which equations to turn on, by writing their numbers after FnOn: for example, FnOn 1 will turn off the first equation, and FnOn 2,3,4,5 will turn the second, third, fourth, and fifth. The numbers you give FnOn have to be valid equation numbers in the graphing mode. When turning equations on and off in sequence mode, use 1 for u, 2 for v, and 3 for w.

          The most common use for FnOn and FnOff is to disable functions when running a program, so that they won't interfere with what you're doing on the graph screen, then enable them again when you're done.

          Error Conditions

          • ERR:DOMAIN is thrown if an equation number isn't valid in the current graphing mode, or at all.

          Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, kg583.

          History

          Calculator OS Version Description
          TI-82 1.0 Added
          Property Value
          Hex Value $97
          Categories
          Localizations
          • FR: FonctNAff

          FnOff

          Overview

          Deselects all Y= functions or specified Y= functions.

          Availability: Token available everywhere.

          Syntax

          FnOff [function#,function#,...,function n]

          Arguments

          NameTypeOptional
          function#Yes
          function#Yes
          function nYes

          Location

          vars, Y-VARS, 4:On/Off2:FnOff

          Description

          The FnOff command is used to turn off equations in the current graphing mode. When you turn off an equation, it's still defined, but isn't graphed; you can reverse this with the FnOn command. To turn functions on and off manually, put your cursor over the = symbol in the equation editor, and press enter.

          When FnOff is used by itself, it will turn off all defined equations in the current graphing mode. You can also specify which equations to turn off, by writing their numbers after FnOff: for example, FnOff 1 will turn off the first equation, and FnOff 2,3,4,5 will off turn the second, third, fourth, and fifth. The numbers you give FnOff have to be valid equation numbers in the graphing mode. When turning equations on and off in sequence mode, use 1 for u, 2 for v, and 3 for w.

          The most common use for FnOn and FnOff is to disable functions when running a program, so that they won't interfere with what you're doing on the graph screen, then enable them again when you're done.

          Error Conditions

          • ERR:DOMAIN is thrown if an equation number isn't valid in the current graphing mode, or at all.

          Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, kg583.

          History

          Calculator OS Version Description
          TI-82 1.0 Added
          Property Value
          Hex Value $98
          Categories
          Localizations
          • FR: SauveImage

          StorePic

          Overview

          Stores current picture in picture Picn.

          Availability: Token available everywhere.

          Syntax

          StorePic n

          Arguments

          NameTypeOptional
          n

          Location

          2nd, draw, STO, 1:StorePic

          Description

          StorePic saves the graph screen to a picture (to recall it later, use RecallPic). Every detail of the graph screen will be stored as it appears, with the sole exception of X and Y labels on the axes (if they are shown).

          The number passed to StorePic must be one of 0 through 9. It has to be a number: StorePic X will not work, even if X contains a value 0 through 9.

          Advanced Uses

          A combination of StorePic and RecallPic can be used to maintain a background over which another sprite moves:

          First, draw the background, and save it to a picture file with StorePic.
          Next, draw the sprite to the screen.
          When you want to move the sprite, erase it, then use RecallPic to draw the background again.
          Then draw the sprite to its new location on the screen again (this can be done before or after using RecallPic).

          Also, if a screen in your program takes more than a second to draw, and is displayed several times, you might want to consider storing it to a picture the first time it's drawn, and then recalling it every next time you want to draw it.

          Error Conditions

          • ERR:DATA TYPE is thrown if the argument is not a number 0 through 9.

          Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, kg583.

          History

          Calculator OS Version Description
          TI-82 1.0 Added
          Property Value
          Hex Value $99
          Categories
          Localizations
          • FR: RappelImage

          RecallPic

          Overview

          Displays the graph and adds the picture stored in Picn.

          Availability: Token available everywhere.

          Syntax

          RecallPic n

          Arguments

          NameTypeOptional
          n

          Location

          2nd, draw, STO, 2:RecallPic

          Description

          RecallPic draws a saved picture to the graph screen (to save a picture, draw it on the graph screen, then save it with StorePic). If something is already drawn on the graph screen, RecallPic will draw new pixels where needed, but it will not erase anything. As a result, you often want to ClrDraw before recalling a picture.

          The number passed to RecallPic must be one of 0 through 9. It has to be a number: RecallPic X will not work, even if X contains a value 0 through 9.

          Advanced Uses

          A combination of StorePic and RecallPic can be used to maintain a background over which another sprite moves:

          1. Draw the background, and save it to a picture file with StorePic.
          2. Next, draw the sprite to the screen.
          3. When you want to move the sprite, erase it, then use RecallPic to draw the background again.
          4. Then draw the sprite to its new location on the screen again (this can be done before or after using RecallPic).

          Also, if a screen in your program takes more than a second to draw, and is displayed several times, you might want to consider storing it to a picture the first time it's drawn, and then recalling it every next time you want to draw it.

          Error Conditions

          • ERR:DATA TYPE is thrown if the argument is not a number 0 through 9.
          • ERR:UNDEFINED is thrown if the requested picture does not exist.

          Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583, Zaphod Beeblebrox.

          History

          Calculator OS Version Description
          TI-82 1.0 Added
          Property Value
          Hex Value $9A
          Categories
          Localizations
          • FR: SauveBDG

          StoreGDB

          Overview

          Stores current graph in database GDBn.

          Availability: Token available everywhere.

          Syntax

          StoreGDB n

          Arguments

          NameTypeOptional
          n

          Location

          2nd, draw, STO, 3:StoreGDB

          Description

          The StoreGDB command stores all graph settings needed to reconstruct the current graph to a GDB (Graph DataBase) variable, one of GDB1, GDB2, …, GDB0 (as indicated by the argument). These settings can then be recalled using the RecallGDB command.

          The settings stored in a GDB include:

          • The graphing mode currently enabled.
          • All equations in the current graphing mode, but NOT other graphing modes.
          • All window variables applicable to the current graphing mode. This does not include zoom variables, table settings, or irrelevant variables such as Tmin when in function mode.
          • The menu settings relevant to graphing (everything in the 2nd FORMAT menu, as well as Connected/Dot and Sequential/Simul settings in the MODE menu)

          The number passed to StoreGDB must be one of 0 through 9. It has to be a number: StoreGDB X will not work, even if X contains a value 0 through 9.

          Advanced Uses

          The StoreGDB and RecallGDB variables are useful in cleaning up after a program finishes running, preserving the user's settings. If your program heavily relies on the graph screen, it may end up editing window size or other graph settings, which the user might want to be saved. This is easily done:

          Add StoreGDB 1 (or any other number) to the beginning of your program.

          Then, feel free to edit any graph settings you like.

          At the end of your program, add RecallGDB 1, followed by DelVar GDB1, to recall the graph settings stored at the beginning.

          GDBs can also be useful in adding extra string storage. You can store strings to the Yn variables, and back them up in a GDB; to retrieve them later, recall the GDB and use Equ►String( to store the equations to the strings again.

          Error Conditions

          • ERR:DATA TYPE is thrown if the argument is not a number 0 through 9.

          See Also

          Source: parts of this page were written by the following TI|BD contributors: DarkerLine, Electromagnet8, GoVegan.

          History

          Calculator OS Version Description
          TI-82 1.0 Added
          Property Value
          Hex Value $9B
          Categories
          Localizations
          • FR: RappelBDG

          RecallGDB

          Overview

          Restores all settings stored in the graph database variable GDBn.

          Availability: Token available everywhere.

          Syntax

          RecallGDB n

          Arguments

          NameTypeOptional
          n

          Location

          2nd, draw, STO, 4:RecallGDB

          Description

          The RecallGDB command recalls graph settings a GDB (Graph DataBase) variable, one of GDB1, GDB2, …, GDB0 (as indicated by the argument). These settings can be stored to a GDB using the StoreGDB command.

          The settings stored in a GDB include:

          • The graphing mode currently enabled.
          • All equations in the current graphing mode, but NOT other graphing modes.
          • All window variables applicable to the current graphing mode. This does not include zoom variables, table settings, or irrelevant variables such as Tmin when in function mode.
          • The menu settings relevant to graphing (everything in the 2nd FORMAT menu, as well as Connected/Dot and Sequential/Simul settings in the MODE menu)

          The number passed to RecallGDB must be one of 0 through 9. It has to be a number: RecallGDB X will not work, even if X contains a value 0 through 9.

          Advanced Uses

          The StoreGDB and RecallGDB variables are useful in cleaning up after a program finishes running, preserving the user's settings. If your program heavily relies on the graph screen, it may end up editing window size or other graph settings, which the user might want to be saved. This is easily done:

          Add StoreGDB 1 (or any other number) to the beginning of your program.

          Then, feel free to edit any graph settings you like.

          At the end of your program, add RecallGDB 1, followed by DelVar GDB1, to recall the graph settings stored at the beginning.

          GDBs can also be useful in adding extra string storage. You can store strings to the Yn variables, and back them up in a GDB; to retrieve them later, recall the GDB and use Equ►String( to store the equations to the strings again.

          Error Conditions

          • ERR:DATA TYPE is thrown if the argument is not a number 0 through 9.
          • ERR:UNDEFINED is thrown if the requested GDB does not exist.

          See Also

          Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Zaphod Beeblebrox.

          History

          Calculator OS Version Description
          TI-82 1.0 Added
          Property Value
          Hex Value $9C
          Categories
          Localizations
          • FR: Ligne(

          Line(

          Overview

          Draws a line from (X1,Y1) to (X2,Y2) with the following options: erase #: 1,0, color #: 10-24, and line style #: 1-4.

          Availability: Token available everywhere.

          Syntax

          Line(X1,Y1,X2,Y2[,erase#,color#,linestyle#])

          Arguments

          NameTypeOptional
          X1
          Y1
          X2
          Y2
          erase#Yes
          color#colorNumYes
          linestyle#integerYes

          Location

          2nd, draw, DRAW, 2:Line(

          Overview

          Erases a line (erase #: 1,0) from (X1,Y1) to (X2,Y2).

          Availability: Token available everywhere.

          Syntax

          Line(X1,Y1,X2,Y2,0[,line#])

          Arguments

          NameTypeOptional
          X1
          Y1
          X2
          Y2
          line#Yes

          Location

          2nd, draw, DRAW, 2:Line(

          Description

          The Line( command is used to draw lines at any angle, as opposed to only drawing vertical or horizontal lines. Line(X1,Y1,X2,Y2) will draw a line from (X1,Y1) to (X2,Y2). Line( is affected by the window settings, although you can use a friendly window so there is no impact on the command.

          :Line(5,5,20,3)

          Advanced Uses

          Line has an optional fifth argument. It can be any real number, but the default is one. If the fifth argument, erase, is something other than 0, then it will simply draw the line. If erase is 0, then it will erase the line.

          :Line(5,5,20,3,0)

          Leave off the ending argument if you are just drawing the line.

          :Line(5,5,20,3,1)
can be
:Line(5,5,20,3)

          The ending argument can be a formula, which is useful for movement applications and other things such as health bars where the lines drawn are constantly different. The following draws or erases a line depending on whether a key is pressed.

          :getKey
:Line(5,5,20,3,not(Ans

          If working on a TI 84+CSE or TI 84+CE, then the fifth argument of the Line( command can be a color name or ID number:

          :Line(5,5,20,3,BROWN

          The last argument, line style, is an optional argument that chooses what style of line to draw on the color calculators.

          1 pixel wide line
:Line(5,5,20,3,RED,1
2 pixel wide line
:Line(5,5,20,3,RED,2
shaded above
:Line(5,5,20,3,RED,3
shaded below
:Line(5,5,20,3,RED,4

          Command Timings

          If you are drawing horizontal or vertical lines that stretch the entire graph screen, such as a border, it is better to use Vertical or Horizontal. These are smaller and are usually faster as well.

          See Also

          Source: parts of this page were written by the following TI|BD contributors: basickevin, burr, DarkerLine, GoVegan, kg583, Lionel Foxcroft, Weregoose, Xphoenix.

          History

          Calculator OS Version Description
          TI-82 1.0 Added
          Property Value
          Hex Value $9D
          Categories
          Localizations
          • FR: Verticale

          Vertical

          Overview

          Draws a vertical line at xwith specified color and line style.
          Color#: 10 - 24 or color name pasted from [vars] COLOR.
          line style #: 1-4.

          Availability: Token available everywhere.

          Syntax

          Vertical x[,color#,linestyle#]

          Arguments

          NameTypeOptional
          x
          color#colorNumYes
          linestyle#integerYes

          Location

          2nd, draw, DRAW, 4:Vertical

          Description

          Vertical X draws a vertical line from the top of the graph screen to the bottom at X. Vertical is usually only used to replace a line that stretches the entire length of the graph screen, along with its counterpart Horizontal.

          Vertical is affected by the window settings, unlike the Pxl- commands.

          :Vertical 5

          Uses on TI 84+C Version Calculators

          The Vertical command takes an additional color argument for TI 84+C version calculators, as shown below:

          Vertical 5,BLACK

          Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583, Xphoenix.

          History

          Calculator OS Version Description
          TI-82 1.0 Added
          Property Value
          Hex Value $9E
          Categories
          Localizations
          • FR: Pt-Aff(

          Pt-On(

          Overview

          Draws a point at (x,y) on the graph area using markand the specified color#.
          Color#: 10 - 24 or color name pasted from [vars] COLOR.

          Availability: Token available everywhere.

          Syntax

          Pt-On(x,y[,mark,color#])

          Arguments

          NameTypeOptional
          x
          y
          markYes
          color#colorNumYes

          Location

          2nd, draw, POINTS, 1:Pt-On(

          Description

          The Pt-On( command is used to draw a point on the graph screen at the given (X,Y) coordinates. Pt-On( is affected by the window settings Xmin, Xmax, Ymin, and Ymax. Make sure to change these accordingly when using it in a program, otherwise, you don't know where the point will show up.

          Advanced Uses

          The Pt-On( command has an optional third argument that determines the shape of the point (its mark). The mark can be 1 (dot), 2 (3x3 box), 3 (3x3 cross), 6 (3x3 box), or 7 (3x3 cross). Note that by using the 3x3 shapes the X,Y coordinates will be the center of the shape and not the upperleft corner of the shape. You don't need to specify the mark when using the first mark because it is the default; also, any value that isn't 2, 3, 6, or 7 will be treated as the default of 1. Remember to use the same mark when turning a point off as you used to turn it on. Note that the mark arguments 6 and 7 are not supported on the TI-84+CE, and using them will return a domain error. The color calculators also include a color argument after the mark argument, which can be used to change the color of the point. Note that the leaving the color argument blank will result in the point being plotted with a default color of blue.

          If you need to convert coordinates in pixel format into point coordinate format, it can easily be done with the following formula:

          (X pixel coordinateΔX)-absolute value(Xmax)=X point
          (Y pixel coordinate          ΔY)-absolute value(Ymax)=Y point

          The ΔX and ΔY variables are available under "VARS", "Window", options 8 and 9. These two variables represent the number of points per pixel on the graph screen, so multiplying the pixel value by the ratio of points to pixels will give you the point value, you then subtract the Xmax/Ymax from this value to calibrate it to the center of the screen. This formula is useful in programs that use the pixel commands for their speed advantage, but need a point value for commands such as Circle( or Line(.

          :Pt-On(5,5,1
should be
:Pt-On(5,5

          Source: parts of this page were written by the following TI|BD contributors: burr, CloudVariable, DarkerLine, GoVegan, my_name, Skwerlman, tyler999.

          History

          Calculator OS Version Description
          TI-82 1.0 Added
          Property Value
          Hex Value $9F
          Categories
          Localizations
          • FR: Pt-Naff(

          Pt-Off(

          Overview

          Erases a point at (x,y) on the graph area using mark. The Off state may be the background color determined by the ImageVar or color setting.
          Color#: 10 - 24 or color name pasted from [vars] COLOR.

          Availability: Token available everywhere.

          Syntax

          Pt-Off(x,y[,mark])

          Arguments

          NameTypeOptional
          x
          y
          markYes

          Location

          2nd, draw, POINTS, 2:Pt-Off(

          Description

          The Pt-Off( command is used to turn off a point (a pixel on the screen) on the graph screen at the given (X,Y) coordinates. Pt-Off( is affected by the window settings, which means you have to change the window settings accordingly, otherwise the point won't show up correctly on the screen.

          Advanced Uses

          The Pt-Off( command has an optional third argument that determines the shape of the point (its mark). The mark can be 1 (dot), 2 (3x3 box), 3 (3x3 cross), 6 (3x3 box), or 7 (3x3 cross). Note that by using the 3x3 shapes the X,Y coördinates will be the center of the shape and not the upperleft corner of the shape. You don't need to specify the mark when using the first mark because it is the default; also, any value that isn't 2, 3, 6, or 7 will be treated as the default of 1.

          :Pt-Off(5,5,1
Remove Mark
:Pt-Off(5,5

          Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, my_name, Skwerlman.

          History

          Calculator OS Version Description
          TI-82 1.0 Added
          Property Value
          Hex Value $A0
          Categories
          Localizations
          • FR: Pt-Change(

          Pt-Change(

          Overview

          Toggles a point on or off at (x,y) on the graph area. Off will be in the Background color and On will be the specified
          Color#: 10 - 24 or color name pasted from [vars] COLOR.

          Availability: Token available everywhere.

          Syntax

          Pt-Change(x,y[,color#])

          Arguments

          NameTypeOptional
          x
          y
          color#colorNumYes

          Location

          2nd, draw, POINTS, 3:Pt-Change(

          Description

          The Pt-Change( command is used to toggle a point (a pixel on the screen) on the graph screen at the given (X,Y) coordinates. If the point is on, it will be turned off and vice versa. Pt-Change( is affected by the window settings, which means you have to change the window settings accordingly, otherwise the point won't show up correctly on the screen.

          Pt-Change( can be an interactive command: when on the graph screen, you can select it from the draw menu, and rather than have to input coordinates, be able to draw directly on the screen. Since you can both draw and erase points easily with Pt-Change(, this use of it is often more convenient than the Pen tool.

          Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

          History

          Calculator OS Version Description
          TI-82 1.0 Added
          Property Value
          Hex Value $A1
          Categories
          Localizations
          • FR: Pxl-Aff(

          Pxl-On(

          Overview

          Draws pixel on the graph area at (row,column) in the specified color.
          Color#: 10 - 24 or color name pasted from [vars] COLOR.

          Availability: Token available everywhere.

          Syntax

          Pxl-On(row,column[,color#])

          Arguments

          NameTypeOptional
          row
          column
          color#colorNumYes

          Location

          2nd, draw, POINTS, 4:Pxl-On(

          Description

          The Pxl-On( command is used to turn on the pixel at the given (Y,X) coordinates. Please note that the coordinates are switched around so that the row comes first and then the column — it's (Y,X) unlike the (X,Y) of the Pt-On( command. Also note that the (0,0) point is the upper left corner of the Graph screen.

          In addition to being easier to use because it is not affected by the window settings (meaning you don't have to set them when using the command), Pxl-On( is faster than its equivalent Pt-On( command, so it should generally be used instead whenever possible.

          Error Conditions

          • ERR:DOMAIN is triggered if the coordinates are not whole numbers or not in the right range ([0..62] for row, [0..94] for column). These bounds are also affected by split screen mode.

          Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, my_name.

          History

          Calculator OS Version Description
          TI-82 1.0 Added
          Property Value
          Hex Value $A2
          Categories
          Localizations
          • FR: Pxl-Naff(

          Pxl-Off(

          Overview

          The Off state will display the set Background Image Var or COLOR.

          Availability: Token available everywhere.

          Syntax

          Pxl-Off(row,column)

          Arguments

          NameTypeOptional
          row
          column

          Location

          2nd, draw, POINTS, 5:Pxl-Off(

          Description

          The Pxl-Off( command is used to turn off the pixel at the given (Y,X) coordinates. Please note that the coordinates are switched around so that the row comes first and then the column — it's (Y,X) instead of (X,Y) like the Pt-Off( command. Also note that the (0,0) point is the upper left corner of the Graph screen.

          In addition to being easier to use because it is not affected by the window settings (meaning you don't have to set them when using the command), Pxl-Off( is faster than its equivalent Pt-Off( command, so it should generally be used instead whenever possible.

          Error Conditions

          • ERR:DOMAIN is triggered if the coordinates are not whole numbers or not in the right range ([0..62] for row, [0..94] for column). These bounds are also affected by split screen mode.

          Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, my_name.

          History

          Calculator OS Version Description
          TI-82 1.0 Added
          Property Value
          Hex Value $A3
          Categories
          Localizations
          • FR: Pxl-Change(

          Pxl-Change(

          Overview

          Toggles Off to On in the graph area: with specified color# Toggles On to Off in the graph area: Off will display the set Background Image Var or Color.
          Color#: 10 - 24 or color name pasted from [vars] COLOR.

          Availability: Token available everywhere.

          Syntax

          Pxl-Change(row,column[,color#])

          Arguments

          NameTypeOptional
          row
          column
          color#colorNumYes

          Location

          2nd, draw, POINTS, 6:Pxl-Change(

          Description

          The Pxl-Change( command is used to toggle the pixel at the given (Y,X) coordinates. If the pixel is on, it will be turned off and vice versa. Please note that the coordinates are switched around so that the row comes first and then the column — it's (Y,X) instead of (X,Y) like the Pt-Change( command. Also note that the row decreases as you go up which can confuse users.

          In addition to being easier to use because it is not affected by the window settings (meaning you don't have to set them when using the command), Pxl-Change( is faster than its equivalent Pt-Change( command, so it should generally be used instead whenever possible.

          Error Conditions

          • ERR:DOMAIN is triggered if the coordinates are not whole numbers or not in the right range ([0..62] for row, [0..94] for column). These bounds are also affected by split screen mode.

          Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, iPhoenixOnTIBD.

          History

          Calculator OS Version Description
          TI-82 1.0 Added
          Property Value
          Hex Value $A4
          Categories
          Localizations
          • FR: Ombre(

          Shade(

          Overview

          Draws lowerfunc and upperfunc in terms of X on the current graph and uses pattern and patres to shade and color the area bounded by lowerfunc, upperfunc, Xleft, and Xright. lowerfuncand upperfuncare shaded in the same specified color.
          Color#: 10 - 24 or color name pasted from [vars] COLOR.

          Availability: Token available everywhere.

          Syntax

          Shade(lowerfunc,upperfunc[,Xleft,Xright,pattern,patres,color#])

          Arguments

          NameTypeOptional
          lowerfunc
          upperfunc
          XleftYes
          XrightYes
          patternYes
          patresYes
          color#colorNumYes

          Location

          2nd, draw, DRAW, 7:Shade(

          Description

          The Shade( command draws two functions and shades the area between them.

          Shade(lower func, upper func, [xmin, xmax, pattern #, resolution])

          • lowerfunc and upperfunc are the two functions (whenever lowerfunc<upperfunc, the area between them will be shaded)
          • xmin and xmax (optional) are left and right boundaries on where to shade.
          • pattern # (optional) is an integer 1-4 determining which pattern to use:
            • 1 — vertical shading (default)
            • 2 — horizontal shading
            • 3 — diagonal shading (negative slope)
            • 4 — diagonal shading (positive slope)
          • resolution (optional) is an integer 1-8 determining the spacing between shading lines. When it's 1 (default), everything is shaded, when it's 2, one pixel is skipped between lines, and so on - when it's 8, seven pixels are skipped.

          Note that if you don't supply the resolution argument, it defaults to 1 and everything gets shaded regardless of the pattern.

          Advanced Uses

          Shade(Ymin,Ymax) is the smallest (though not the fastest) way to shade the entire screen.

          See Also

          Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Timothy Foster.

          History

          Calculator OS Version Description
          TI-82 1.0 Added
          Property Value
          Hex Value $A5
          Categories
          Localizations
          • FR: Cercle(

          Circle(

          Overview

          Draws a circle with center (X,Y) and radius with specified
          Color#: 10 - 24 or color name pasted from [vars] COLOR.
          linestyle#: 1-2.

          Availability: Token available everywhere.

          Syntax

          Circle(X,Y,radius[,color#,linestyle#])

          Arguments

          NameTypeOptional
          X
          Y
          radius
          color#colorNumYes
          linestyle#integerYes

          Location

          2nd, draw, DRAW, 9:Circle(

          Description

          Circle(X,Y,r) will draw a circle at (X,Y) with radius r. X and Y will be affected by the window settings. The radius will also be affected by the window settings.

          :Circle(5,5,5)

          Advanced Uses

          The radius of a circle is affected by the window settings. This means that if the x- and y-increment is two, the radius will be two pixels. However, there is another way to take advantage of this to draw ellipses. If the x- and y-increment are different, then the shape will not be a circle. For instance, with Xmin=0, Xmax=20, Ymin=0, and Ymax=31, Circle(10,10,2) will draw an ellipse, where the width is greater than the height.

          Optimization

          If a complex list such as {𝑖} is passed to Circle( as the fourth argument, the "fast circle" routine is used instead, which uses the symmetries of the circle to only do 1/8 of the trig calculations. For example:

          :Circle(0,0,5
can be
:Circle(0,0,5,{i

          Any list of complex numbers will work as the fourth argument in the same way, but there's no benefit to using any other list.

          Note: The "fast circle" routine is not available on the TI-84+CSE or TI-84+CE calculators.

          Command Timings

          The ordinary Circle( is extremely slow. The fast circle trick discussed above cuts the time down to only about 30% of the "slow Circle(" time! While still not instant, this is faster than any replacement routine that can be written in TI-Basic.

          For small radii, replace Circle( with Pt-On( instead.

          Source: parts of this page were written by the following TI|BD contributors: 15274, burr, CloudVariable, DarkerLine, GoVegan, jonbush, Myles_Zadok, Xphoenix, Zaphod Beeblebrox.

          History

          Calculator OS Version Description
          TI-82 1.0 Added
          Property Value
          Hex Value $A6
          Categories
          Localizations
          • FR: Horizontale

          Horizontal

          Overview

          Draws a horizontal line at y in a specified
          Color#: 10 - 24 or color name pasted from [vars] COLOR.
          line style #: 1-4.

          Availability: Token available everywhere.

          Syntax

          Horizontal y[,color#,linestyle#]

          Arguments

          NameTypeOptional
          y
          color#colorNumYes
          linestyle#integerYes

          Location

          2nd, draw, DRAW, 3:Horizontal

          Description

          Horizontal Y draws a vertical line from the left of the graph screen to the right at Y. Horizontal is usually only used to replace a line that stretches the entire length of the graph screen, along with its counterpart Vertical.

          Horizontal is affected by the window settings, unlike the Pxl- commands.

          :Horizontal 5

          Advanced Uses

          One of the fastest ways to make the entire screen black is by drawing horizontal lines from the bottom of the screen to the top.

          :For(A,Ymin,Ymax,ΔY
:Horizontal A
:End

          If working with TI 84+C version calculators, the Horizontal command takes an additional color argument, as shown below:

          Horizontal 5,GRAY

          Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583, Xphoenix.

          History

          Calculator OS Version Description
          TI-82 1.0 Added
          Property Value
          Hex Value $A7
          Categories
          Localizations
          • FR: Tangente(

          Tangent(

          Overview

          Draws a line tangent to expression at X=value with specified color #: 10-24 and line style linestyle #:1-2.
          Color#: 10 - 24 or color name pasted from [vars] COLOR.

          Availability: Token available everywhere.

          Syntax

          Tangent(expression,value[,color#,linestyle#])

          Arguments

          NameTypeOptional
          expressionexpression
          value
          color#colorNumYes
          linestyle#integerYes

          Location

          2nd, draw, DRAW, 5:Tangent(

          Description

          The Tangent( command draws a graph of an expression and then draws a line tangent to that expression, with the line touching the graph at the point of the specified value. You can either use a equation variable (such as Y1) or an expression in terms of X (such as X²). Though you can use equation variables from any graphing mode, they will be treated as functions in terms of X. Tangent( also ignores the graphing mode currently selected.

          Here is a simple example, where we are graphing the parabola X2 and then drawing a tangent line at the value X=2.

          :"X²→Y₁
:Tangent(Y₁,2

          or

          :Tangent(X²,2

          Advanced Uses

          Whether the graph shows up or not is dependent on the window dimensions of the graph screen, and you should use a friendly window to ensure it shows up as you intended.

          Tangent( will update X and Y for each coordinate drawn (like DrawF and DrawInv), and exit with the last coordinate still stored.

          When evaluating the expression using Tangent(, the calculator will ignore the following errors: ERR:DATA TYPE, ERR:DIVIDE BY 0, ERR:DOMAIN, ERR:INCREMENT, ERR:NONREAL ANS, ERR:OVERFLOW, and ERR:SINGULAR MAT. If one of these errors occurs, the data point will be omitted. However, the errors will still be thrown if they occur when evaluating the function at the point of tangency.

          Using Ans as an optimization for storing to an equation will not work. For example, the following code returns ERR:DATA TYPE because Ans is a string, not an equation variable.

          :"X²
:Tangent(Ans,2

          Of course, you can use Ans in the equation, if it's a real number, but that's usually not as useful.

          Error Conditions

          • ERR:INVALID is thrown if you try to use an equation variable that is undefined.

          Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

          History

          Calculator OS Version Description
          TI-82 1.0 Added
          Property Value
          Hex Value $A8
          Categories
          Localizations
          • FR: DessRecip

          DrawInv

          Overview

          Draws the inverse of expression by plotting X values on the y-axis and Y values on the x-axis with specified
          Color#: 10 - 24 or color name pasted from [vars] COLOR.

          Availability: Token available everywhere.

          Syntax

          DrawInvexpression[,color#]

          Arguments

          NameTypeOptional
          expressionexpression
          color#colorNumYes

          Location

          2nd, draw, DRAW, 8:DrawInv

          Description

          The DrawInv command draws the inverse of a curve in terms of X. Its single argument is an expression in terms of X.

          For example, DrawInv X² will draw the inverse of the equation Y=X2. The inverse reverses the variables X and Y, so that the curve X=Y2 will be graphed. In this case, the inverse of the function has a simple form: Y=√(X) and Y=-√(X); most functions, however, do not have an inverse expressible as Y= equation, making this command particularly useful.

          You can also think of this as graphing the expression but with X representing the vertical direction, and Y representing the horizontal.

          DrawInv requires the calculator to be in Func mode, and is affected by the Connected/Dot setting.

          Advanced Uses

          DrawInv will update X and Y for each coordinate drawn (like Tangent( and DrawF), and exit with the last coordinate still stored.

          When evaluating the expression using DrawInv, the calculator will ignore the following errors: ERR:DATA TYPE, ERR:DIVIDE BY 0, ERR:DOMAIN, ERR:INCREMENT, ERR:NONREAL ANS, ERR:OVERFLOW, and ERR:SINGULAR MAT. If one of these errors occurs, the data point will be omitted.

          For this reason, DrawInv can sometimes behave in an unexpected fashion: for example, it doesn't throw an error for list or matrix expressions (it won't graph anything, either).

          Error Conditions

          • ERR:MODE is thrown if the calculator is not in Func mode when using DrawInv.

          Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, kg583.

          History

          Calculator OS Version Description
          TI-82 1.0 Added
          Property Value
          Hex Value $A9
          Categories
          Localizations
          • FR: DessFonct

          DrawF

          Overview

          Draws expression (in terms of X) on the graph with specified
          Color#:10 - 24 or color name pasted from [vars] COLOR.

          Availability: Token available everywhere.

          Syntax

          DrawFexpression[,color#]

          Arguments

          NameTypeOptional
          expressionexpression
          color#colorNumYes

          Location

          2nd, draw, DRAW, 6:DrawF

          Description

          The DrawF commands draws a single expression on the graph screen in terms of X using Func graphing mode, regardless of what graphing mode the calculator is actually in. For example, DrawF X² will draw a parabola in the shape of a U on the screen. Of course, how it is displayed all depends on the window dimensions of the graph screen; you should use a friendly window to ensure it shows up as you intend.

          Advanced Uses

          DrawF will update X and Y for each coordinate drawn (like Tangent( and DrawInv), and exit with the last coordinate still stored.

          When evaluating the expression using DrawF, the calculator will ignore the following errors: ERR:DATA TYPE, ERR:DIVIDE BY 0, ERR:DOMAIN, ERR:INCREMENT, ERR:NONREAL ANS, ERR:OVERFLOW, and ERR:SINGULAR MAT. If one of these errors occurs, the data point will be omitted.

          For this reason, DrawF can sometimes behave in an unexpected fashion: for example, it doesn't throw an error for list or matrix expressions (it won't graph anything, either).

          You can use DrawF to draw an expression instead of having to store an expression to a Y# variable and then displaying it. At the same time, if you plan on manipulating the expression (either changing the value or changing the expression itself), it would be better to simply use the Y# variable.

          Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583.

          History

          Calculator OS Version Description
          TI-82 1.0 Added
          Property Value
          Hex Value $AA
          Categories
          Localizations
          • FR: VARSTRING

          VARSTRING

          Overview

          Syntax

          VARSTRING

          Description

          Examples

          Explanation 1

          code 1

          Explanation 2

          code 2

          Error Conditions

          Advanced Notes

          History

          Calculator OS Version Description
          Property Value
          Hex Value $AA00
          Categories
          Localizations
          • FR: Chaine1

          Str1

          Overview

          Availability: Token available everywhere.

          Syntax

          Str1

          Description

          Examples

          Explanation 1

          code 1

          Explanation 2

          code 2

          Error Conditions

          Advanced Notes

          History

          Calculator OS Version Description
          TI-83 0.01013 Added
          Property Value
          Hex Value $AA01
          Categories
          Localizations
          • FR: Chaine2

          Str2

          Overview

          Availability: Token available everywhere.

          Syntax

          Str2

          Description

          Examples

          Explanation 1

          code 1

          Explanation 2

          code 2

          Error Conditions

          Advanced Notes

          History

          Calculator OS Version Description
          TI-83 0.01013 Added
          Property Value
          Hex Value $AA02
          Categories
          Localizations
          • FR: Chaine3

          Str3

          Overview

          Availability: Token available everywhere.

          Syntax

          Str3

          Description

          Examples

          Explanation 1

          code 1

          Explanation 2

          code 2

          Error Conditions

          Advanced Notes

          History

          Calculator OS Version Description
          TI-83 0.01013 Added
          Property Value
          Hex Value $AA03
          Categories
          Localizations
          • FR: Chaine4

          Str4

          Overview

          Availability: Token available everywhere.

          Syntax

          Str4

          Description

          Examples

          Explanation 1

          code 1

          Explanation 2

          code 2

          Error Conditions

          Advanced Notes

          History

          Calculator OS Version Description
          TI-83 0.01013 Added
          Property Value
          Hex Value $AA04
          Categories
          Localizations
          • FR: Chaine5

          Str5

          Overview

          Availability: Token available everywhere.

          Syntax

          Str5

          Description

          Examples

          Explanation 1

          code 1

          Explanation 2

          code 2

          Error Conditions

          Advanced Notes

          History

          Calculator OS Version Description
          TI-83 0.01013 Added
          Property Value
          Hex Value $AA05
          Categories
          Localizations
          • FR: Chaine6

          Str6

          Overview

          Availability: Token available everywhere.

          Syntax

          Str6

          Description

          Examples

          Explanation 1

          code 1

          Explanation 2

          code 2

          Error Conditions

          Advanced Notes

          History

          Calculator OS Version Description
          TI-83 0.01013 Added
          Property Value
          Hex Value $AA06
          Categories
          Localizations
          • FR: Chaine7

          Str7

          Overview

          Availability: Token available everywhere.

          Syntax

          Str7

          Description

          Examples

          Explanation 1

          code 1

          Explanation 2

          code 2

          Error Conditions

          Advanced Notes

          History

          Calculator OS Version Description
          TI-83 0.01013 Added
          Property Value
          Hex Value $AA07
          Categories
          Localizations
          • FR: Chaine8

          Str8

          Overview

          Availability: Token available everywhere.

          Syntax

          Str8

          Description

          Examples

          Explanation 1

          code 1

          Explanation 2

          code 2

          Error Conditions

          Advanced Notes

          History

          Calculator OS Version Description
          TI-83 0.01013 Added
          Property Value
          Hex Value $AA08
          Categories
          Localizations
          • FR: Chaine9

          Str9

          Overview

          Availability: Token available everywhere.

          Syntax

          Str9

          Description

          Examples

          Explanation 1

          code 1

          Explanation 2

          code 2

          Error Conditions

          Advanced Notes

          History

          Calculator OS Version Description
          TI-83 0.01013 Added
          Property Value
          Hex Value $AA09
          Categories
          Localizations
          • FR: Chaine0

          Str0

          Overview

          Availability: Token available everywhere.

          Syntax

          Str0

          Description

          Examples

          Explanation 1

          code 1

          Explanation 2

          code 2

          Error Conditions

          Advanced Notes

          History

          Calculator OS Version Description
          TI-83 0.01013 Added
          Property Value
          Hex Value $AB
          Categories
          Localizations
          • FR: NbrAléat

          rand

          Overview

          Returns a random number between 0 and 1 for a specified number of trials numtrials.

          Availability: Token available everywhere.

          Syntax

          rand[(numtrials)]

          Arguments

          NameTypeOptional
          numtrialsYes

          Location

          math, PRB, 1:rand

          Description

          rand generates a uniformly-distributed pseudorandom number (this page and others will sometimes drop the pseudo- prefix for simplicity) between 0 and 1. rand(n) generates a list of n uniformly-distributed pseudorandom numbers between 0 and 1. seed→rand seeds (initializes) the built-in pseudorandom number generator. The factory default seed is 0.

          L'Ecuyer's algorithm is used by TI calculators to generate pseudorandom numbers.

          0→rand
     0
rand
     .9435974025
rand(2)
     {.908318861 .1466878292}

          Note: Due to specifics of the random number generating algorithm, the smallest number possible to generate is slightly greater than 0. The largest number possible is actually 1, but since returning a result of 1 would mess up the output of randBin( and randNorm(, the actual value returned in such cases is 1-1.11e-12 (which is displayed as 1, and is "equal" to 1 for the purposes of the = command). To see 1, store 196164532 to rand and then run the random number generator. If you instead try to store the “random” value directly to a list element, the value as viewed inside of the list editor will be 1-1.11e-12, displayed as 0.99999999999889.

          Advanced Uses

          To seed the random number generator, store a positive integer to rand (the command will ignore any decimals, and the sign of the number). Seeding the random number generator has several uses:

          When writing a program that uses random numbers, you may add a 0→rand instruction to the beginning of the program — this ensures that the program's actions will be repeatable, making it easier to fix a bug. Just don't forget to take it out when you've finished writing the program.

          Seeding the random number generator can also be used to create fairly secure (unbreakable without a computer) encryption. Pick a secret key, and store it to rand as a seed. Then, perform some randomly generated manipulations on the data you want to encode — for example, shifting each character of a string by a random number. Decoding the message is simple: store the secret key to rand and perform the opposite of those random operations. However, this is impossible to do if you don't know the secret key.

          When seeding the random number generator, as above, you make every random number generated afterwards predictable. This may be problematic even if your program doesn't need random numbers, because other programs might. To prevent this, use the following code to save and restore "randomness":

          :randInt(1,E9)→N

          (code that involves seeding the RNG here)

          :N→rand

          Since generating random numbers is a fairly time-consuming operation, the rand(# of numbers) syntax is very effective at generating a delay in your program — just add the line:

          :rand(N)

          The bigger N is, the longer the delay. In relation to the commonly used For( loop delay, the number used in the rand( delay is about 10 times smaller. However, this code has a side effect of storing a list of random numbers to Ans, which may be undesirable. To avoid this, use this somewhat longer line:

          :If dim(rand(N))

          Despite the presence of an If statement, you don't have to worry about the next line being skipped, since dim(rand(N)) will always be true.

          Error Conditions

          • ERR:DOMAIN if you try to generate a list of random numbers and the list length isn't an integer 1-999.

          Source: parts of this page were written by the following TI|BD contributors: builderboy, burr, CloudVariable, DarkerLine, Deoxal, GoVegan, MrTanookiMario, thornahawk, Timothy Foster, ztrumpet.

          History

          Calculator OS Version Description
          TI-82 1.0 Added
          Property Value
          Hex Value $AC
          Categories
          Localizations
          • FR: π

          π

          Overview

          Availability: Token available everywhere.

          Syntax

          π

          Description

          Examples

          Explanation 1

          code 1

          Explanation 2

          code 2

          Error Conditions

          Advanced Notes

          History

          Calculator OS Version Description
          TI-82 1.0 Added
          Property Value
          Hex Value $AD
          Categories
          Localizations
          • FR: codetouch(

          getKey

          Overview

          Returns the key code for the current keystroke, or 0, if no key is pressed.

          Availability: Token only available from within the Basic editor.

          Syntax

          getKey

          Location

          prgm, I/O, 7:getKey

          Description

          The getKey command returns the value of the last key pressed since the last time getKey was executed. Reading key presses with getKey allows a program to transfer control to the user, and you can combine getKey with other commands to create menus, movement, or whatever else you want.

          Every key has a number assigned to it, except for ON (which is used for breaking out of programs). The numbering system consists of a row and column: the rows go from one to ten, starting at the top; and the columns go from one to six, starting from the left. You just put the row and column together to get the key's number — for example, the ENTER key is located in row 10, column 5, making its value 105. The arrow keys look like they would be numbered separately from the other keys, but they actually follow this pattern as well. See the key codes page for a picture of the key codes on the calculator.

          The value of getKey is cleared every time you read from it, until a new key is pressed. For this reason, except in very rare cases, you do not want to use the value of getKey in an expression directly, but store it to a variable first. It is also common to use getKey inside of a Repeat loop, so that the program can wait for the user to press a key.

          :Repeat Ans
:getKey
:End
:Ans→K

          Advanced Uses

          You can put getKey in the condition of a loop, to make the loop repeat until any key or a particular key is pressed by the user. The same thing can be done with conditionals as well. This is useful if you don't want to store getKey to a variable, but you still want to have the user press a key. This works because of the way 'true' and 'false' get interpreted in TI-Basic.

          :Repeat max(getKey={24,25,26,34
:End

          Unlike the other keys, the arrow and DEL keys can actually be held down, which will cause the key to keep being repeated until it is unpressed. This functionality is very useful in games where the user needs to repeatedly press a key to move or shoot, although it does completely disable the other keys from being able to be pressed (which is important in multiplayer games, where everybody must share the keys).

          Sometimes your program may do something for several seconds without user input (say, playing an animation), then pause and wait for a key to be pressed. The problem is that if a key is pressed during the animation, the next getKey will return the value of that key, and any loop set up to wait for a key press will exit immediately. The solution is to run a "dummy" getKey just before the loop begins — its value won't be used for anything, and it will reset the value of getKey to 0. This can also be used to clear keypresses meant for loading programs from inside a shell.

          Error Conditions

          • ERR:INVALID occurs if this statement is used outside a program.

          See Also

          Source: parts of this page were written by the following TI|BD contributors: basickevin, burr, DarkerLine, Edward H, GoVegan, iPhoenixOnTIBD, Myles_Zadok, Weregoose.

          History

          Calculator OS Version Description
          TI-82 1.0 Added
          Property Value
          Hex Value $AE
          Categories
          Localizations
          • FR: '

          '

          Overview

          Availability: Token available everywhere.

          Syntax

          '

          Description

          Examples

          Explanation 1

          code 1

          Explanation 2

          code 2

          Error Conditions

          Advanced Notes

          History

          Calculator OS Version Description
          TI-82 1.0 Added
          Property Value
          Hex Value $AF
          Categories
          Localizations
          • FR: ?

          ?

          Overview

          Availability: Token available everywhere.

          Syntax

          ?

          Description

          Examples

          Explanation 1

          code 1

          Explanation 2

          code 2

          Error Conditions

          Advanced Notes

          History

          Calculator OS Version Description
          TI-82 1.0 Added
          Property Value
          Hex Value $B0
          Categories
          Localizations
          • FR: ⁻

          ⁻

          Overview

          Availability: Token available everywhere.

          Syntax

          ⁻

          Description

          Examples

          Explanation 1

          code 1

          Explanation 2

          code 2

          Error Conditions

          Advanced Notes

          History

          Calculator OS Version Description
          TI-82 1.0 Added
          Property Value
          Hex Value $B1
          Categories
          Localizations
          • FR: partEnt(

          int(

          Overview

          Returns the largest integer ≤ a real or complex number, expression, list, or matrix.

          Availability: Token available everywhere.

          Syntax

          int(value)

          Arguments

          NameTypeOptional
          value

          Location

          math, NUM, 5:int(

          Description

          int(X) is the floor function. It returns the greatest integer less than or equal to X, and also works on complex numbers, lists and matrices.

          int(5.32)
               5
int(4/5)
               0
int(‾5.32)
               ‾6
int(‾4/5)
               ‾1

          The difference between iPart( and int( is subtle, and many people aren't even aware of it, but it exists. Whereas iPart( always truncates its parameters, simply removing the fractional part, int( always rounds down. This means that they return the same answers for positive numbers, but int( will return an answer 1 less than iPart( for (non-integer) negative numbers. For example, iPart(-5.32) is -5, while int(-5.32) is -6.

          Most of the time, however, you're dealing with only positive numbers anyway. In this case, the decision to use iPart( or int( is mostly a matter of preference - some people use int( because it is shorter; some use iPart( when there is a corresponding fPart( taken. However, if speed is a consideration, one should check the Command Timings section.

          Advanced Uses

          int(, along with iPart( and fPart(, can be used for integer compression.

          Command Timings

          The following table compares the speeds of int( and iPart(. Each command was timed over 2000 iterations to find a noticeable difference.

          Format

          Bars

          Pixels

          Total

          iPart(1

          10

          1

          81

          iPart(1.643759

          10

          1

          81

          int(1

          8

          7

          71

          int(1.643759

          10

          2

          82

          Conclusion: int( scales with the length of its input while iPart( does not. For fewer than 6 decimals, int( will most often be faster; for 6 or more decimals, consider using iPart(.

          See Also

          Source: parts of this page were written by the following TI|BD contributors: burr, CloudVariable, DarkerLine, GoVegan, kg583, Timtech.

          History

          Calculator OS Version Description
          TI-82 1.0 int added
          TI-83 0.01013 Renamed int to int(
          Property Value
          Hex Value $B2
          Categories
          Localizations
          • FR: abs(

          abs(

          Overview

          Returns the absolute value of a real number, expression, list, or matrix.

          Availability: Token available everywhere.

          Syntax

          abs(value)

          Arguments

          NameTypeOptional
          valuereal|expression|real[]|matrix

          Location

          math, NUM, 1:abs(

          Overview

          Returns the magnitude of a complex number or list.

          Availability: Token available everywhere.

          Syntax

          abs(complex value)

          Arguments

          NameTypeOptional
          complex valuecomplex|complex[]

          Location

          math, CMPLX, 5:abs(

          Description

          abs(x) returns the absolute value of the real number x. Also works on a list or matrix of real numbers.

          abs(3)
     3

abs(‾3)
     3

          For complex numbers, abs(z) returns the absolute value (also known as the complex modulus, norm, or a hundred other terms) of the complex number z. If z is represented as x+i_y_ where x and y are both real, abs(z) returns √(_x_²+_y_²). Also works on a list of complex numbers.

          abs(3+4i)
     5

          Optimization

          The abs( command, used properly, may be a smaller method of testing if a variable is in some range. For example:

          :If 10<X and X<20
can be
:If 5>abs(X-15

          In general, the first number, A, in the expression A>abs(X-B) should be half the length of the range, half of 10 in this case, and the second number, B, should be the midpoint of the range (here, 15).

          This can be taken to extreme degrees. For example, the following code uses abs( three times to test if X is the getKey keycode of one of the keys 1, 2, 3, 4, 5, 6, 7, 8, or 9:

          :If 2>abs(5-abs(5-abs(X-83

          For complex numbers given by a separate real and complex part, abs(X+iY) can be optimized to R►Pr(X,Y).

          Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, kg583, Myles_Zadok, thornahawk, Trenly.

          History

          Calculator OS Version Description
          TI-82 1.0 abs added
          TI-83 0.01013 Renamed abs to abs(
          Property Value
          Hex Value $B3
          Categories
          Localizations
          • FR: dét(

          det(

          Overview

          Returns determinant of matrix.

          Availability: Token available everywhere.

          Syntax

          det(matrix)

          Arguments

          NameTypeOptional
          matrixmatrix

          Location

          2nd, matrix, MATH, 1:det(

          Description

          The det( command calculates the determinant of a square matrix. If its argument is not a square matrix, ERR:INVALID DIM will be thrown.

          Advanced Uses

          If [A] is an N×N matrix, then the roots of det([A]-X identity(N)) are the eigenvalues of [A].

          Formulas

          For 2×2 matrices, the determinant is simply

          (1) \(\begin{align} \det\left( \begin{bmatrix} a & b\\c & d \end{bmatrix} \right) = \begin{vmatrix} a & b\\c & d \end{vmatrix} = ad-bc \end{align}\)

          For larger matrices, the determinant can be computed using the Laplace expansion, which allows you to express the determinant of an n×n matrix in terms of the determinants of (n-1)×(n-1) matrices. However, since the Laplace expansion takes \(O\left( n! \right)\) operations, the method usually used in calculators is Gaussian elimination, which only needs \(O\left( n^3 \right)\) operations.

          The matrix is first decomposed into a unit lower-triangular matrix and an upper-triangular matrix using elementary row operations:

          (2) \(\begin{pmatrix} {1}&{}&{}\\ {\vdots}&{\ddots}&{}\\ {\times}&{\cdots}&{1}\end{pmatrix} \begin{pmatrix}{\times}&{\cdots}&{\times}\\ {}&{\ddots}&{\vdots}\\ {}&{}&{\times} \end{pmatrix}\)

          The determinant is then calculated as the product of the diagonal elements of the upper-triangular matrix.

          Error Conditions

          Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Myles_Zadok, thornahawk.

          History

          Calculator OS Version Description
          TI-82 1.0 det added
          TI-83 0.01013 Renamed det to det(
          Property Value
          Hex Value $B4
          Categories
          Localizations
          • FR: identité(

          identity(

          Overview

          Returns the identity matrix of dimension rows x dimension columns.

          Availability: Token available everywhere.

          Syntax

          identity(dimension)

          Arguments

          NameTypeOptional
          dimension

          Location

          2nd, matrix, MATH, 5:identity(

          Description

          The identity( command generates an identity matrix: that is, a matrix [B] such that for any other matrix [A], [A]*[B]=[A] (if [A] is the right size to make the multiplication valid).

          The identity matrix is square (that is, the row dimension equals the column dimension); all of its elements are 0 except for the elements along the main diagonal (the diagonal going from top left to bottom right).

          The command itself takes one argument: the size of the matrix, used for both row and column size, that is, identity(n) creates an n by n matrix.

          :dim([A]
:identity(Ans(2→[B]
:[A][B]=[A]  // should always return 1, meaning 'true'

          Optimization

          The identity( command can be used as a quick way to create an empty square matrix: 0identity(n) will create an n by n matrix containing only 0 as an element. This is faster and smaller than the dim( and Fill( commands used for the same purpose:

          :{5,5→dim([A]
:Fill(0,[A]
can be
:0identity(5→[A]

          Error Conditions

          • ERR:INVALID DIM occurs if the size is not an integer 1-99. In practice, however, identity(21) is already too large for the calculator to generate.
          • ERR:MEMORY occurs if the size of the created matrix exceeds memory limits. This limit is hard-fixed to 3611 bytes (the size of a 20x20 matrix), regardless of having sufficient RAM to hold a larger matrix.

          Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583.

          History

          Calculator OS Version Description
          TI-82 1.0 identity added
          TI-83 0.01013 Renamed identity to identity(
          Property Value
          Hex Value $B5
          Categories
          Localizations
          • FR: dim(

          dim(

          Overview

          Returns the dimension of listname.

          Availability: Token available everywhere.

          Syntax

          dim(listname)

          Arguments

          NameTypeOptional
          listnamelist

          Location

          2nd, list, OPS, 3:dim(

          Overview

          Returns the dimension of matrixname as a list.

          Availability: Token available everywhere.

          Syntax

          dim(matrixname)

          Arguments

          NameTypeOptional
          matrixnamematrix

          Location

          2nd, matrix, MATH, 3:dim(

          Overview

          Assigns a new dimension (length) to a new or existing listname.

          Availability: Token available everywhere.

          Syntax

          length→dim(listname)

          Arguments

          NameTypeOptional
          lengthinteger
          listnamelist

          Location

          2nd, list, OPS, 3:dim(

          Overview

          Assigns new dimensions to a new or existing matrixname.

          Availability: Token available everywhere.

          Syntax

          {rows,columns}→dim(matrixname)

          Arguments

          NameTypeOptional
          rowsinteger
          columnsinteger
          matrixnamematrix

          Location

          2nd, matrix, MATH, 3:dim(

          Description

          The dim( command is used to find the size of an existing list or matrix. It takes only one argument - the list or matrix you want the size of. For a list, it returns the number of elements; for a matrix, it returns a two-element list of the number of rows and the number of columns.

          :dim(L1
    5
:dim([A]
    {2,3}

          The dim( command can also be used to change the size of a list or matrix; this is perhaps its most important use. To do this, just store the desired size to the list or matrix (the dim( command is the only one you can store in as though it were a variable).

          :7→dim(L1
:{2,2→dim([A]

          For a list, if this increases the size, zero elements will be added to the end of the list; if this decreases the size, elements will be removed starting from the end.

          For a matrix, if this increases the number of rows or columns, new rows or columns filled with zeros will be added to the bottom and right respectively. If this decreases the number of rows and columns, those rows and columns will be removed starting from the bottom (for rows) and right (for columns).

          If a list or matrix doesn't exist before its size is changed, the dim( command will actually create it with the correct size. All the elements, in this case, will be set to 0.

          Advanced Uses

          In the case of lists, the dim( command is used in adding an element to the end of a list. Although augment( can be used for the same task, dim( is faster - but takes more memory. For example, to add the element 5 to the end of L1:

          :5→L1(1+dim(L1

          It's also possible, using the dim( command, to set the size of a list to 0. In this case, the list exists, but doesn't take up any memory, and cannot be used in expressions (similar to the output of ClrList). This is not really useful.

          Optimization

          When creating a list or matrix using dim(, all the elements are preset to 0; this can be used in place of the Fill( command to set a list or matrix to a bunch of zeros in a program. Since we don't usually know for sure that the list or matrix doesn't exist, we must first delete it with DelVar.

          :{5,5→dim([A]
:Fill(0,[A]
can be
:DelVar [A]{5,5→dim([A]

          Error Conditions

          • ERR:INVALID DIM is thrown if you try to make a list or matrix bigger than 999 or 99x99 elements respectively, or if you try to create a matrix that isn't 2-dimensional.

          Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Myles_Zadok.

          History

          Calculator OS Version Description
          TI-82 1.0 dim added
          TI-83 0.01013 Renamed dim to dim(
          Property Value
          Hex Value $B6
          Categories
          Localizations
          • FR: somme(

          sum(

          Overview

          Returns the sum of elements of list from start to end.

          Availability: Token available everywhere.

          Syntax

          sum(list[,start,end])

          Arguments

          NameTypeOptional
          listlist
          startYes
          endYes

          Location

          2nd, list, MATH, 5:sum(

          Description

          The sum( command calculates the sum of all or part of a list.

          When you use it with only one argument, the list, it sums up all the elements of the list. You can also give it a bound of start and end and it will only sum up the elements starting and ending at those indices (inclusive).

          sum({1,2,3,4,5})
    15
sum({1,2,3,4,5},2,4)
    9
sum({1,2,3,4,5},3)
    12

          Optimization

          If the value of end is the last element of the list, it can be omitted:

          sum({1,2,3,4,5},3,5)
can be
sum({1,2,3,4,5},3)

          Error Conditions

          • ERR:DOMAIN is thrown if the starting or ending value aren't positive integers.
          • ERR:INVALID DIM is thrown if the starting or ending value exceed the size of the list, or are in the wrong order.

          Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

          History

          Calculator OS Version Description
          TI-82 1.0 sum added
          TI-83 0.01013 Renamed sum to sum(
          Property Value
          Hex Value $B7
          Categories
          Localizations
          • FR: prod(

          prod(

          Overview

          Returns product of list elements between start and end

          Availability: Token available everywhere.

          Syntax

          prod(list[,start,end])

          Arguments

          NameTypeOptional
          listlist
          startYes
          endYes

          Location

          2nd, list, MATH, 6:prod(

          Description

          The prod( command calculates the product of all or part of a list.

          When you use it with only one argument, the list, it multiplies all the elements of the list. You can also give it a bound of start and end and it will only multiply the elements starting and ending at those indices (inclusive).

          prod({1,2,3,4,5})
    120
prod({1,2,3,4,5},2,4)
    24
prod({1,2,3,4,5},3)
    60

          Optimization

          If the value of end is the last element of the list, it can be omitted:

          prod({1,2,3,4,5},3,5)
can be
prod({1,2,3,4,5},3)

          Error Conditions

          • ERR:DOMAIN if the starting or ending value aren't positive integers.
          • ERR:INVALID DIM if the starting or ending value exceed the size of the list, or are in the wrong order.

          Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan.

          History

          Calculator OS Version Description
          TI-82 1.0 Added
          Property Value
          Hex Value $B8
          Categories
          Localizations
          • FR: non(

          not(

          Overview

          Returns 0 if value is ≠ 0. value can be a real number, expression, or list.

          Availability: Token available everywhere.

          Syntax

          not(value)

          Arguments

          NameTypeOptional
          value

          Location

          2nd, test, LOGIC, 4:not(

          Description

          The last logical operator available on the 83 series takes only one value as input. not( comes with its own parentheses to make up for this loss. Quite simply, it negates the input: False becomes True (1) and True returns False (0). not( can be nested; one use is to make any True value into a 1.

          :not(0)
           1

:not(-20 and 14)

           0

:not(not(2))
           1

          Advanced Uses

          not(not(X)) will make any value X into 1 if it's not 0, and will keep it 0 if it is.

          Optimization

          not(X) and X=0 have the same truth value, but not( is shorter if the closing parenthesis is omitted:

          :If A=0
can be
:If not(A

          Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan.

          History

          Calculator OS Version Description
          TI-82 1.0 Added
          Property Value
          Hex Value $B9
          Categories
          Localizations
          • FR: ent(

          iPart(

          Overview

          Returns the integer part of a real or complex number, expression, list, or matrix.

          Availability: Token available everywhere.

          Syntax

          iPart(value)

          Arguments

          NameTypeOptional
          value

          Location

          math, NUM, 3:iPart(

          Description

          iPart(value) returns the integer part of value, and extends to complex numbers, lists, and matrices.

          iPart(5.32)
               5
iPart(4/5)
               0
iPart(‾5.32)
               ‾5
iPart(‾4/5)
               0

          iPart is sometimes used with it's corresponding partner fPart. While iPart trims off the part before the decimal point, fPart trims off the part after it.

          The difference between iPart( and int( is subtle; while iPart( always truncates its parameters, simply removing the integer part, int( always rounds down. This means that they return the same answers for positive numbers, but int( will return an answer 1 less than iPart( for (non-integer) negative numbers. For example, iPart(-5.32) is -5, while int(-5.32) is -6.

          In this case of positive values, though, the decision to use iPart( or int( is mostly a matter of preference - some people only use int( because it is shorter, some people use iPart( when there is a corresponding fPart( taken. However, see the Command Timings section.

          Watch Out For Precision Issues

          1/3*3→X   // X is expected to be 1
X         // Displays 1, but is actually 0.99999999999999 in memory
iPart(X)  // Displays 0
fPart(X)  // Displays 1, but is actually 0.99999999999999 in memory

          Somewhat unintuitively, the code above displays the results 1, 0 and 1. This is due to the calculator storing values to 14 digits of precision, but rounding the value to 10 digits to fit on the home screen.

          Tip: If you enter a value in the list editor screen, you will be able to see all 14 digits of precision. This can help you troubleshoot issues like these.

          One workaround is to round the numbers prior to calling iPart() or fPart(), if you don't mind the slight loss in precision from 14 significant digits to 9 decimal places:

          1/3*3→X
iPart(round(X,9))   // Displays the expected result 1
fPart(round(X,9))   // Displays the expected result 0

          (The parameter 9 is not technically required here since 9 is the default, but is shown for clarity and in case you want to customize the level of precision.)

          Advanced Uses

          iPart(, along with fPart( and int(, can be used for integer compression.

          Command Timings

          The following table compares the speeds of int( and iPart(. Each command was timed over 2000 iterations to find a noticeable difference.

          Format

          Bars

          Pixels

          Total

          iPart(1

          10

          1

          81

          iPart(1.643759

          10

          1

          81

          int(1

          8

          7

          71

          int(1.643759

          10

          2

          82

          Conclusion: With 5 or fewer decimal places, you should consider using int( because of its speed, but with more decimals, iPart( remains constant to eventually beat out its counterpart.

          See Also

          Source: parts of this page were written by the following TI|BD contributors: burr, CloudVariable, DarkerLine, GoVegan, kg583, Timtech.

          History

          Calculator OS Version Description
          TI-82 1.0 iPart added
          TI-83 0.01013 Renamed iPart to iPart(
          Property Value
          Hex Value $BA
          Categories
          Localizations
          • FR: partDéc(

          fPart(

          Overview

          Returns the fractional part or parts of a real or complex number, expression, list, or matrix.

          Availability: Token available everywhere.

          Syntax

          fPart(value)

          Arguments

          NameTypeOptional
          value

          Location

          math, NUM, 4:fPart(

          Description

          fPart(value) returns the fractional part of value, be it a variable, list, or matrix.

          fPart(5.32)
             .32
fPart(4/5)
              .8
fPart(‾5.32)
             ‾.32
fPart(‾4/5)
              ‾.8

          fPart is sometimes used with it's corresponding partner iPart. While iPart trims off the part before the decimal point, fPart trims off the part after it.

          Watch Out For Precision Issues

          1/3*3→X   // X is expected to be 1
X         // Displays 1, but is actually 0.99999999999999 in memory
iPart(X)  // Displays 0
fPart(X)  // Displays 1, but is actually 0.99999999999999 in memory

          Somewhat unintuitively, the code above displays the results 1, 0 and 1. This is due to the calculator storing values to 14 digits of precision, but rounding the value to 10 digits to fit on the home screen. Because of this, fPart() can appear to return values of 1 or -1.

          Tip: If you enter a value in the list editor screen, you will be able to see all 14 digits of precision. This can help you troubleshoot issues like these.

          One workaround is to round the numbers prior to calling iPart() or fPart(), if you don't mind the slight loss in precision from 14 significant digits to 9 decimal places:

          1/3*3→X
iPart(round(X,9))   // Displays the expected result 1
fPart(round(X,9))   // Displays the expected result 0

          (The parameter 9 is not technically required here since 9 is the default, but is shown for clarity and in case you want to customize the level of precision.)

          Advanced Uses

          Modulus

          fPart( is an easy way to find A mod B (the positive remainder when A is divided by B).

          B(A<0)+iPart(BfPart(A/B))

          If A is guaranteed to be positive, the following shorter code can be used, omitting B(A<0):

          iPart(BfPart(A/B))

          Detect Whole Numbers

          The easiest way to check if a number is a whole number is not(fPart(X:

          If not(fPart(X:Then
  // X is an integer
Else
  // X is not an integer
End

          This can be used, for example, to check if a number is divisible by another: if X is divisible by N, then X/N is a whole number. This is useful for finding the factors of a number.

          Compression

          fPart(, along with int( or iPart(, can be used for integer compression.

          See Also

          Source: parts of this page were written by the following TI|BD contributors: burr, CloudVariable, DarkerLine, ePIi, GoVegan, kg583.

          History

          Calculator OS Version Description
          TI-82 1.0 fPart added
          TI-83 0.01013 Renamed fPart to fPart(
          Property Value
          Hex Value $BB00
          Categories
          Localizations
          • FR: vactNet(

          npv(

          Overview

          Computes the sum of the present values for cash inflows and outflows.

          Availability: Token available everywhere.

          Syntax

          npv(interest rate,CF0,CFList[,CFFreq])

          Arguments

          NameTypeOptional
          interest rate
          CF0
          CFList
          CFFreqYes

          Location

          apps, 1:Finance, CALC, 7:npv(

          Description

          The npv( command computes the net present value of money over a specified time period. If a positive value is returned after executing npv(, that means it was a positive cashflow; otherwise it was a negative cashflow. The npv( command takes four arguments, and the fourth one is optional:

          • interest rate — the percentage of the money that is paid for the use of that money over each individual period of time.
          • CF0 — the initial amount of money that you start out with; this number must be a real number, otherwise you will get a ERR:DATA TYPE error.
          • CFList — the list of cash flows added or subtracted after the initial money.
          • CFFreq — the list of frequencies of each cash flow added after the initial money; if this is left off, each cash flow in the cash flow list will just appear once by default.

          Sample Problem

          Your mom recently opened a bank account for you, with $500 as a gift to start you off. This is welcome news to you, until you find out that the bank charges 5% as the interest rate for the account. So, you get a job at Rocco's Pizzas delivering pizzas, which brings in \(1,000-\)2,000 each month. For the last five months, in particular, you have earned $1,250, $1,333, $1,575, $1,100, and $1,900. (Assume there are no other expenses, such as gas, car payment, etc.)

          Plugging in all of the different values into the npv( command, this is what our code looks like:

          :npv(5,500,{1250,1333,1575,1100,1900

          Optimization

          The npv( command's optional fourth argument should be left off if each cash flow of money in the list of cash flows just appears once.

          :npv(5,1550,{2E3,3E3,4E3},{1,1,1
can be
:npv(5,1550,{2E3,3E3,4E3

          At the same time, if there are cash flows that occur multiple times, it can be smaller to just use the frequency argument:

          :npv(8,0,{200,200,300,300,300
can be
:npv(8,0,{200,300},{2,3

          Formulas

          Without a frequency list, the formula for npv( is the following:

          (1) \(\begin{align} \texttt{npv}(i,\texttt{CF}_0,\{\texttt{CF}_j\})=\sum_{j=0}^N{\texttt{CF}_j\left(1+\frac{i}{100}\right)^{-j}} \end{align}\)

          When a frequency list is used, the same formula can be applied if we expand the list with frequencies into a long list without frequencies. However, it's possible to do the calculation directly. We define the cumulative frequency Sj as the sum of the first j frequencies (S0 is taken to be 0):

          (2) \(\begin{align} \texttt{npv}(i,\texttt{CF}_0,\{\texttt{CF}_j\},\{n_j\}) =\texttt{CF}_0+\sum_{j=1}^N{\texttt{CF}_j\left(1+\frac{i}{100}\right)^{S_{j-1}}\frac{(1-(1+\frac{i}{100})^{-n_j})}{i}} \end{align}\)

          Error Conditions

          • ERR:DATA TYPE is thrown if you try to use anything other than a real number for the interest rate.
          • ERR:DIM MISMATCH is thrown if the list of cash flows and the list of cash flow frequencies have different dimensions.

          Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583.

          History

          Calculator OS Version Description
          TI-83 0.01013 Added
          Property Value
          Hex Value $BB01
          Categories
          Localizations
          • FR: tauxRi(

          irr(

          Overview

          Returns the interest rate at which the net present value of the cash flow is equal to zero.

          Availability: Token available everywhere.

          Syntax

          irr(CF0,CFList[,CFFreq])

          Arguments

          NameTypeOptional
          CF0
          CFList
          CFFreqYes

          Location

          apps, 1:Finance, CALC, 8:irr(

          Description

          The irr( command finds the Internal Rate of Return of an investment, which is a measure of its efficiency. Its mathematical interpretation is the interest rate for which npv( will return 0 for the same cash flows.

          irr( takes three arguments: an initial cash flow (CF0), a list of further cash flows (CFList), and an optional frequency list.

          Advanced Uses

          irr( can be used to find a root of a polynomial of any degree, give by a list of its coefficients:

          1+.01irr(0,{list of coefficients})

          However, this method is limited to finding roots greater than 0, and will throw an error (ERR:NO SIGN CHG or ERR:DIVIDE BY 0) if it can't find such roots. By reversing the list of coefficients and taking the reciprocal of the roots found, you could find roots less than 0, but this would still result in errors if such roots don't exist either.

          Using solve( to find roots of polynomials is less efficient, but more reliable, since it doesn't throw an error unless there are no roots at all to be found.

          Formulas

          Solving for irr( requires solving a polynomial with degree equal to the total number of cash flows. As such, there is no general formula for calculating irr(, though numerical methods are possible for finding an approximate solution.

          The polynomial associated with the calculation is:

          (1) \(\begin{align} \sum_{i=0}^{N}{C_i\left(1+\frac{\mathrm{Irr}}{100}\right)^{N-i}}=0 \end{align}\)

          Here, Irr is the internal rate of return, N is the number of cash flows, and Ct is the t th cash flow.

          To the calculator, only roots for which Irr>0 are considered to be viable.

          Error Conditions

          Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, kg583.

          History

          Calculator OS Version Description
          TI-83 0.01013 Added
          Property Value
          Hex Value $BB02
          Categories
          Localizations
          • FR: paSolde(

          bal(

          Overview

          Computes the balance at npmtfor an amortization schedule using stored values for PV, I%, and PMT and rounds the computation to roundvalue.

          Availability: Token available everywhere.

          Syntax

          bal(npmt[,roundvalue])

          Arguments

          NameTypeOptional
          npmt
          roundvalueYes

          Location

          apps, 1:Finance, CALC, 9:bal(

          Description

          The bal( command calculates the remaining balance after n payments in an amortization schedule. It has only one required argument: n, the payment number. However, it also uses the values of the finance variables PV, PMT, and I% in its calculations.

          The optional argument, roundvalue, is the number of digits to which the calculator will round all internal calculations. Since this rounding affects further steps, this isn't the same as using round( to round the result of bal( to the same number of digits.

          Usually, you will know the values of N, PV, and I%, but not PMT. This means you'll have to use the finance solver to solve for PMT before calculating bal(); virtually always, FV will equal 0.

          Sample Problem

          Imagine that you have taken out a 30-year fixed-rate mortgage. The loan amount is $100000, and the annual interest rate (APR) is 8%. Payments will be made monthly. After 15 years, what amount is still left to pay?

          We know the values of N, I%, and PV, though we still need to convert them to monthly values (since payments are made monthly). N is 30*12, and I% is 8/12. PV is just 100000.

          Now, we use the finance solver to solve for PMT. Since you intend to pay out the entire loan, FV is 0. Using either the interactive TVM solver, or the tvm_Pmt command, we get a value of about -$733.76 for PMT.

          We are ready to use bal(. We are interested in the payment made after 15 years; this is the 15*12=180th payment. bal(180) gives us the result $76781.55 — as you can see, most of the loan amount is still left to pay after 15 years.

          Formulas

          The calculator uses a recursive formula to calculate bal():

          (1) \(\begin{align} \texttt{bal}(0)=\texttt{PV} \end{align}\) (2) \(\begin{align} \texttt{bal}(m)=\left(1-\frac{I\%}{100}\right)\texttt{bal}(m-1)+\texttt{PMT} \end{align}\)

          In the case that roundvalue is given as an argument, the rounding is done at each step of the recurrence (which virtually forces us to use this formula). Otherwise, if no rounding is done (and assuming I% is not 0), we can solve the recurrence relation to get:

          (3) \(\begin{align} \texttt{bal}(m)=\frac{1-\left(1-\frac{I\%}{100}\right)^m}{\frac{I\%}{100}}\texttt{PMT}+\left(1-\frac{I\%}{100}\right)^m\texttt{PV} \end{align}\)

          Error Conditions

          • ERR:DOMAIN is thrown if the payment number is negative or a decimal.

          Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Myles_Zadok, Timothy Foster, Trenly.

          History

          Calculator OS Version Description
          TI-83 0.01013 Added
          Property Value
          Hex Value $BB03
          Categories
          Localizations
          • FR: paSomPrinc(

          ΣPrn(

          Overview

          Computes the sum, rounded to roundvalue, of the principal amount between pmt1 and pmt2 for an amortization schedule.

          Availability: Token available everywhere.

          Syntax

          ΣPrn(pmt1,pmt2[,roundvalue])

          Arguments

          NameTypeOptional
          Σ
          pmt1
          pmt2Yes
          roundvalueYes

          Location

          apps, 1:Finance, CALC, 0:Prn(

          Description

          The ΣPrn( command calculates, for an amortization schedule, the principal amount over a range of payments: the portion of those payments that went toward paying off the principal. Its two required arguments are payment1 and payment2, which define the range of payments we're interested in. However, it also uses the values of the finance variables PV, PMT, and I% in its calculations.

          The optional argument, roundvalue, is the number of digits to which the calculator will round all internal calculations. Since this rounding affects further steps, this isn't the same as using round( to round the result of ΣPrn( to the same number of digits.

          Usually, you will know the values of N, PV, and I%, but not PMT. This means you'll have to use the finance solver to solve for PMT before calculating ΣPrn(; virtually always, FV will equal 0.

          Sample Problem

          Imagine that you have taken out a 30-year fixed-rate mortgage. The loan amount is $100000, and the annual interest rate (APR) is 8%. Payments will be made monthly. How much of the principal amount was paid in the first five years?

          We know the values of N, I%, and PV, though we still need to convert them to monthly values (since payments are made monthly). N is 30*12, and I% is 8/12. PV is just 100000.

          Now, we use the finance solver to solve for PMT. Since you intend to pay out the entire loan, FV is 0. Using either the interactive TVM solver, or the tvm_Pmt command, we get a value of about -$733.76 for PMT.

          We are ready to use ΣPrn(. We are interested in the payments made during the first five years; that is, between the 1st payment and the 5*12=60th payment. ΣPrn(1,60) gives us the answer: -$4930.14 (the negative sign simply indicates the direction of cash flow)

          Formulas

          The formula that the calculator uses for ΣPrn( is in terms of bal(:

          (1) \(\begin{align} \texttt{\Sigma Prn}(n_1,n_2)=\texttt{bal}(n_2)-\texttt{bal}(n_1) \end{align}\)

          When the roundvalue argument isn't given, we can substitute the explicit formula for bal( and simplify to get the following formula:

          (2) \(\begin{align} \texttt{\Sigma Prn}(n_1,n_2)=\left(\texttt{PV}-\frac{\texttt{PMT}}{I\%/100}\right)\left[\left(1-\frac{I\%}{100}\right)^{n_1}-\left(1-\frac{I\%}{100}\right)^{n_2}\right] \end{align}\)

          Error Conditions

          • ERR:DOMAIN is thrown if either payment number is negative or a decimal.

          Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, kg583.

          History

          Calculator OS Version Description
          TI-83 0.01013 Added
          Property Value
          Hex Value $BB04
          Categories
          Localizations
          • FR: ΣInt(

          ΣInt(

          Overview

          Computes the sum, rounded to roundvalue, of the interest amount between pmt1 and pmt2 for an amortization schedule.

          Availability: Token available everywhere.

          Syntax

          ΣInt(pmt1,pmt2[,roundvalue])

          Arguments

          NameTypeOptional
          Σ
          pmt1
          pmt2Yes
          roundvalueYes

          Location

          apps, 1:Finance, CALC, A:Int(

          Description

          The ΣInt( command calculates, for an amortization schedule, the interest over a range of payments: the portion of those payments that went toward paying interest. Its two required arguments are payment1 and payment2, which define the range of payments we're interested in. However, it also uses the values of the finance variables PV, PMT, and I% in its calculations.

          The optional argument, roundvalue, is the number of digits to which the calculator will round all internal calculations. Since this rounding affects further steps, this isn't the same as using round( to round the result of ΣInt( to the same number of digits.

          Usually, you will know the values of N, PV, and I%, but not PMT. This means you'll have to use the finance solver to solve for PMT before calculating ΣInt(; virtually always, FV will equal 0.

          Sample Problem

          Imagine that you have taken out a 30-year fixed-rate mortgage. The loan amount is $100000, and the annual interest rate (APR) is 8%. Payments will be made monthly. How much of the amount that was paid in the first five years went towards interest?

          We know the values of N, I%, and PV, though we still need to convert them to monthly values (since payments are made monthly). N is 30*12, and I% is 8/12. PV is just 100000.

          Now, we use the finance solver to solve for PMT. Since you intend to pay out the entire loan, FV is 0. Using either the interactive TVM solver, or the tvm_Pmt command, we get a value of about -$733.76 for PMT.

          We are ready to use ΣInt(. We are interested in the payments made during the first five years; that is, between the 1st payment and the 5*12=60th payment. ΣInt(1,60) gives us the answer: -$39095.73 (the negative sign simply indicates the direction of cash flow)

          Formulas

          ΣInt( is calculated in terms of ΣPrn(, for which a recurrence exists. Since the total amount paid during an interval is known (it's the payment size, multiplied by the number of payments), we can subtract ΣPrn( from this total to get ΣInt(:

          (1) \(\begin{align} \texttt{\Sigma Int}(n_1,n_2)=(n_2-n_1+1)\texttt{PMT}-\texttt{\Sigma Prn}(n_1,n_2) \end{align}\)

          Error Conditions

          • ERR:DOMAIN is thrown if either payment number is negative or a decimal.

          Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583.

          History

          Calculator OS Version Description
          TI-83 0.01013 Added
          Property Value
          Hex Value $BB05
          Categories
          Localizations
          • FR: ►Nom(

          ►Nom(

          Overview

          Computes the nominal interest rate.

          Availability: Token available everywhere.

          Syntax

          ►Nom(effective rate,compounding periods)

          Arguments

          NameTypeOptional
          effective rate
          compounding periods

          Location

          apps, 1:Finance, CALC, B:►Nom(

          Description

          The ►Nom( command converts from an effective interest rate to a nominal interest rate. In other words, it converts an interest rate that takes compounding periods into account into one that doesn't. The two arguments are 1) the interest rate and 2) the number of compounding periods.

          For example, you want to know the interest rate, compounded monthly, that will yield a total increase of 10% per year:

          ►Nom(10,12)
    9.568968515

          Formulas

          The formula for converting from an effective rate to a nominal rate is:

          (1) \(\begin{align} \texttt{Nom}=100 \texttt{CP} \left(\sqrt[\texttt{CP}]{\frac{\texttt{Eff}}{100}+1}-1\right) \end{align}\)

          Here, Eff is the effective rate, Nom is the nominal rate, and CP is the number of compounding periods.

          Error Conditions

          • ERR:DOMAIN is thrown if the number of compounding periods is not positive, or if the nominal rate is -100% or lower (an exception's made for the nominal rate if there is only one compounding period, since ►Nom(X,1)=X).

          Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Xeda Elnara.

          History

          Calculator OS Version Description
          TI-83 0.01013 Added
          Property Value
          Hex Value $BB06
          Categories
          Localizations
          • FR: ►Eff(

          ►Eff(

          Overview

          Computes the effective interest rate.

          Availability: Token available everywhere.

          Syntax

          ►Eff(nominal rate,compounding periods)

          Arguments

          NameTypeOptional
          nominal rate
          compounding periods

          Location

          apps, 1:Finance, CALC, C:►Eff(

          Description

          The ►Eff( command converts from a nominal interest rate to an effective interest rate. In other words, it converts an interest rate that does not take into account compounding periods into one that does. The two arguments are 1) the interest rate and 2) the number of compounding periods.

          For example, take an interest rate of 7.5% per year, compounded monthly. You can use ►Eff( to find out the actual percent of interest per year:

          ►Eff(7.5,12)
    7.663259886

          Formulas

          The formula for converting from a nominal rate to an effective rate is:

          (1) \(\begin{align} \texttt{Eff}=100\left(\left(1+\frac{\texttt{Nom}}{100 \texttt{CP}}\right)^{\texttt{CP}}-1\right) \end{align}\)

          Here, Eff is the effective rate, Nom is the nominal rate, and CP is the number of compounding periods.

          Error Conditions

          • ERR:DOMAIN is thrown if the number of compounding periods is not positive, or if the nominal rate is -100% or lower (an exception's made for the nominal rate if there is only one compounding period, since ►Eff(X,1)=X)

          Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, jonbush, Myles_Zadok.

          History

          Calculator OS Version Description
          TI-83 0.01013 Added
          Property Value
          Hex Value $BB07
          Categories
          Localizations
          • FR: jed(

          dbd(

          Overview

          Calculates the number of days between date1 and date2 using the actual-day-count method.

          Availability: Token available everywhere.

          Syntax

          dbd(date1,date2)

          Arguments

          NameTypeOptional
          date1
          date2

          Location

          apps, 1:Finance, CALC, D:dbd(

          Description

          The dbd( command calculates the number of days between two dates. Each date is encoded as a single number in one of two formats (two formats can be mixed in the same command):

          • day, month, year — DDMM.YY (e.g. April 26, 1989 would be 2604.89)
          • month, day, year — MM.DDYY (e.g. April 26, 1989 would be 04.2689 or just 4.2689)

          Because this is just a number like any other, leading zeroes and trailing zeroes after the decimal can be dropped. For example, January 1, 2000 does not have to be formatted as 0101.00 but can be simply 101.

          Since there are only two digits for the year, obviously only a century's worth of dates can be handled. The calculator assumes this range to be from January 1, 1950 to December 31, 2049.

          If the second date comes before the first, dbd( will return a negative number of days, so the range of possible results is from -36524 to 36524.

          Finally, dbd( will also work for list inputs in the usual manner: a single date will be compared against every date in a list, and two lists of dates will be paired up.

          dbd(612.07,2512.07
    19
dbd(1.0207,1.0107
    -1
dbd(1.0107,{2.0107,3.0107,4.0107})
    {31 59 90}

          Advanced Uses

          The dbd( command can be used to calculate the day of week without using the dayOfWk( command, which is only available on the TI-84+ or higher.

          Error Conditions

          • ERR:DOMAIN is thrown if a date is improperly formatted.

          See Also

          Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583, Weregoose.

          History

          Calculator OS Version Description
          TI-83 0.01013 Added
          Property Value
          Hex Value $BB08
          Categories
          Localizations
          • FR: ppcm(

          lcm(

          Overview

          Returns the least common multiple of valueA and valueB, which can be real numbers or lists.

          Availability: Token available everywhere.

          Syntax

          lcm(valueA,valueB)

          Arguments

          NameTypeOptional
          valueAreal|expression|real[]
          valueBreal|expression|real[]

          Location

          math, NUM, 8:lcm(

          Description

          Returns the least common multiple (LCM) of two nonnegative integers; lcm(a,b) is equivalent to a__b/gcd(a,b). Also works on lists.

          lcm(8,6)
     24
lcm({9,12},6)
     {18 12}
lcm({14,12},{6,8})
     {42 24}

          Error Conditions

          • ERR:DIM MISMATCH is thrown if the arguments are two lists that don't have the same number of elements.
          • ERR:DOMAIN is thrown if the arguments aren't positive integers (or lists of positive integers) less than 1e12.

          Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, thornahawk.

          History

          Calculator OS Version Description
          TI-83 0.01013 Added
          Property Value
          Hex Value $BB09
          Categories
          Localizations
          • FR: pgcd(

          gcd(

          Overview

          Returns the greatest common divisor of valueA and valueB, which can be real numbers or lists.

          Availability: Token available everywhere.

          Syntax

          gcd(valueA,valueB)

          Arguments

          NameTypeOptional
          valueAreal|expression|real[]
          valueBreal|expression|real[]

          Location

          math, NUM, 9:gcd(

          Description

          The gcd( command returns the greatest common divisor (GCD) of two nonnegative integers. It also works on lists.

          gcd(8,6)
     2
gcd({9,12},6)
     {3 6}
gcd({14,12},{6,8})
     {2 4}

          Advanced Uses

          A gcd( command can be nested inside another gcd( command to compare up to four numbers.

          Error Conditions

          • ERR:DIM MISMATCH is thrown if the arguments are two lists that don't have the same number of elements.
          • ERR:DOMAIN is thrown if the arguments aren't positive integers (or lists of positive integers) less than 1E12.

          See Also

          Source: parts of this page were written by the following TI|BD contributors: burr, CloudVariable, DarkerLine, GoVegan, kg583, Myles_Zadok, thornahawk, Trenly.

          History

          Calculator OS Version Description
          TI-83 0.01013 Added
          Property Value
          Hex Value $BB0A
          Categories
          Localizations
          • FR: entAléat(

          randInt(

          Overview

          Generates and displays a random integer within a range specified by lower and upper integer bounds for a specified number of trials numtrials.

          Availability: Token available everywhere.

          Syntax

          randInt( lower,upper [,numtrials])

          Arguments

          NameTypeOptional
          lower
          upper
          numtrialsYes

          Location

          math, PRB, 5:randInt(

          Description

          randInt(min,max) generates a uniformly-distributed pseudorandom integer between min and max inclusive. randInt(min,max,n) generates a list of n uniformly-distributed pseudorandom integers between min and max.

          seed→rand affects the output of randInt(.

          0→rand
     0
randInt(1,10)
     10
randInt(1,10,5)
     {10 2 6 5 8}

          Optimization

          When the lower bound of randInt( is 0, you can replace it with int(#rand to save space. For example:

          :randInt(0,12
can be
:int(13rand

          Similarly, if you don't want to include zero in the range, you can use a variant of 1-#int(#rand:

          :1-2int(2rand

          In this particular example, the only values that you will ever get are -1 or 1.

          Formulas

          The value of randInt( for a given seed can be expressed in terms of rand:

          randInt(A,B)=

          • when A<B, A+int((B-A+1)rand
          • otherwise, B+int((A-B+1)rand

          This is identical to the output of randInt( in the sense that for the same seed, both expressions will generate the same random numbers.

          Error Conditions

          • ERR:DOMAIN is thrown if any of the arguments is a decimal.
          • ERR: DATA TYPE is given if you use imaginary numbers like 6i or something like Matrices or Lists. This error is used instead of ERR:DOMAIN for "i".

          Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, nap386, Xeda Elnara.

          History

          Calculator OS Version Description
          TI-83 0.01013 Added
          Property Value
          Hex Value $BB0B
          Categories
          Localizations
          • FR: BinAléat(

          randBin(

          Overview

          Generates and displays a random real number from a specified Binomial distribution.

          Availability: Token available everywhere.

          Syntax

          randBin(numtrials,prob[,numsimulations])

          Arguments

          NameTypeOptional
          numtrials
          prob
          numsimulationsYes

          Location

          math, PRB, 7:randBin(

          Description

          randBin(n,p) generates a pseudorandom integer between 0 and n inclusive according to the binomial distribution B(n,p) - that is, n trials of an event with probability of success p are performed, and the number of successes is returned. randBin(n,p,simulations) performs the above calculation simulations times, and returns a list of the results. The expected (average) result is n*p.

          n should be an integer greater than or equal to 1, while p should be a real number between 0 and 1 inclusive.

          seed→rand affects the output of randBin(

          0→rand
     0
randBin(5,1/2
     2
randBin(5,1/2,10
     {3 3 2 4 3 2 2 2 4 3}

          Formulas

          The value of randBin( for a given seed can be expressed in terms of rand:

          randBin(N,P)=sum(P>rand(N

          This is identical to the output of randBin( in the sense that for the same seed, both expressions will generate the same random numbers.

          Error Conditions

          • ERR:DOMAIN is triggered if the probability is not on the interval from 0 to 1.

          Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, MrTanookiMario, nap386, Timothy Foster, Xeda Elnara.

          History

          Calculator OS Version Description
          TI-83 0.01013 Added
          Property Value
          Hex Value $BB0C
          Categories
          Localizations
          • FR: Sous-chaine(

          sub(

          Overview

          Returns a string that is a subset of another string, from begin to length.

          Availability: Token available everywhere.

          Syntax

          sub(string,begin,length)

          Arguments

          NameTypeOptional
          stringstring
          begin
          lengthinteger

          Location

          2nd, catalog, sub(

          Overview

          Divides a real number, expression, or list by 100.

          Availability: Token available everywhere.

          Syntax

          sub(value)

          Arguments

          NameTypeOptional
          valuereal|expression|real[]

          Location

          2nd, catalog, sub(

          Description

          The sub( command is used to get a substring, or a specific part of a string. It takes three arguments: string is the source string to get the substring from, start is the index of the token to start from, and length is the length of the substring you want. For example:

          :sub("TI-BASIC",4,5
    "BASIC"
:sub("TI-BASIC",5,2
    "AS"

          Keep in mind that you can't have an empty string, so the length argument can't be equal to 0.

          When the length argument is 1, sub(string,N,1 returns the Nth token in the string.

          Advanced Uses

          If only one argument is given, and it contains an expression that evaluates to a real or complex number or list of numbers, the sub( command will divide the result by 100.

          :sub(225
    2.25
:sub({3+5i,-4i►Frac
    {3/100+1/20i,-1/25i}

          Much like the use of the % symbol, this is an undocumented feature that was introduced in OS version 1.15. Thus, care should be taken when using sub( in this way, as older versions will not support it.

          Together with the inString( command, sub( can be used to store a "list of strings" in a string, that you can then get each individual string from. To do this, think of a delimiter, such as a comma, to separate each individual string in the "list" (the delimiter must never occur in an individual string). The code will be simpler if the delimiter also occurs at the end of the string, as in "CAT,DOG,RAT,FISH,".

          This routine will display each string in a "list of strings". You can adapt it to your own needs.

          :1→I
:inString(Str1,",→J
:While Ans
:Disp sub(Str1,I,J-I
:J+1→I
:inString(Str1,",",Ans→J
:End

          Alternatively, instead of using inString, you can start each individual string at the length of the longest string length, plus 1. If there are smaller strings that are not the same length, use spaces.

          For example, if you wanted to display the suits for a card game, do the following:

          :"SPADES--DIAMONDSHEARTS--CLUB----→Str1
:sub(Str1,1+8A,8

          (Spaces have been replaced with dashes for visual clarity.)

          Broken down, by manipulating A, different portions of the string can be displayed without the hassle of searching for characters. Setting A as 0 would display "SPADES—", but thanks to the spaces, the extra two characters would not be seen. A may be replaced with (A-1) if the 1st name would like to be displayed by setting A to 1.

          This method is more preferable when using the Home Screen, as the spaces would wipe the last end characters of any previous strings displayed.

          You can use this command as a number to character converter, too, as shown:

          //Letter Number for Q
:17→Q
//Converter:
:sub("ABCDEFGHIJKLMNOPQRSTUVWXYZ",Q,1→Str1
:Disp Str1

          Error Conditions

          • ERR:ARCHIVED is thrown if you try to take the substring of an archived string.
          • ERR:DOMAIN is thrown if the starting and/or length value is less than 1, or if it is not an integer.
          • ERR:INVALID DIM is thrown if the starting and/or length value is beyond the length of the string.
          • ERR:UNDEFINED is thrown if you try to take the substring of a non-existent string.

          Source: parts of this page were written by the following TI|BD contributors: 7thAce, burr, DarkerLine, GoVegan, louwenus, luby19, Michael2_3B, QubicQuantum, Toothless the Dragon, Weregoose.

          History

          Calculator OS Version Description
          TI-83 0.01013 Added
          Property Value
          Hex Value $BB0D
          Categories
          Localizations
          • FR: Ecart-type(

          stdDev(

          Overview

          Returns the standard deviation of the elements in list with frequency freqlist.

          Availability: Token available everywhere.

          Syntax

          stdDev(list[,freqlist])

          Arguments

          NameTypeOptional
          listlist
          freqlistlistYes

          Location

          2nd, list, MATH, 7:stdDev(

          Description

          The stdDev( command finds the sample standard deviation of a list, a measure of the spread of a distribution. It takes a list of real numbers as a parameter. For example:

          :Prompt L1
:Disp "STD. DEV. OF L1",stdDev(L1

          Caution: the standard deviation found by this command is the sample standard deviation, not the population standard deviation, which is the one most commonly used when dealing with a sample rather than the whole population. The formula for population standard deviation is similar, but N-1 is replaced by N. There is no single command that will calculate population standard deviation for you, but 1-Var Stats will return both (sample standard deviation, the one returned by stdDev(), is Sx, while population standard deviation is σx). You can also calculate population standard deviation of L1 with the following code:

          :stdDev(augment(L1,{mean(L1

          Advanced Uses

          Frequency lists don't need to be whole numbers. Amazing as that may sound, your calculator can handle being told that one element of the list occurs 1/3 of a time, and another occurs 22.7 times. It can even handle a frequency of 0 - it will just ignore that element, as though it weren't there. One caveat, though - if all of the elements occur 0 times, there's no elements actually in the list and your calculator will throw an error.

          Formulas

          The formula for standard deviation used by this command is:

          (1) \(\begin{align} s = \sqrt{\frac{1}{N-1} \sum_{i=1}^N (x_i - \overline{x})^2} \end{align}\)

          This is the formula for sample standard deviation. The formula for population standard deviation, which this command does not use, varies slightly:

          (2) \(\begin{align} \sigma = \sqrt{\frac{1}{N} \sum_{i=1}^N (x_i - \overline{x})^2} \end{align}\)

          Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

          History

          Calculator OS Version Description
          TI-83 0.01013 Added
          Property Value
          Hex Value $BB0E
          Categories
          Localizations
          • FR: variance(

          variance(

          Overview

          Returns the variance of the elements in list with frequency freqlist.

          Availability: Token available everywhere.

          Syntax

          variance(list[,freqlist])

          Arguments

          NameTypeOptional
          listlist
          freqlistlistYes

          Location

          2nd, list, MATH, 8:variance(

          Description

          The variance( command finds the sample variance of a list, a measure of the spread of a distribution. It takes a list of real numbers as a parameter. For example:

          :Prompt L1
:Disp "VARIANCE OF L1",variance(L1

          Advanced Uses

          Frequency lists don't need to be whole numbers; your calculator can handle being told that one element of the list occurs 1/3 of a time, and another occurs 22.7 times. It can even handle a frequency of 0 - it will just ignore that element, as though it weren't there.

          Formulas

          The formula for variance used by this command is:

          (1) \(\begin{align} s_n^2 = \frac{1}{N-1} \sum_{i=1}^N (x_i - \overline{x})^2 \end{align}\)

          This is the formula for sample variance. The formula for population variance, which this command does not use, varies slightly:

          (2) \(\begin{align} \sigma^2 = \frac{1}{N} \sum_{i=1}^N (x_i - \overline{x})^2 \end{align}\)

          If the population variance is required, just multiply the result of variance() by \(1-1/N\).

          With frequencies wi, the formula becomes

          (3) \(\begin{align} s_n^2 = \frac{\sum_{i=1}^N w_i(x_i - \overline{x})^2}{\sum_{i=1}^N (w_i)-1} \end{align}\)

          where \(\overline{x}\) is the mean with frequencies included.

          Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583, thornahawk.

          History

          Calculator OS Version Description
          TI-83 0.01013 Added
          Property Value
          Hex Value $BB0F
          Categories
          Localizations
          • FR: carChaine(

          inString(

          Overview

          Returns the character position in string of the first character of substringbeginning at start.

          Availability: Token available everywhere.

          Syntax

          inString(string,substring[,start])

          Arguments

          NameTypeOptional
          stringstring
          substringstring
          startYes

          Location

          2nd, catalog, inString(

          Description

          The inString( command searches a string for occurrences of a smaller string (similar to the Find feature on a computer), and returns the first such occurrence.

          The source string is the string you want to search through; the search string is the substring you want to find. inString( will return the index of the first letter of the first occurrence of the search string found, or 0 if the search string is not present. For example:

          :inString("TI-BASIC","BASIC
    4
:inString("TI-BASIC","TI
    1
:inString("TI-BASIC","I
    2
:inString("TI-BASIC","ELEPHANT
    0

          You can also provide the optional starting point argument, 1 by default, that will tell the command where it should start looking. If you provide a value higher than 1 here, the command will skip the beginning of the string. This can be used to find where the search string occurs past the first occurrence. For example:

          :inString("TI-BASIC","I
    2
:inString("TI-BASIC","I",2
    2
:inString("TI-BASIC","I",3
    7

          Advanced Uses

          You can use inString( to convert a character to a number. For example:

          :inString("ABCDEFGHIJKLMNOPQRSTUVWXYZ",Str1→N

          Assuming Str1 is one character long and contains a capital letter, N will hold a value of 1-26 that corresponds to that letter. This value can then be stored in a real number, list, or matrix, where a character of a string couldn't be stored. To get the character value of the number, you can use the sub( command:

          :sub("ABCDEFGHIJKLMNOPQRSTUVWXYZ",N,1→Str1

          Using the starting point argument of inString(, you can write a routine to return all occurrences of the search string in the source string:

          :0→dim(L1
:inString(Str0,Str1
:Repeat not(Ans
:Ans→L1(1+dim(L1
:inString(Str0,Str1,Ans+1
:End

          If the search string is not found, this routine will return {0} in L₁. If it is found, the result will be a list of all the places the string was found.

          Optimization

          The inString( command can replace checking if a string is one of a number of values. Just put all the values in a string, one after the other, and try to find the string to be checked in the string of those values:

          :If Str1="." or Str1=",
can be
:If inString(".,",Str1

          Be careful, because if Str1 were ".," in the above example, this would also be treated like "." or ",". If this is a problem, you can separate the values you want to check for by a character you know can't be in the string:

          :If Str1="HELLO" or Str1="HI
can be
:If inString("HELLO,HI",Str1

          This approach assumes that a comma would never be in Str1, and words like "HELL" or "I" are also impossible. If words like these can appear in the input, the following works:

          :If inString("HELLO,HI,",Str+",

          (still assumes commas aren't in Str1)

          Error Conditions

          • ERR:DOMAIN is thrown if starting point is not a positive integer (starting point may be longer than the length of the source string, though).

          Source: parts of this page were written by the following TI|BD contributors: brt93yoda, burr, CloudVariable, ConorOBrien, DarkerLine, GoVegan, kg583, Lionel Foxcroft, Mr Dino, Trenly.

          History

          Calculator OS Version Description
          TI-83 0.01013 Added
          Property Value
          Hex Value $BB10
          Categories
          Localizations
          • FR: normalFRép(

          normalcdf(

          Overview

          Computes the normal distribution probability between lowerbound and upperbound for the specified μ and σ.

          Availability: Token available everywhere.

          Syntax

          normalcdf(lowerbound,upperbound[,μ,σ])

          Arguments

          NameTypeOptional
          lowerbound
          upperbound
          μYes
          σYes

          Location

          2nd, distr, DISTR, 2:normalcdf(

          Description

          normalcdf( is the normal (Gaussian) cumulative density function. If some random variable follows a normal distribution, you can use this command to find the probability that this variable will fall in the interval you supply.

          There are two ways to use normalcdf(. With two arguments (lower bound and upper bound), the calculator will assume you mean the standard normal distribution, and use that to find the probability corresponding to the interval between "lower bound" and "upper bound". You can also supply two additional arguments to use the normal distribution with a specified mean and standard deviation. For example:

          for the standard normal distribution
:normalcdf(-1,1

for the normal distribution with mean 10 and std. dev. 2.5
:normalcdf(5,15,10,2.5

          Advanced

          Often, you want to find a "tail probability" - a special case for which the interval has no lower or no upper bound. For example, "what is the probability x is greater than 2?". The TI-83+ has no special symbol for infinity, but you can use E99 to get a very large number that will work equally well in this case (E is the decimal exponent obtained by pressing [2nd] [EE]). Use E99 for positive infinity, and -E99 for negative infinity.

          The normal distribution is often used to approximate the binomial distribution when there are a lot of trials. This isn't really necessary on the TI-83+ because the binompdf( and binomcdf( commands are already very fast - however, the normal distribution can be slightly faster, and the skill can come in handy if you don't have access to a calculator but do have a table of normal distributions (yeah, right). Here is how to convert a binomial distribution to a normal one:

          :binompdf(N,P,X
can be
:normalcdf(X-.5,X+.5,NP,√(NP(1-P

:binomcdf(N,P,X,Y
can be
:normalcdf(X-.5,Y+.5,NP,√(NP(1-P

          How much faster this is will depend on N and P, since the binomial distribution takes a long time to evaluate for large values of N, but the normal distribution takes about the same time for any mean and standard deviation. Also, this is an approximation that is only valid for some binomial distributions - a common rule of thumb is NP>10.

          Formulas

          As with other continuous distributions, any probability is an integral of the probability density function. Here, too, we can define normalcdf( for the standard normal case in terms of normalpdf(:

          (1) \(\begin{align} \texttt{normalcdf}(a,b)=\int_a^b \texttt{normalpdf}(x) \, \mathrm{d}x=\frac1{\sqrt{2\pi\,}} \int_a^b e^{-\frac1{2}x^2} \, \mathrm{d}x \end{align}\)

          or in terms of the error function:

          (2) \(\begin{align} \texttt{normalcdf}(a,b)=\frac1{2}\left(\texttt{erf}\left(\frac{b}{\sqrt{2}}\right)-\texttt{erf}\left(\frac{a}{\sqrt{2}}\right)\right) \end{align}\)

          For the arbitrary mean μ and standard deviation σ, normalcdf( is defined in terms of the standard normal distribution, with the bounds of the interval standardized:

          (3) \(\begin{align} \texttt{normalcdf}(a,b,\mu,\sigma)=\texttt{normalcdf}\left(\frac{a-\mu}{\sigma},\frac{b-\mu}{\sigma} \right) \end{align}\)

          Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, thornahawk, Weregoose.

          History

          Calculator OS Version Description
          TI-83 0.01013 Added
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          • FR: FracNormale(

          invNorm(

          Overview

          Computes the inverse cumulative normal distribution function for a given area under the normal distribution curve specified by μ and s.. The optional argument tail can be LEFT (-∞,-a), CENTER [-a,a] or RIGHT (a, ∞) for Real a.
          The tokens LEFT, CENTER and RIGHT can be found in [catalog].

          Availability: Token available everywhere.

          Syntax

          invNorm(area[,µ,σ,tail])

          Arguments

          NameTypeOptional
          area
          µ
          σ
          tail

          Location

          2nd, distr, DISTR, 3:invNorm(

          Overview

          Computes the inverse cumulative normal distribution function for a given area under the normal distribution curve specified by μ and s.. The optional argument tail can be LEFT (-∞,-a), CENTER [-a,a] or RIGHT (a, ∞) for Real a.
          The tokens LEFT, CENTER and RIGHT can be found in [catalog].

          Availability: Token available everywhere.

          Syntax

          tail [catalog]: LEFT, CENTER, RIGHT

          Arguments

          NameTypeOptional
          tail catalog: LEFT
          CENTER
          RIGHT

          Location

          2nd, distr, DISTR, 3:invNorm(

          Description

          invNorm( is the inverse of the cumulative normal distribution function: given a probability, it will give you a z-score with that tail probability. The probability argument of invNorm( is between 0 and 1; 0 will give -1E99 instead of negative infinity, and 1 will give 1E99 instead of positive infinity

          There are two ways to use invNorm(. With three arguments, the inverse of the cumulative normal distribution for a probability with specified mean and standard deviation is calculated. With one argument, the standard normal distribution is assumed (zero mean and unit standard deviation). For example:

          for the standard normal distribution
:invNorm(.975

for the normal distribution with mean 10 and std. dev. 2.5
:invNorm(.975,10,2.5

          Advanced

          This is the only inverse of a probability distribution function available (at least on the TI-83/84/+/SE calculators), so it makes sense to use it as an approximation for other distributions. Since the normal distribution is a good approximation for a binomial distribution with many trials, we can use invNorm( as an approximation for the nonexistent "invBinom(". The following code gives the number of trials out of N that will succeed with probability X if the probability of any trial succeeding is P (rounded to the nearest whole number):

          :int(.5+invNorm(X,NP,√(NP(1-P

          You can also use invNorm() to approximate the inverse of a t-distribution. Since a normal distribution is a t-distribution with infinite degrees of freedom, this will be an overestimate for probabilities below 1/2, and an underestimate for probabilities above 1/2.

          Formulas

          Unlike the normalpdf( and normalcdf( commands, the invNorm( command does not have a closed-form formula. It can however be expressed in terms of the inverse error function:

          (1) \(\begin{align} \texttt{invNorm}(p) = \sqrt{2}\,\texttt{erf}^{-1}(2p-1) \end{align}\)

          For the arbitrary normal distribution with mean μ and standard deviation σ:

          (2) \(\begin{align} \texttt{invNorm}(p,\mu,\sigma)=\mu+\sigma\texttt{invNorm}(p) \end{align}\)

          Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, kg583, thornahawk.

          History

          Calculator OS Version Description
          TI-83 0.01013 Added
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          • FR: studentFRép(

          tcdf(

          Overview

          Computes the Student-t distribution probability between lowerbound andupperbound for the specified degrees of freedomdf.

          Availability: Token available everywhere.

          Syntax

          tcdf(lowerbound,upperbound,df)

          Arguments

          NameTypeOptional
          lowerbound
          upperbound
          df

          Location

          2nd, distr, DISTR, 6:tcdf(

          Description

          tcdf( is the Student's t cumulative density function. If some random variable follows this distribution, you can use this command to find the probability that this variable will fall in the interval you supply.

          Unlike normalcdf(, this command only works for the standardized distribution with mean 0 and standard deviation 1. To use it for non-standardized values you will have to standardize them by calculating (X-μ)/σ (where μ is the mean and σ the standard deviation). Do this for both lower and upper.

          Advanced

          Often, you want to find a "tail probability" - a special case for which the interval has no lower or no upper bound (the form frequently used in one-tailed tests). For example, "what is the probability x is greater than 2?". The TI-83+ has no special symbol for infinity, but you can use E99 to get a very large number that will work equally well in this case (E is the decimal exponent obtained by pressing [2nd] [EE]). Use E99 for +∞, and -E99 for -∞.

          Alternatively, you can exploit the identity

          (1) \(\begin{align} \texttt{tcdf}(-\infty,0,\nu)=\frac1{2} \end{align}\)

          (similarly for the interval from 0 to ∞)

          and thus

          (2) \(\begin{align} \texttt{tcdf}(-\infty,x,\nu)=\frac1{2}+\texttt{tcdf}(0,x,\nu) \end{align}\)

          For the form used in two-tailed tests, the following identity may be useful:

          (3) \(\begin{align} \texttt{tcdf}(-x,x,\nu)=2\texttt{tcdf}(0,x,\nu) \end{align}\)

          Formulas

          As with any other continuous distribution, tcdf( can be defined in terms of the probability density function, tpdf(:

          (4) \(\begin{align} \texttt{tcdf}(a,b,\nu)=\int_a^b \texttt{tpdf}(t,\nu)\mathrm{d}t \end{align}\)

          The function can also be expressed in terms of an incomplete beta function.

          For one degree of freedom (ν=1), tcdf( is expressible in terms of simpler functions:

          (5) \(\begin{align} \texttt{tcdf}(a,b,1)=\frac1{\pi}\left(\tan^{-1}\left(b\right)-\tan^{-1}\left(a\right)\right) \end{align}\)

          This is the so-called Cauchy distribution.

          Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, thornahawk.

          History

          Calculator OS Version Description
          TI-83 0.01013 Added
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          • FR: X²FRép(

          χ²cdf(

          Overview

          Computes the χ²distribution probability between lowerbound andupperbound for the specified degrees of freedom df.

          Availability: Token available everywhere.

          Syntax

          χ²cdf(lowerbound,upperbound,df)

          Arguments

          NameTypeOptional
          χ²
          lowerbound
          upperbound
          df

          Location

          2nd, distr, DISTR, 8:cdf(

          Description

          χ²cdf( is the χ² cumulative density function. If some random variable follows a χ² distribution, you can use this command to find the probability that this variable will fall in the interval you supply.

          The command takes three arguments. lower and upper define the interval in which you're interested. df specifies the degrees of freedom (choosing one of a family of χ² distributions).

          Advanced Uses

          Often, you want to find a "tail probability" - a special case for which the interval has no lower or no upper bound. For example, "what is the probability x is greater than 2?". The TI-83+ has no special symbol for infinity, but you can use E99 to get a very large number that will work equally well in this case (E is the decimal exponent obtained by pressing [2nd] [EE]). Use E99 for positive infinity, and -E99 for negative infinity.

          The χ²cdf( command is crucial to performing a χ² goodness of fit test, which the early TI-83 series calculators do not have a command for (the χ²-Test( command performs the χ² test of independence, which is not the same thing, although the manual always just refers to it as the "χ² Test"). This test is used to test if an observed frequency distribution differs from the expected, and can be used, for example, to tell if a coin or die is fair.

          The Goodness-of-Fit Test routine on the routines page will perform a χ² goodness of fit test for you. Or, if you have a TI-84+/SE with OS version 2.30 or higher, you can use the χ²GOF-Test( command.

          Formulas

          As with other continuous distributions, we can define χ²cdf( in forms of the probability density function:

          (1) \(\begin{align} \texttt{\chi^2cdf}(a,b,k) = \int_a^b \texttt{\chi^2pdf}(x,k)\,dx \end{align}\)

          See Also

          Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583.

          History

          Calculator OS Version Description
          TI-83 0.01013 Added
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          • FR: 𝐅FRép(

          𝐅cdf(

          Overview

          Computes the 𝐅 distribution probability between lowerboundand upperbound for the specified numerator df (degrees of freedom) and denominator df.

          Availability: Token available everywhere.

          Syntax

          𝐅cdf(lowerbound,upperbound,numerator df,denominator df)

          Arguments

          NameTypeOptional
          𝐅
          lowerbound
          upperbound
          numerator df
          denominator df

          Location

          2nd, distr, DISTR, 0:cdf(

          Description

          Examples

          Explanation 1

          code 1

          Explanation 2

          code 2

          Error Conditions

          Advanced Notes

          History

          Calculator OS Version Description
          TI-83 0.01013 Added
          Property Value
          Hex Value $BB15
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          • FR: binomfdp(

          binompdf(

          Overview

          Computes a probability at x for the discrete binomial distribution with the specified numtrials and probability p of success on each trial.

          Availability: Token available everywhere.

          Syntax

          binompdf(numtrials,p[,x])

          Arguments

          NameTypeOptional
          numtrials
          p
          xYes

          Location

          2nd, distr, DISTR, A:binompdf(

          Description

          This command is used to calculate the binomial probability. In plainer language, it solves a specific type of often-encountered probability problem, that occurs under the following conditions:

          1. A specific event has only two outcomes, which we will call "success" and "failure"
          2. This event is going to repeat a specific number of times, or "trials"
          3. Success or failure is determined randomly with the same probability of success each time the event occurs
          4. We're interested in the probability that there are exactly N successes

          For example, consider a couple that intends to have 4 children. What is the probability that 3 of them are girls?

          1. The event here is a child being born. It has two outcomes "boy" or "girl". We can call either one a success, but we'll choose to be sexist towards guys and call a girl a success in this problem
          2. The event is going to repeat 4 times, so we have 4 trials
          3. The probability of a girl being born is 50% or 1/2 each time
          4. We're interested in the probability that there are exactly 3 successes (3 girls)

          The syntax here is binompdf(trials, probability, value). In this case:

          :binompdf(4,.5,3

          This will give .25 when you run it, so there's a .25 (1/4) probability out of 4 children, 3 will be girls.

          An alternate syntax for binompdf( leaves off the last argument, value. This tells the calculator to compute a list of the results for all values. For example:

          :binompdf(4,.5

          This will come to {.0625 .25 .375 .25 .0625} when you run it. These are the probabilities of all 5 outcomes (0 through 4 girls) for 4 children with an equal probability of being born. There's a .0625 probability of no girls, a .25 probability of 1 girl, etc.

          Advanced (for programmers)

          The binompdf( and binomcdf( commands are the only ones apart from seq( that can return a list of a given length, and they do it much more quickly. It therefore makes sense, in some situations, to use these commands as substitutes for seq(.

          Here's how to do it:

          1. cumSum(binomcdf(N,0 gives the list {1 2 … N+1}, and cumSum(not(binompdf(N,0 gives the list {0 1 2 … N}.
          2. With seq(, you normally do math inside the list: for example, seq(3I2,I,0,5
          3. With these commands, you do the same math outside the list: 3Ans2 where Ans is the list {0 1 … 5}.

          An example:

          :seq(2^I,I,1,5
can be
:cumSum(binomcdf(4,0
:2^Ans
which in turn can be
:2^cumSum(binomcdf(4,0

          In general (where f() is some operation or even several operations):

          :seq(f(I),I,1,N
can be
:cumSum(binomcdf(N-1,0
:f(Ans
which can sometimes be
:f(cumSum(binomcdf(N-1,0

          If the lower bound on I in the seq( statement is 0 and not 1, you can use binompdf( instead:

          :seq(f(I),I,0,N
can be
:cumSum(not(binompdf(N,0
:f(Ans
which can sometimes be
:f(cumSum(not(binompdf(N,0

          This will not work if some command inside seq( can take only a number and not a list as an argument. For example, seq(L1(I),I,1,5 cannot be optimized this way.

          Formulas

          The value of binompdf( is given by the formula

          (1) \(\begin{align} \texttt{binompdf}(n,p,k) = \binom{n}{k}\,p^k\,(1-p)^{n-k} = \frac{n!}{k!\,(n-k)!}\,p^k\,(1-p)^{n-k} \end{align}\)

          This formula is fairly intuitive. We want to know the probability that out of n trials, exactly k will be successes, so we take the probability of k successes - \(p^k\) - multiplied by the probability of (n-k) failures - \((1-p)^{n-k}\) - multiplied by the number of ways to choose which k trials will be successes - \(\binom{n}{k}\).

          Error Conditions

          • ERR:DOMAIN is thrown if the number of trials is at least 1 000 000 (unless the other arguments make the problem trivial).
          • ERR:INVALID DIM is thrown if you try to generate a list of probabilities with at least 999 trials.

          Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583, Myles_Zadok, Timothy Foster, Trenly.

          History

          Calculator OS Version Description
          TI-83 0.01013 Added
          Property Value
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          • FR: binomFRép(

          binomcdf(

          Overview

          Computes a cumulative probability at x for the discrete binomial distribution with the specified numtrials and probability p of success on each trial.

          Availability: Token available everywhere.

          Syntax

          binomcdf(numtrials,p[,x])

          Arguments

          NameTypeOptional
          numtrials
          p
          xYes

          Location

          2nd, distr, DISTR, B:binomcdf(

          Description

          This command is used to calculate the binomial cumulative probability function. In plainer language, it solves a specific type of often-encountered probability problem, that occurs under the following conditions:

          1. A specific event has only two outcomes, which we will call "success" and "failure"
          2. This event is going to repeat a specific number of times, or "trials"
          3. Success or failure is determined randomly with the same probability of success each time the event occurs
          4. We're interested in the probability that there are at most N successes

          For example, consider a couple that intends to have 4 children. What is the probability that at most 2 are girls?

          1. The event here is a child being born. It has two outcomes "boy" or "girl". In this case, since the question is about girls, it's easier to call "girl" a success.
          2. The event is going to repeat 4 times, so we have 4 trials
          3. The probability of a girl being born is 50% or 1/2 each time
          4. We're interested in the probability that there are at most 2 successes (2 girls)

          The syntax here is binomcdf(trials, probability, value). In this case:

          :binomcdf(4,.5,2

          This will give .6875 when you run it, so there's a .6875 probability out of 4 children, at most 2 will be girls.

          An alternate syntax for binomcdf( leaves off the last argument, value. This tells the calculator to compute a list of the results for all values. For example:

          :binomcdf(4,.5

          This will come to {.0625 .3125 .6875 .9375 1} when you run it. These are all the probabilities we get when you replace "at most 2 girls" with "at most 0", "at most 1", etc. Here, .0625 is the probability of "at most 0" girls (or just 0 girls), .3125 is the probability of at most 1 girl (1 or 0 girls), etc.

          Several other probability problems actually are the same as this one. For example, "less than N" girls, just means "at most N-1" girls. "At least N" girls means "at most (total-N)" boys (here we switch our definition of what a success is). "No more than", of course, means the same as "at most".

          Advanced (for programmers)

          The binompdf( and binomcdf( commands are the only ones apart from seq( that can return a list of a given length, and they do it much more quickly. It therefore makes sense, in some situations, to use these commands as substitutes for seq(.

          Here's how to do it:

          1. cumSum(binomcdf(N,0 gives the list {1 2 … N+1}, and cumSum(not(binompdf(N,0 gives the list {0 1 2 … N}.
          2. With seq(, you normally do math inside the list: seq(3I2,I,0,5
          3. With these commands, you do the same math outside the list: 3Ans2 where Ans is the list {0 1 … 5}.
          :seq(2^I,I,1,5
can be
:cumSum(binomcdf(4,0
:2^Ans
which in turn can be
:2^cumSum(binomcdf(4,0

          In general (where f() is some operation or even several operations):

          :seq(f(I),I,1,N
can be
:cumSum(binomcdf(N-1,0
:f(Ans
which can sometimes be
:f(cumSum(binomcdf(N-1,0

          If the lower bound on I in the seq( statement is 0 and not 1, you can use binompdf( instead:

          :seq(f(I),I,0,N
can be
:cumSum(not(binompdf(N,0
:f(Ans
which can sometimes be
:f(cumSum(not(binompdf(N,0

          This will not work if some command inside seq( can take only a number and not a list as an argument. For example, seq(L1(I),I,1,5 cannot be optimized this way.

          Formulas

          Since "at most N" is equivalent to "0 or 1 or 2 or 3 or … N", and since we can combine these probabilities by adding them, we can come up with an expression for binomcdf( by adding up values of binompdf(:

          (1) \(\begin{align} \texttt{binomcdf}(n,p,k) = \sum_{i=0}^{k}\texttt{binompdf}(n,p,i) = \sum_{i=0}^{k}\binom{n}{i}\,p^i\,(1-p)^{n-i} \end{align}\)

          (If you're not familiar with sigma notation, \(\sum_{i=0}^{k}\) just means "add the following up for each value of i 0 through k")

          Error Conditions

          • ERR:DATATYPE is thrown if you try to generate a list of probabilities with p equal to 0 or 1, and at least 257 trials.
          • ERR:DOMAIN is thrown if the number of trials is at least 1 000 000 (unless the other arguments make the problem trivial).
          • ERR:INVALID DIM is thrown if you try to generate a list of probabilities with at least 999 trials.

          Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583, Myles_Zadok, Timothy Foster, Trenly.

          History

          Calculator OS Version Description
          TI-83 0.01013 Added
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          • FR: poissonFdp(

          poissonpdf(

          Overview

          Computes a probability at x for the discrete Poisson distribution with the specified mean μ.

          Availability: Token available everywhere.

          Syntax

          poissonpdf(μ,x)

          Arguments

          NameTypeOptional
          μ
          x

          Location

          2nd, distr, DISTR, C:poissonpdf(

          Description

          This command is used to calculate Poisson distribution probability. In plainer language, it solves a specific type of often-encountered probability problem, that occurs under the following conditions:

          1. A specific event happens at a known average rate (X occurrences per time interval)
          2. Each occurrence is independent of the time since the last occurrence
          3. We're interested in the probability that the event occurs a specific number of times in a given time.

          The poissonpdf( command takes two arguments: The mean is the average number of times the event will happen during the time interval we're interested in. The value is the number of times we're interested in the event happening (so the output is the probability that the event happens value times in the interval).

          For example, consider point on a city street where an average of 5 cars pass by each minute. What is the probability that in a given minute, 8 cars will drive by?

          1. The event is a car passing by, which happens at an average rate of 5 occurrences per time interval (a minute)
          2. Each occurrence is independent of the time since the last occurrence (we'll assume this is true, though traffic might imply a correlation here)
          3. We're interested in the probability that the event occurs 8 times in the time interval

          The syntax in this case is:

          :poissonpdf(5,8

          This will give about .065 when you run it, so there's a .065 probability that in a given minute, 8 cars will drive by.

          Formulas

          The value of poissonpdf( is given by the formula

          (1) \(\begin{align} \texttt{poissonpdf}(\lambda,k) = \frac{e^{-\lambda}\lambda^k}{k!} \end{align}\)

          Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583.

          History

          Calculator OS Version Description
          TI-83 0.01013 Added
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          Hex Value $BB18
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          • FR: poissonFRép(

          poissoncdf(

          Overview

          Computes a cumulative probability at x for the discrete Poisson distribution with specified mean μ.

          Availability: Token available everywhere.

          Syntax

          poissoncdf(μ,x)

          Arguments

          NameTypeOptional
          μ
          x

          Location

          2nd, distr, DISTR, D:poissoncdf(

          Description

          This command is used to calculate Poisson distribution cumulative probability. In plainer language, it solves a specific type of often-encountered probability problem, that occurs under the following conditions:

          1. A specific event happens at a known average rate (X occurrences per time interval)
          2. Each occurrence is independent of the time since the last occurrence
          3. We're interested in the probability that the event occurs at most a specific number of times in a given time interval.

          The poissoncdf( command takes two arguments: The mean is the average number of times the event will happen during the time interval we're interested in. The value is the number of times we're interested in the event happening (so the output is the probability that the event happens at most value times in the interval). Note that you may need to convert the mean so that the time intervals in both cases match up. This is done by a simple proportion: if the event happens 10 times per minute, it happens 20 times per two minutes.

          For example, consider point on a city street where an average of 5 cars pass by each minute. What is the probability that in a given minute, no more than 3 cars will drive by?

          1. The event is a car passing by, which happens at an average rate of 5 occurences per time interval (a minute)
          2. Each occurrence is independent of the time since the last occurrence (we'll assume this is true, though traffic might imply a correlation here)
          3. We're interested in the probability that the event occurs at most 3 times in the time interval.

          The syntax in this case is:

          :poissoncdf(5,3

          This will give about .265 when you run it, so there's a .265 probability that in a given minute, no more than 3 cars will drive by.

          Formulas

          The poissoncdf( command can be seen as a sum of poissonpdf( commands:

          (1) \(\begin{align} \texttt{poissoncdf}(\lambda,k)=\sum_{i=0}^k \texttt{poissonpdf}(\lambda,i) = \sum_{i=0}^k \frac {e^{-\lambda} \lambda^i}{i!} \end{align}\)

          We can also write the poissoncdf( command in terms of the incomplete gamma function:

          (2) \(\begin{align} \texttt{poissoncdf}(\lambda,k)=\frac{\Gamma(k+1,\lambda)}{k!} \end{align}\)

          Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583.

          History

          Calculator OS Version Description
          TI-83 0.01013 Added
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          • FR: géomtFdp(

          geometpdf(

          Overview

          Computes a probability at x, the number of the trial on which the first success occurs, for the discrete geometric distribution with the specified probability of success p.

          Availability: Token available everywhere.

          Syntax

          geometpdf(p,x)

          Arguments

          NameTypeOptional
          p
          x

          Location

          2nd, distr, DISTR, E:geometpdf(

          Description

          This command is used to calculate geometric probability. In plainer language, it solves a specific type of often-encountered probability problem, that occurs under the following conditions:

          1. A specific event has only two outcomes, which we will call "success" and "failure"
          2. The event is going to keep happening until a success occurs
          3. Success or failure is determined randomly with the same probability of success each time the event occurs
          4. We're interested in the probability that it takes a specific amount of trials to get a success.

          For example, consider a basketball player that always makes a shot with 1/3 probability. He will keep throwing the ball until he makes a shot. What is the probability that it takes him 3 shots?

          1. The event here is throwing the ball. A "success", obviously, is making the shot, and a "failure" is missing.
          2. The event is going to happen until he makes the shot: a success.
          3. The probability of a success - making a shot - is 1/3
          4. We're interested in the probability that it takes 3 trials to get a success

          The syntax here is geometpdf(probability, trials). In this case:

          :geometpdf(1/3,3

          This will give about .148 when you run it, so there's a .148 probability that it will take him 3 shots until he makes one (he'll make it on the 3rd try).

          Formulas

          The value of geometpdf( is given by the formula

          (1) \(\begin{align} \texttt{geometpdf}(p,n) = p(1-p)^{n-1} \end{align}\)

          This formula can be intuitively understood: the probability that the first success is the nth trial is the probability of getting a success - \(p\) - times the probability of missing it the first n-1 times - \((1-p)^{n-1}\).

          For the trivial value of n=0, however, the above formula gives the incorrect value of 1. It should actually be 0, since the first success can never be the 0th trial. However, since you're not likely to ever be interested in this probability, this drawback doesn't really matter.

          Source: parts of this page were written by the following TI|BD contributors: burr, CloudVariable, DarkerLine, GoVegan, kg583, Timothy Foster, Trenly.

          History

          Calculator OS Version Description
          TI-83 0.01013 Added
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          • FR: géomtFRép(

          geometcdf(

          Overview

          Computes a cumulative probability at x, the number of the trial on which the first success occurs, for the discrete geometric distribution with the specified probability of success p.

          Availability: Token available everywhere.

          Syntax

          geometcdf(p,x)

          Arguments

          NameTypeOptional
          p
          x

          Location

          2nd, distr, DISTR, F:geometcdf(

          Description

          This command is used to calculate cumulative geometric probability. In plainer language, it solves a specific type of often-encountered probability problem, that occurs under the following conditions:

          1. A specific event has only two outcomes, which we will call "success" and "failure"
          2. The event is going to keep happening until a success occurs
          3. Success or failure is determined randomly with the same probability of success each time the event occurs
          4. We're interested in the probability that it takes at most a specific amount of trials to get a success.

          For example, consider a basketball player that always makes a shot with 1/4 probability. He will keep throwing the ball until he makes a shot. What is the probability that it takes him no more than 4 shots?

          1. The event here is throwing the ball. A "success", obviously, is making the shot, and a "failure" is missing.
          2. The event is going to happen until he makes the shot: a success.
          3. The probability of a success - making a shot - is 1/4
          4. We're interested in the probability that it takes at most 4 trials to get a success

          The syntax here is geometcdf(probability, trials). In this case:

          :geometcdf(1/4,4

          This will give about .684 when you run it, so there's a .684 probability that he'll make a shot within 4 throws.

          Note the relationship between geometpdf( and geometcdf(. Since geometpdf( is the probability it will take exactly N trials, we can write that geometcdf(1/4,4) = geometpdf(1/4,1) + geometpdf(1/4,2) + geometpdf(1/4,3) + geometpdf(1/4,4).

          Formulas

          Going off of the relationship between geometpdf( and geometcdf(, we can write a formula for geometcdf( in terms of geometpdf(:

          (1) \(\begin{align} \texttt{geometcdf}(p,n) = \sum_{i=1}^{n} \texttt{geometpdf}(p,i) = \sum_{i=1}^{n} p\,(1-p)^{i-1} \end{align}\)

          (If you're unfamiliar with sigma notation, \(\sum_{i=1}^{n}\) just means "add up the following for all values of i from 1 to n")

          However, we can take a shortcut to arrive at a much simpler expression for geometcdf(. Consider the opposite probability to the one we're interested in, the probability that it will not take "at most N trials", that is, the probability that it will take more than N trials. This means that the first N trials are failures. So geometcdf(p,N) = (1 - "probability that the first N trials are failures"), or:

          (2) \(\begin{align} \texttt{geometcdf}(p,n) = 1-(1-p)^n \end{align}\)

          Source: parts of this page were written by the following TI|BD contributors: burr, CloudVariable, DarkerLine, GoVegan, Joe_Young, kg583, Timothy Foster, Weregoose.

          History

          Calculator OS Version Description
          TI-83 0.01013 Added
          Property Value
          Hex Value $BB1B
          Categories
          Localizations
          • FR: normalFdp(

          normalpdf(

          Overview

          Computes the probability density function for the normal distribution at a specified x value for the specified μ and σ.

          Availability: Token available everywhere.

          Syntax

          normalpdf(x[,μ,σ])

          Arguments

          NameTypeOptional
          x
          μYes
          σYes

          Location

          2nd, distr, DISTR, 1:normalpdf(

          Description

          normalpdf( is the normal (Gaussian) probability density function.

          Since the normal distribution is continuous, the value of normalpdf( doesn't represent an actual probability - in fact, one of the only uses for this command is to draw a graph of the normal curve. You could also use it for various calculus purposes, such as finding inflection points.

          The command can be used in two ways: normalpdf(x) will evaluate the standard normal p.d.f. (with mean at 0 and a standard deviation of 1) at x, and normalpdf(x,μ,σ) will work for an arbitrary normal curve, with mean μ and standard deviation σ.

          Formulas

          For the standard normal distribution, normalpdf(x) is defined as

          (1) \(\begin{align} \texttt{normalpdf}(x)=\frac1{\sqrt{2\pi\,}} \, e^{-\frac1{2}x^2} \end{align}\)

          For other normal distributions, normalpdf( is defined in terms of the standard distribution:

          (2) \(\begin{align} \texttt{normalpdf}(x,\mu,\sigma)=\frac{1}{\sigma} \, \texttt{normalpdf} \left(\frac{x-\mu}{\sigma}\right) \end{align}\)

          Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, thornahawk.

          History

          Calculator OS Version Description
          TI-83 0.01013 Added
          Property Value
          Hex Value $BB1C
          Categories
          Localizations
          • FR: StudentFdp(

          tpdf(

          Overview

          Computes the probability density function (pdf) for the Student-t distribution at a specified x value with specified degrees of freedom df.

          Availability: Token available everywhere.

          Syntax

          tpdf(x,df)

          Arguments

          NameTypeOptional
          x
          df

          Location

          2nd, distr, DISTR, 5:tpdf(

          Description

          tpdf( is the Student's t probability density function.

          Since the t distribution is continuous, the value of tpdf( doesn't represent an actual probability — in fact, one of the few uses for this command is to draw a graph of the bell curve. You could also use it for various calculus purposes, such as finding inflection points.

          The command takes two arguments: the first is the value where the PDF is to be evaluated, and the second is the number of degrees of freedom (so the calculator knows which t distribution to use). As the degrees of freedom increases without bound, tpdf( approaches normalpdf(; i.e.

          (1) \(\begin{align} \lim_{\nu\rightarrow\infty}\texttt{tpdf}(x,\nu)=\texttt{normalpdf}(x) \end{align}\)

          Formulas

          The value of tpdf( is given by

          (2) \(\begin{align} \texttt{tpdf}(t,\nu) = \frac{\Gamma((\nu+1)/2)}{\sqrt{\nu\pi}\,\Gamma(\nu/2)}\,\left(1+\frac{t^2}{\nu}\right)^{-\frac1{2}(\nu+1)} \end{align}\)

          (where Γ is the gamma function), or alternatively

          (3) \(\begin{align} \texttt{tpdf}(t,\nu) = \frac1{\sqrt{\nu}B(\nu/2,1/2)}\,\left(1+\frac{t^2}{\nu}\right)^{-\frac1{2}(\nu+1)} \end{align}\)

          (where B is the beta function)

          Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583, thornahawk.

          History

          Calculator OS Version Description
          TI-83 0.01013 Added
          Property Value
          Hex Value $BB1D
          Categories
          Localizations
          • FR: Χ²Fdp(

          χ²pdf(

          Overview

          Computes the probability density function (pdf) for the χ² distribution at a specified x value for the specified degrees of freedom df.

          Availability: Token available everywhere.

          Syntax

          χ²pdf(x,df)

          Arguments

          NameTypeOptional
          χ²
          x
          df

          Location

          2nd, distr, DISTR, 7:pdf(

          Description

          χ²pdf( is the χ² probability density function.

          Since the χ² distribution is continuous, the value of χ²pdf( doesn't represent an actual probability — in fact, one of the only uses for this command is to draw a graph of the χ² curve. You could also use it for various calculus purposes, such as finding inflection points.

          The command takes two arguments: the value at which to evaluate the p.d.f., and df, the number of 'degrees of freedom'.

          Formulas

          The value of χ²pdf( is given by

          (1) \(\begin{align} \texttt{\chi^2pdf}(x,k)=\frac{(1/2)^{k/2}}{(k/2-1)!}\,x^{k/2-1}e^{-x/2} \end{align}\)

          Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583.

          History

          Calculator OS Version Description
          TI-83 0.01013 Added
          Property Value
          Hex Value $BB1E
          Categories
          Localizations
          • FR: 𝐅fdp(

          𝐅pdf(

          Overview

          Computes the 𝐅 distribution probability between lowerboundand upperbound for the specified numerator df (degrees of freedom) and denominator df.

          Availability: Token available everywhere.

          Syntax

          𝐅pdf(x,numerator df,denominator df)

          Arguments

          NameTypeOptional
          𝐅
          x
          numerator df
          denominator df

          Location

          2nd, distr, DISTR, 9:pdf(

          Description

          Fpdf( is the F-distribution probability density function.

          Since the F-distribution is continuous, the value of Fpdf( doesn't represent an actual probability - in fact, one of the only uses for this command is to draw a graph of the distribution. You could also use it for various calculus purposes, such as finding inflection points.

          The command takes 3 arguments: x is the point at which to evaluate the function (when graphing, use X for this argument), numerator df and denominator df are the numerator degrees of freedom and denominator degrees of freedom respectively (these specify a single Fpdf( curve out of an infinite family).

          The F-distribution is used mainly in significance tests of variance.

          Formulas

          The value of the Fpdf( is given by

          (1) \(\begin{align} \texttt{Fpdf}(x,d_1,d_2) = \frac{\left( \frac{d_1x}{d_1x+d_2} \right)^{d_1/2} \left(1-\frac{d_1x}{d_1x+d_2}\right)^{d_2/2}}{x \texttt{B}(d_1/2,d_2/2)} \end{align}\)

          where B(x,y) is the Beta function.

          Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583.

          History

          Calculator OS Version Description
          TI-83 0.01013 Added
          Property Value
          Hex Value $BB1F
          Categories
          Localizations
          • FR: normAléat(

          randNorm(

          Overview

          Generates and displays a random real number from a specified Normal distribution specified by μ and σ for a specified number of trials numtrials.

          Availability: Token available everywhere.

          Syntax

          randNorm(μ,σ[,numtrials])

          Arguments

          NameTypeOptional
          μ
          σ
          numtrials

          Location

          math, PRB, 6:randNorm(

          Description

          randNorm(µ,σ) generates a normally-distributed pseudorandom number with mean µ and standard deviation σ. The result returned will most probably be within the range µ±3_σ_. randNorm(µ,σ,n) generates a list of n normally-distributed pseudorandom numbers with mean µ and standard deviation σ.

          seed→rand affects the output of randNorm(.

          0→rand
     0
randNorm(0,1)
     -1.585709623
randNorm(0,1,3)
     {-1.330473604 1.05074514 -.0368606663}

          Although a theoretical normally distributed variable could take on any real value, numbers on a calculator have a limited precision, which leads to a maximum range of approximately µ±7.02_σ_ for values of randNorm(.

          Optimization

          When the mean is 0 and the standard deviation 1, invNorm(rand) and invNorm(rand(N)) save space over randNorm(0,1) and randNorm(0,1,N) respectively.

          Formulas

          The value of randNorm( for a given seed can be expressed in terms of rand:

          randNorm(µ,σ)=µ-σinvNorm(rand

          This is identical to the output of randNorm( in the sense that for the same seed, both expressions will generate the same random numbers.

          The following formula can be used to get a target interval where A and B are two real intervals.

          µ=(A+B)/2
σ=(-A+B)/6

          Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, MrTanookiMario, Silver Phantom, Timothy Foster, Weregoose.

          History

          Calculator OS Version Description
          TI-83 0.01013 Added
          Property Value
          Hex Value $BB20
          Categories
          Localizations
          • FR: tvm_Pmt

          tvm_Pmt

          Overview

          Computes the amount of each payment.

          Comment:pre-CE french was vatPmt

          Availability: Token available everywhere.

          Syntax

          tvm_Pmt[(𝗡,I%,PV,FV,P/Y,C/Y)]

          Arguments

          NameTypeOptional
          𝗡Yes
          I%Yes
          PVYes
          FVYes
          P/YYes
          C/YYes

          Location

          apps, 1:Finance, CALC, 2:tvm_Pmt

          Description

          The tvm__VAR_ commands use the TVM (Time Value of Money) solver to solve for the variable VAR. They're usually used in programs, since outside a program it's easier to use the interactive solver (the first option in the finance menu).

          All five commands can be used by themselves, with no arguments. In that case, they will return the value of VAR solved from the current values of the other finance variables.

          If you give them arguments, the values you give will replace the values of the finance variables. You can supply as many or as few arguments as needed, and the finance variables will be replaced in the order: N, I%, PV, PMT, FV, P/Y, C/Y (skipping the one you're solving for).

          Error Conditions

          • ERR:ITERATIONS is thrown if the maximum amount of iterations was exceeded in computing I% (this usually means there is no solution)
          • ERR:NO SIGN CHG is thrown if calculating I% when FV, (N*PMT), and PV all have the same sign.

          Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, J_Walker87.

          History

          Calculator OS Version Description
          TI-83 0.01013 Added
          Property Value
          Hex Value $BB21
          Categories
          Localizations
          • FR: tvm_I%

          tvm_I%

          Overview

          Computes the annual interest rate.

          Comment:pre-CE french was vat_I

          Availability: Token available everywhere.

          Syntax

          tvm_I%[(𝗡,PV,PMT,FV,P/Y,C/Y)]

          Arguments

          NameTypeOptional
          I%Yes
          𝗡Yes
          PVYes
          PMTYes
          FVYes
          P/YYes
          C/YYes

          Location

          apps, 1:Finance, CALC, 3:tvm_

          Description

          The tvm__VAR_ commands use the TVM (Time Value of Money) solver to solve for the variable VAR. They're usually used in programs, since outside a program it's easier to use the interactive solver (the first option in the finance menu).

          All five commands can be used by themselves, with no arguments. In that case, they will return the value of VAR solved from the current values of the other finance variables.

          If you give them arguments, the values you give will replace the values of the finance variables. You can supply as many or as few arguments as needed, and the finance variables will be replaced in the order: N, I%, PV, PMT, FV, P/Y, C/Y (skipping the one you're solving for).

          Error Conditions

          • ERR:ITERATIONS is thrown if the maximum amount of iterations was exceeded in computing I% (this usually means there is no solution)
          • ERR:NO SIGN CHG is thrown if calculating I% when FV, (N*PMT), and PV all have the same sign.

          Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, J_Walker87.

          History

          Calculator OS Version Description
          TI-83 0.01013 Added
          Property Value
          Hex Value $BB22
          Categories
          Localizations
          • FR: tvm_VA

          tvm_PV

          Overview

          Computes the present value.

          Comment:pre-CE french was vat_Vact

          Availability: Token available everywhere.

          Syntax

          tvm_PV[(𝗡,I%,PMT,FV,P/Y,C/Y)]

          Arguments

          NameTypeOptional
          𝗡Yes
          I%Yes
          PMTYes
          FVYes
          P/YYes
          C/YYes

          Location

          apps, 1:Finance, CALC, 4:tvm_PV

          Description

          The tvm__VAR_ commands use the TVM (Time Value of Money) solver to solve for the variable VAR. They're usually used in programs, since outside a program it's easier to use the interactive solver (the first option in the finance menu).

          All five commands can be used by themselves, with no arguments. In that case, they will return the value of VAR solved from the current values of the other finance variables.

          If you give them arguments, the values you give will replace the values of the finance variables. You can supply as many or as few arguments as needed, and the finance variables will be replaced in the order: N, I%, PV, PMT, FV, P/Y, C/Y (skipping the one you're solving for).

          Error Conditions

          • ERR:ITERATIONS is thrown if the maximum amount of iterations was exceeded in computing I% (this usually means there is no solution)
          • ERR:NO SIGN CHG is thrown if calculating I% when FV, (N*PMT), and PV all have the same sign.

          Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, J_Walker87.

          History

          Calculator OS Version Description
          TI-83 0.01013 Added
          Property Value
          Hex Value $BB23
          Categories
          Localizations
          • FR: tvm_𝗡

          tvm_𝗡

          Overview

          Computes the number of payment periods.

          Comment:pre-CE french was vat_𝗡

          Availability: Token available everywhere.

          Syntax

          tvm_𝗡[(I%,PV,PMT,FV,P/Y,C/Y)]

          Arguments

          NameTypeOptional
          𝗡Yes
          I%Yes
          PVYes
          PMTYes
          FVYes
          P/YYes
          C/YYes

          Location

          apps, 1:Finance, CALC, 5:tvm_

          Description

          The tvm__VAR_ commands use the TVM (Time Value of Money) solver to solve for the variable VAR. They're usually used in programs, since outside a program it's easier to use the interactive solver (the first option in the finance menu).

          All five commands can be used by themselves, with no arguments. In that case, they will return the value of VAR solved from the current values of the other finance variables.

          If you give them arguments, the values you give will replace the values of the finance variables. You can supply as many or as few arguments as needed, and the finance variables will be replaced in the order: N, I%, PV, PMT, FV, P/Y, C/Y (skipping the one you're solving for).

          Error Conditions

          • ERR:ITERATIONS is thrown if the maximum amount of iterations was exceeded in computing I% (this usually means there is no solution)
          • ERR:NO SIGN CHG is thrown if calculating I% when FV, (N*PMT), and PV all have the same sign.

          Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, J_Walker87.

          History

          Calculator OS Version Description
          TI-83 0.01013 Added
          Property Value
          Hex Value $BB24
          Categories
          Localizations
          • FR: tvm_VAC

          tvm_FV

          Overview

          Computes the future value.

          Comment:pre-CE french was vat_vacq

          Availability: Token available everywhere.

          Syntax

          tvm_FV[(𝗡,I%,PV,PMT,P/Y,C/Y)]

          Arguments

          NameTypeOptional
          𝗡Yes
          I%Yes
          PVYes
          PMTYes
          P/YYes
          C/YYes

          Location

          apps, 1:Finance, CALC, 6:tvm_FV

          Description

          The tvm__VAR_ commands use the TVM (Time Value of Money) solver to solve for the variable VAR. They're usually used in programs, since outside a program it's easier to use the interactive solver (the first option in the finance menu).

          All five commands can be used by themselves, with no arguments. In that case, they will return the value of VAR solved from the current values of the other finance variables.

          If you give them arguments, the values you give will replace the values of the finance variables. You can supply as many or as few arguments as needed, and the finance variables will be replaced in the order: N, I%, PV, PMT, FV, P/Y, C/Y (skipping the one you're solving for).

          Error Conditions

          • ERR:ITERATIONS is thrown if the maximum amount of iterations was exceeded in computing I% (this usually means there is no solution)
          • ERR:NO SIGN CHG is thrown if calculating I% when FV, (N*PMT), and PV all have the same sign.

          Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, J_Walker87.

          History

          Calculator OS Version Description
          TI-83 0.01013 Added
          Property Value
          Hex Value $BB25
          Categories
          Localizations
          • FR: conj(

          conj(

          Overview

          Returns the complex conjugate of a complex number or list of complex numbers.

          Availability: Token available everywhere.

          Syntax

          conj(value)

          Arguments

          NameTypeOptional
          valuecomplex|complex[]

          Location

          math, CMPLX, 1:conj(

          Description

          conj(z) returns the complex conjugate of the complex number z. If z is represented as x+i_y_ where x and y are both real, conj(z) returns x-i_y_. Also works on a list of complex numbers.

          conj(3+4i)
     3-4i

          The conjugate of a number \(z\) is often written \(\overline{z}\), and is useful because it has the property that \(z\overline{z}\) and \(z+\overline{z}\) are real numbers.

          Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583.

          History

          Calculator OS Version Description
          TI-83 0.01013 Added
          Property Value
          Hex Value $BB26
          Categories
          Localizations
          • FR: reel(

          real(

          Overview

          Returns the real part of a complex number or list of complex numbers.

          Availability: Token available everywhere.

          Syntax

          real(value)

          Arguments

          NameTypeOptional
          valuecomplex|complex[]

          Location

          math, CPLX, 2:real(

          Description

          real(z) returns the real part of the complex number z. If z is represented as x+i_y_ where x and y are both real, real(z) returns x. Also works on a list of complex numbers.

          real(3+4i)
     3

          Advanced Uses

          The real( command is expanded by several assembly libraries (such as xLIB and Omnicalc) to call their own routines. If xLib is installed, then real( will no longer work as intended even in programs that want to use it for its intended purpose.

          If you actually want to take the real part of a complex number, and want the program to work with one of these assembly libraries, you could use the imag( command instead - real(Z) is equivalent to imag(Z𝑖). Alternatively, you could tell people using your program to uninstall xLIB or Omnicalc first.

          If a program you downloaded has an error and 2:Goto takes you to a line with real( and a bunch of arguments, this is probably because the program uses Omnicalc or xLIB which you don't have installed.

          See Also

          Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

          History

          Calculator OS Version Description
          TI-83 0.01013 Added
          Property Value
          Hex Value $BB27
          Categories
          Localizations
          • FR: imag(

          imag(

          Overview

          Returns the imaginary (non-real) part of a complex number or list of complex numbers.

          Availability: Token available everywhere.

          Syntax

          imag(value)

          Arguments

          NameTypeOptional
          valuecomplex|complex[]

          Location

          math, CMPLX, 3:imag(

          Description

          imag(z) returns the imaginary part of the complex number z. If z is represented as x+i_y_ where x and y are both real, imag(z) returns y. Also works on a list of complex numbers.

          imag(3+4i)
     4

imag({3+4i,-2i,17})
     {4,-2,0}

          Source: parts of this page were written by the following TI|BD contributors: alexrudd, DarkerLine, GoVegan, kg583, Weregoose.

          History

          Calculator OS Version Description
          TI-83 0.01013 Added
          Property Value
          Hex Value $BB28
          Categories
          Localizations
          • FR: argument(

          angle(

          Overview

          Returns the polar angle of a complex number or list of complex numbers.

          Availability: Token available everywhere.

          Syntax

          angle(value)

          Arguments

          NameTypeOptional
          valuecomplex|complex[]

          Location

          math, CMPLX, 4:angle(

          Description

          angle(z) returns the complex argument (also known as the polar angle) of the complex number z. If z is represented as x+i_y_ where x and y are both real, angle(z) returns R►Pθ(x,y) (which is equivalent to tanֿ¹(y__/x) if x is nonzero). Also works on a list of complex numbers.

          angle(3+4i)
     .927295218
R►Pθ(3,4)
     .927295218

          When writing a complex number z in the form \(re^{i\theta}\) (or, equivalently, \(r(\cos\theta+i\sin\theta)\)), then \(\theta\) is equal to the value of angle(z), suitably reduced so that the result returned is in the interval \(-\pi<\theta\leq\pi\).

          The angle( command also works on matrices, though not in any useful way: angle([A] will return a matrix of the same size as [A], but with all elements 0. If you plan to use this, don't: 0[A] does the same thing, but is smaller and not as questionable (because this behavior is clearly unintentional on TI's part, and may be changed in an OS update).

          Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583, Myles_Zadok, thornahawk, Trenly.

          History

          Calculator OS Version Description
          TI-83 0.01013 Added
          Property Value
          Hex Value $BB29
          Categories
          Localizations
          • FR: somCum(

          cumSum(

          Overview

          Returns a list of the cumulative sums of the elements in list, starting with the first element.

          Availability: Token available everywhere.

          Syntax

          cumSum(list)

          Arguments

          NameTypeOptional
          listlist

          Location

          2nd, list, OPS, 6:cumSum(

          Overview

          Returns a matrix of the cumulative sums of matrix elements. Each element in the returned matrix is a cumulative sum of a matrix column from top to bottom.

          Availability: Token available everywhere.

          Syntax

          cumSum(matrix)

          Arguments

          NameTypeOptional
          matrixmatrix

          Location

          2nd, matrix, MATH, 0:cumSum(

          Description

          cumSum( calculates the cumulative sums of a list, or of the columns of a matrix, and outputs them in a new list or matrix variable.

          For a list, this means that the Nth element of the result is the sum of the first N elements of the list:

          cumSum({1,3,5,7,9})
    {1 4 9 16 25}

          For a matrix, cumSum( is applied to each column in the same way as it would be for a list (but numbers in different columns are never added):

          [[0,1,1][0,1,3][0,1,5][0,1,7]]
    [[0 1 1]
     [0 1 3]
     [0 1 5]
     [0 1 7]]
cumSum(Ans)
    [[0 1 1]
     [0 2 4]
     [0 3 9]
     [0 4 16]]

          Advanced Uses

          The ΔList( command is very nearly the inverse of the cumSum( command - it calculates the differences between consecutive elements. For any list, ΔList(cumSum(list)) will return the same list, but without its first element:

          ΔList(cumSum({1,2,3,4,5,6,7}))
    {2 3 4 5 6 7}

          Removing the first element would otherwise be a difficult procedure involving the seq( command, so this is a useful trick to know.

          For a matrix, if you want to sum up the rows instead of the columns, use the T (transpose) command.

          Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Myles_Zadok.

          History

          Calculator OS Version Description
          TI-83 0.01013 Added
          Property Value
          Hex Value $BB2A
          Categories
          Localizations
          • FR: expr(

          expr(

          Overview

          Converts the character string contained in string to an expression and executes the expression. string can be a string or a string variable.

          Availability: Token only available from within the Basic editor.

          Syntax

          expr(string)

          Arguments

          NameTypeOptional
          stringstring

          Location

          prgm

          Description

          The expr( command is used to evaluate an expression that's stored in a string (an expression is merely anything that returns a value - of any type). Expressions are occasionally stored to strings, rather than evaluated outright, so that their value has the capacity to change when the variables stored inside them change. The expr( command's result depends on the kind of expression that's in the string you pass it — it may return a number, a list, a matrix, or even another string.

          As a special case of an expression, the expr( command can also be used to convert a string like "123" to the number 123. Going in the reverse direction (123 to "123") is more complicated.

          The expr( command has limitations. Here are the situations in which expr( will not work:

          • When the code in the string does not return an answer, and thus is not an expression: e.g. expr("Line(0,0,1,1" or expr("prgmHELLO" is invalid

          • When the expression in the string contains an expr( command itself, e.g. expr("expr(Str1" — this will throw an ERR:ILLEGAL NEST error.

          • In place of a variable (rather than an expression), e.g. 5→expr("X" isn't a substitute for 5→X because expr("X" evaluates to the value of X and not to X itself.

          Advanced Usage with Lists

          expr( is often used in conjunction with the Input command to prompt the user to enter a list. Although the Input command can already handle lists, it requires the user to enter the opening bracket that signifies a list. With expr(, this can be avoided.

          If you want the user to enter a list separated by commas, instead of:

          Input L₁

          Use this:

          Input Str1
expr("{"+Str1→L₁

          This will automatically put the curly bracket in so the user does not have to.

          Just be aware that you cannot access individual list items directly after the expr() function, unlike how you can with Ans. The following code will multiply the entire list by 2 rather than return the second item:

          expr("{1,2}")(2)

          Instead, to access the second item in the list you could split this across two lines and use Ans:

          expr("{1,2}")
Ans(2)

          Optimization

          Evaluating an expression inside a string is more complicated than evaluating a normal expression; you should therefore try to take as much out of an expr( statement as possible to speed up your code. For example:

          expr("sum({"+Str1

          can be:

          sum(expr("{"+Str1

          Error Conditions

          • ERR:ILLEGAL NEST is thrown when the string to be evaluated contains an expr( itself.
          • ERR:INVALID is thrown when trying to evaluate the empty string.
          • ERR:SYNTAX is thrown when trying to evaluate a command that doesn't return a value.

          Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

          History

          Calculator OS Version Description
          TI-83 0.01013 Added
          Property Value
          Hex Value $BB2B
          Categories
          Localizations
          • FR: longueur(

          length(

          Overview

          Returns the number of characters in string.

          Availability: Token available everywhere.

          Syntax

          length(string)

          Arguments

          NameTypeOptional
          stringstring

          Location

          2nd, catalog, length(

          Description

          This command is used to determine the length of a string. Unlike the dim( command for lists and matrices, it cannot be used to change this length, as there is no null character for strings (the null value is 0 for lists and matrices).

          :length("HELLO
    5

          Keep in mind that the length is measured in the number of tokens, and not the number of letters in the string. For example, although the sin( command contains 4 characters ("s", "i", "n", and "("), it will only add 1 to the total length of a string it's in. The execution time for length( is directly proportional to the length of the string.

          Advanced Uses

          The code for looping over each character (technically, each token) of a string involves length(:

          :For(N,1,length(Str1
...
use sub(Str1,N,1 for the Nth character
...
:End

          Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, jonbush, kg583, Michael2_3B.

          History

          Calculator OS Version Description
          TI-83 0.01013 Added
          Property Value
          Hex Value $BB2C
          Categories
            Localizations
            • FR: Δliste(

            ΔList(

            Overview

            Returns a list containing the differences between consecutive elements in list.

            Availability: Token available everywhere.

            Syntax

            ΔList(list)

            Arguments

            NameTypeOptional
            Δ
            listlist

            Location

            2nd, list, OPS, 7:List(

            Description

            ΔList( calculates the differences between consecutive terms of a list, and returns them in a new list.

            ΔList({0,1,4,9,16,25,36})
    {1 3 5 7 9 11}

            Advanced Uses

            The ΔList( command is very nearly the inverse of the cumSum( command, which calculates the cumulative sums of a list. For any list, ΔList(cumSum(list)) will return the same list, but without its first element:

            ΔList(cumSum({1,2,3,4,5,6,7}))
    {2 3 4 5 6 7}

            Removing the first element would otherwise be a difficult procedure involving the seq( command, so this is a useful trick to know.

            If a list is sorted in ascending order, min(ΔList(list)) will return 0 (false) if there are repeating values in the list, and a value corresponding to true if they are all distinct. The number of repeating elements can be determined similarly via 1+sum(0≠ΔList(list)) (again, so long as the list is sorted).

            Error Conditions

            Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, kg583, Timothy Foster.

            History

            Calculator OS Version Description
            TI-83 0.01013 Added
            Property Value
            Hex Value $BB2D
            Categories
            Localizations
            • FR: Gauss(

            ref(

            Overview

            Returns the row-echelon form of a matrix.

            Availability: Token available everywhere.

            Syntax

            ref(matrix)

            Arguments

            NameTypeOptional
            matrixmatrix

            Location

            2nd, matrix, MATH, A:ref(

            Description

            Given a matrix with at least as many columns as it has rows, the ref( command uses a technique called Gaussian elimination to put the matrix into row-echelon form.

            This means that the leftmost N columns (if the matrix has N rows) of the matrix are upper triangular - all entries below the main diagonal are zero. What's more, every entry on the main diagonal is either 0 or 1.

            [[1,2,5,0][2,2,1,2][3,4,6,2]]
    [[1 2 5 0]
     [2 2 1 2]
     [3 4 6 2]
ref(Ans)►Frac
    [[1 4/3 2   2/3]
     [0 1   9/2 -1 ]
     [0 0   0   0  ]]

            Advanced Uses

            In theory, a system of linear equations in N variables can be solved using the ref( command - an equation of the form \(a_1x_1+\dots + a_nx_n = b\) becomes a row \(a_1, \dots, a_n, b\), and is put into the matrix. If there is a sufficient number of conditions, the last row of the reduced matrix will give you the value of the last variable, and back-substitution will give you the others.

            In practice, it's easier to use rref( instead for the same purpose.

            Error Conditions

            Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, kg583, Timothy Foster.

            History

            Calculator OS Version Description
            TI-83 0.01013 Added
            Property Value
            Hex Value $BB2E
            Categories
            Localizations
            • FR: Gauss-Jordan(

            rref(

            Overview

            Returns the reduced row-echelon form of a matrix.

            Availability: Token available everywhere.

            Syntax

            rref(matrix)

            Arguments

            NameTypeOptional
            matrixmatrix

            Location

            2nd, matrix, MATH, B:rref(

            Description

            Given a matrix with at least as many columns as rows, the rref( command puts a matrix into reduced row-echelon form using Gaussian elimination.

            This means that as many columns of the result as possible will contain a pivot entry of 1, with all entries in the same column, or to the left of the pivot, being 0.

            [[1,2,5,0][2,2,1,2][3,4,6,2]]
    [[1 2 5 0]
     [2 2 1 2]
     [3 4 7 3]]
rref(Ans)
    [[1 0 0 6   ]
     [0 1 0 -5.5]
     [0 0 1 1   ]]

            Advanced Uses

            The rref( command can be used to solve a system of linear equations. First, take each equation, in the standard form of \(a_1x_1+\dots + a_nx_n = b\), and put the coefficients into a row of the matrix.

            Then, use rref( on the matrix. There are three possibilities now:

            • If the system is solvable, the left part of the result will look like the identity matrix. Then, the final column of the matrix will contain the values of the variables.
            • If the system is inconsistent, and has no solution, then it will end with rows that are all 0 except for the last entry.
            • If the system has infinitely many solutions, it will end with rows that are all 0, including the last entry.

            This process can be done by a program fairly easily. However, unless you're certain that the system will always have a unique solution, you should check that the result is in the correct form, before taking the values in the last column as your solution. The Matr►list( command can be used to store this column to a list.

            Error Conditions

            Source: parts of this page were written by the following TI|BD contributors: Battlesquid, DarkerLine, GoVegan, kg583.

            History

            Calculator OS Version Description
            TI-83 0.01013 Added
            Property Value
            Hex Value $BB2F
            Categories
            Localizations
            • FR: ►Rect

            ►Rect

            Overview

            Displays complex value or list in rectangular format.

            Availability: Token available everywhere.

            Syntax

            complex value ►Rect

            Arguments

            NameTypeOptional
            complex valuecomplex

            Location

            math, CMPLX, 6:Rect

            Description

            The ►Rect command can be used when displaying a complex number on the home screen, or with the Disp and Pause commands. It will then format the number as though a+b𝑖 mode were enabled, even when it's not. It also works with lists.

            i►Polar
    1𝑒^(1.570796327i)
Ans►Rect
    i

            It will also work when displaying a number by putting it on the last line of a program by itself. It does not work with Output(, Text(, or any other more complicated display commands.

            To actually separate a number into the components of rectangular form, use real( and imag(.

            Error Conditions

            • ERR:SYNTAX is thrown if the command is used somewhere other than the allowed display commands.
            • ERR:DATA TYPE is thrown if the value is real.

            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

            History

            Calculator OS Version Description
            TI-83 0.01013 Added
            Property Value
            Hex Value $BB30
            Categories
            Localizations
            • FR: ►Polaire

            ►Polar

            Overview

            Displays complex value in polar format.

            Availability: Token available everywhere.

            Syntax

            complex value ►Polar

            Arguments

            NameTypeOptional
            complex valuecomplex

            Location

            math, CMPLX, 7:Polar

            Description

            The ►Polar command can be used when displaying a complex number on the home screen, or with the Disp and Pause commands. It will then format the number as though r𝑒^θ𝑖 mode were enabled. It also works with lists.

            i
    i
i►Polar
    1𝑒^(1.570796327i)
{1,i}►Polar
    {1 1𝑒^(1.570796327i)}

            It will also work when displaying a number by putting it on the last line of a program by itself. It does not work with Output(, Text(, or any other more complicated display commands.

            To actually separate a number into the components of polar form, use abs( and angle(.

            Error Conditions

            • ERR:SYNTAX is thrown if the command is used somewhere other than the allowed display commands.
            • ERR:DATA TYPE is thrown if the value is real.

            Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan.

            History

            Calculator OS Version Description
            TI-83 0.01013 Added
            Property Value
            Hex Value $BB31
            Categories
            Localizations
            • FR: 𝑒

            𝑒

            Overview

            Returns decimal approximation of the constant 𝑒.

            Availability: Token available everywhere.

            Syntax

            𝑒

            Location

            2nd, e

            Description

            e is a constant on the TI-83 series calculators. The constant holds the approximate value of Euler's number, fairly important in calculus and other higher-level mathematics.

            The approximate value, to as many digits as stored in the calculator, is 2.718281828459…

            The main use of e is as the base of the exponential function 𝑒^( (which is also a separate function on the calculator), and its inverse, the natural logarithm ln(. From these functions, others such as the trigonometric functions (e.g. sin() and the hyperbolic functions (e.g. sinh() can be defined. In r𝑒^θ𝑖 mode, e is used in an alternate form of expressing complex numbers.

            Important as the number e is, nine times out of ten you won't need the constant itself when using your calculator, but rather the 𝑒^( and ln( functions.

            Source: parts of this page were written by the following TI|BD contributors: alexrudd, burr, DarkerLine, GoVegan, Myles_Zadok, simplethinker, Timothy Foster.

            History

            Calculator OS Version Description
            TI-83 0.01013 Added
            Property Value
            Hex Value $BB32
            Categories
            Localizations
            • FR: RegSin

            SinReg

            Overview

            Attempts iterations times to fit a sinusoidal regression model to Xlistname and Ylistname using a period guess, and stores the regression equation to regequ.

            Availability: Token available everywhere.

            Syntax

            SinReg [iterations,Xlistname,Ylistname,period,regequ]

            Arguments

            NameTypeOptional
            iterationsYes
            XlistnamelistYes
            YlistnamelistYes
            periodYes
            regequYes

            Location

            stat, CALC, C:SinReg

            Description

            SinReg tries to fit a sine wave to a given list of points. To use it, you must first store the points to two lists: one of the x-coordinates and one of the y-coordinates, ordered so that the ith element of one list matches up with the ith element of the other list (i.e. the first element of the x-list and the first element of the y-list make up an ordered pair). L₁ and L₂ are the default lists used, and the List Editor (STAT > Edit…) is a useful window for entering the points.

            SinReg requires that the lists contain at least 4 points. Also, if you do not provide two data points per cycle, the calculator may return a wrong answer. These conditions are an absolute minimum, and the command may fail to work even when they are met, and throw a ERR:SINGULAR MAT error. This is also likely to happen if the data are not actually periodic in nature.

            In addition, to use SinReg in its simplest form, the x-coordinates must be sorted in increasing order, and the difference between consecutive x-coordinates must be the same throughout (i.e., x𝑖+1-x𝑖 should be the same for all i). You can then call SinReg with no arguments, and it will attempt to fit a sine wave to the data in L₁ and L₂:

            :{1,2,3,4,5,6,7,8,9,10,11,12→L₁
:{21,24,34,46,58,67,72,70,61,50,40,27→L₂
:SinReg

            On the home screen, or as the last line of a program, this will display the equation of the curve: you'll be shown the format, y=a*sin(b__x+c)+d, and the values of a, b, c and d. It will also be stored in the RegEQ variable, but you will not be able to use this variable in a program - accessing it just pastes the equation wherever your cursor was. Finally, the statistical variables a, b, c, and d will be set to the values computed as well. There are no correlation statistics available for SinReg even if Diagnostic Mode is turned on (see DiagnosticOn and DiagnosticOff).

            A word of caution: the calculator assumes that Radian mode is enabled. If the calculator is set to Degree mode, the equation will still be in terms of radians: it will be correct, but values plugged in will give wrong answers. You will have to either switch to Radian mode, or multiply the values of b and c by 180/π.

            You do not have to do the regression on L₁ and L₂, in which case you'll have to enter the names of the lists after the command. For example:

            :{1,2,3,4,5,6,7,8,9,10,11,12→MONTH
:{21,24,34,46,58,67,72,70,61,50,40,27→TEMP
:SinReg ʟMONTH,ʟTEMP

            Unlike the other regression commands, SinReg does not allow you to use a frequency list for data. You can get around this by adding repeating coordinates multiple times.

            The optional argument iterations should come before the data lists, and if provided will change the amount of time and effort the calculator spends on the problem. The value should be an integer 1 to 16; larger numbers mean greater precision, but a longer calculation time. The default value is 3, and for good reason: with a high precision value, the calculation may take a minute to complete, or longer, depending on the complexity of the problem.

            The optional argument period should be given after the data lists - this is the length of a complete cycle in the data, if known. You might know the exact value of the period, for example, when the calculation involves time - a complete cycle could be a day, a month, or a year. Providing this argument is strongly recommended whenever it is available: this removes conditions on the x-coordinates' order and increment, and makes the calculation much faster and more accurate. If you have previously done a SinReg fit and desire a refined estimate, the value 2π_/b_ can be given as the period.

            Finally, you can enter an equation variable (such as Y₁) after the command, so that the curve's equation is stored to this variable automatically. This does not require you to supply the names of the lists, but if you do, the equation variable must come last. You can use polar, parametric, or sequential variables as well, but since the equation will be in terms of X anyway, this does not make much sense.

            An example of SinReg with all the optional arguments:

            :{1,2,3,4,5,6,7,8,9,10,11,12→MONTH
:{21,24,34,46,58,67,72,70,61,50,40,27→TEMP
:SinReg 16,ʟMONTH,ʟTEMP,12,Y₁

            The Levenberg-Marquardt nonlinear least-squares algorithm is used by SinReg.

            Error Conditions

            • ERR:SINGULAR MAT is thrown if you don't provide the calculator at least 4 points, or two data points per cycle.

            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, thornahawk, Timothy Foster.___

            History

            Calculator OS Version Description
            TI-83 0.01013 Added
            Property Value
            Hex Value $BB33
            Categories
            Localizations
            • FR: Logistique

            Logistic

            Overview

            Fits a logistic regression model toXlistnameand Ylistname with frequency freqlist, and stores the regression equation to regequ.

            Availability: Token available everywhere.

            Syntax

            Logistic [Xlistname,Ylistname,freqlist,regequ]

            Arguments

            NameTypeOptional
            XlistnamelistYes
            YlistnamelistYes
            freqlistlistYes
            regequYes

            Location

            CALC, B:Logistic

            Description

            Logistic tries to fit a logistic curve (y=c/(1+ae-bx)) through a set of points. To use it, you must first store the points to two lists: one of the x-coordinates and one of the y-coordinates, ordered so that the ith element of one list matches up with the ith element of the other list. L₁ and L₂ are the default lists used, and the List Editor (STAT > Edit…) is a useful window for entering the points.

            The explanation for the odd format of a logistic curve is that it is the solution to a differential equation that models population growth with a limiting factor: a population that grows according to a logistic curve will start out growing exponentially, but will slow down before reaching a carrying capacity and approach this critical value without reaching it. The logistic curve also has applications, for example, in physics.

            In its simplest form, Logistic takes no arguments, and fits a logistic curve through the points in L₁ and L₂:

            :{9,13,21,30,31,31,34→L₁
:{260,320,420,530,560,550,590→L₂
:Logistic

            On the home screen, or as the last line of a program, this will display the equation of the curve: you'll be shown the format, y=c/(1+a__e^(-b_x)), and the values of _a, b and c. It will also be stored in the RegEQ variable, but you won't be able to use this variable in a program - accessing it just pastes the equation wherever your cursor was. Finally, the statistical variables a, b, and c will be set as well. There are no correlation statistics available for Logistic even if Diagnostic Mode is turned on (see DiagnosticOn and DiagnosticOff).

            You do not have to do the regression on L₁ and L₂, in which case you will have to enter the names of the lists after the command. For example:

            :{9,13,21,30,31,31,34→FAT
:{260,320,420,530,560,550,590→CALS
:Logistic ʟFAT,ʟCALS

            You can attach frequencies to points, for when a point occurs more than once, by supplying an additional argument - the frequency list. This list does not have to contain integer frequencies. If you add a frequency list, you must supply the names of the x-list and y-list as well, even when they're L₁ and L₂.

            Finally, you can enter an equation variable (such as Y₁) after the command, so that the curve's equation is stored to this variable automatically. This does not require you to supply the names of the lists, but if you do, the equation variable must come last. You can use polar, parametric, or sequential variables as well, but since the equation will be in terms of X anyway, this doesn't make much sense.

            An example of Logistic with all the optional arguments:

            :{9,13,21,30,31,31,34→FAT
:{260,320,420,530,560,550,590→CALS
:{2,1,1,1,2,1,1→FREQ
:Logistic ʟFAT,ʟCALS,ʟFREQ,Y₁

            Warning: if your data is not even slightly logistic in nature, then the calculator may return an error such as ERR:OVERFLOW. This happens when the calculator tries to calculate a carrying capacity, c, for the data, but since the rate of change in data doesn't seem to be slowing down, it assumes that the carrying capacity is still very far off, and tries large values for it. These values may get so large as to cause an overflow.

            The Levenberg-Marquardt nonlinear least-squares algorithm is used by Logistic.

            Error Conditions

            • ERR:ARGUMENT is thrown by using only one list.
            • ERR:DIM MISMATCH is thrown if the dimensions of two lists do not match.
            • ERR:DOMAIN is thrown if Logistic is left without using lists or enough instructions.
            • ERR:DATA TYPE is thrown if lists are not used, or a list contains a number like "4i".

            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, nap386, thornahawk, Timothy Foster.___

            History

            Calculator OS Version Description
            TI-83 0.01013 Added
            Property Value
            Hex Value $BB34
            Categories
            Localizations
            • FR: RegLinTTest

            LinRegTTest

            Overview

            Performs a linear regression and a t-test. alternative=-1 is <; alternative=0 is ≠; alternative=1 is >.

            Availability: Token only available from within the Basic editor.

            Syntax

            LinRegTTest [Xlistname,Ylistname,freqlist,alternative,regequ]

            Arguments

            NameTypeOptional
            XlistnamelistYes
            YlistnamelistYes
            freqlistlistYes
            alternativeYes
            regequYes

            Location

            stat, TESTS, F:LinRegTTest

            Description

            Like LinReg(ax+b) and similar commands, LinRegTTest finds the best fit line through a set of points. However, LinRegTTest adds another method of checking the quality of the fit, by performing a t-test on the slope, testing the null hypothesis that the slope of the true best fit line is 0 (which implies the absence of correlation between the two variables, since a relation with a slope of zero means the x-variable does not affect the y-variable at all). If the p-value of the test is not low enough, then there is not enough data to assume a linear relation between the variables.

            To use LinRegTTest, you must first store the points to two lists: one of the x-coordinates and one of the y-coordinates, ordered so that the nth element of one list matches up with the nth element of the other list. L₁ and L₂ are the default lists to use, and the List Editor (STAT > Edit…) is a useful window for entering the points.

            In its simplest form, LinRegTTest takes no arguments, and calculates a best fit line through the points in L₁ and L₂:

            :{9,13,21,30,31,31,34→L₁
:{260,320,420,530,560,550,590→L₂
:LinRegTTest

            The output will look as follows:

            LinRegTTest
 y=a+bx
 β≠0 and ρ≠0
 t=53.71561274
 p=4.2285344e-8
 df=5
 a=145.3808831
 b=13.09073265
 s=5.913823968
 r²=.9982701159
 r=.9991346836

            (the last two lines will only appear if diagnostics have been turned on - see DiagnosticOn)

            • β and ρ: this line represents the alternative hypothesis. β is the true value of the statistic b (it is what we would get if the regression was done on the entire population, rather than a sample); ρ is the true value of the statistic r.
            • t is the test statistic, used to calculate p.
            • p is the probability that we'd get a correlation this strong by chance, assuming the null hypothesis that there is no actual correlation. When it's low, as here, this is evidence against the null hypothesis. Since p<.01, the data is significant on a 1% level, so we reject the null hypothesis and conclude that there is a correlation.
            • df is the degrees of freedom, equal to the number of points minus two
            • a and b are the parameters of the equation y=a+bx, the regression line we've calculated
            • s is the standard error about the line, a measure of the typical size of a residual (the numbers stored in ʟRESID). It is the square root of the sum of squares of the residuals divided by the degrees of freedom. Smaller values indicate that the points tend to be close to the fitted line, while large values indicate scattering.
            • r² and r are respectively the coefficients of determination and correlation: a value near 1 or -1 for the former, and near 1 for the latter, indicates a good fit.

            You do not have to do the regression on L₁ and L₂, but if you don't you'll have to enter the names of the lists after the command. For example:

            :{9,13,21,30,31,31,34→FAT
:{260,320,420,530,560,550,590→CALS
:LinRegTTest ʟFAT,ʟCALS

            You can attach frequencies to points, for when a point occurs more than once, by supplying an additional argument - the frequency list. This list does not have to contain integer frequencies. If you add a frequency list, you must supply the names of the x-list and y-list as well, even when they are L₁ and L₂.

            You can add the alternative argument to change the alternative hypothesis from the default (β≠0 and ρ≠0). This is used when you have prior knowledge either that a negative relation is impossible, or that a positive one is impossible. The values of the alternative argument are as follows:

            • negative: the alternative hypothesis is β<0 and ρ<0 (we have prior knowledge that there can be no positive relation)
            • 0: the alternative hypothesis is β≠0 and ρ≠0 (we have no prior knowledge)
            • positive: the alternative hypothesis is β>0 and ρ>0 (we have prior knowledge that there can be no negative relation)

            Obviously, if you want the alternative hypothesis to be β≠0 and ρ≠0, the default, you don't need to supply this argument. However, if you do, you must enter the names of the lists as well, even if they're L₁ and L₂.

            Finally, you can enter an equation variable (such as Y₁) after the command, so that the line of best fit is stored to this equation automatically. This doesn't require you to supply the names of the lists, but if you do, the equation variable must come last. You can use polar, parametric, or sequential variables as well, but since the line of best fit will be in terms of X anyway, this doesn't make much sense.

            An example of LinRegTTest with all the optional arguments:

            :{9,13,21,30,31,31,34→FAT
:{260,320,420,530,560,550,590→CALS
:{2,1,1,1,2,1,1→FREQ
:LinRegTTest ʟFAT,ʟCALS,ʟFREQ,1,Y₁

            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Myles_Zadok, thornahawk, Timothy Foster.

            History

            Calculator OS Version Description
            TI-83 0.01013 Added
            Property Value
            Hex Value $BB35
            Categories
            Localizations
            • FR: OmbreNorm(

            ShadeNorm(

            Overview

            Draws the normal density function specified by μ and σ and shades and colors the area between lowerbound and upperbound.
            Color#: 10 - 24 or color name pasted from [vars] COLOR.

            Availability: Token available everywhere.

            Syntax

            ShadeNorm(lowerbound,upperbound[,μ,σ,color#])

            Arguments

            NameTypeOptional
            lowerbound
            upperbound
            μYes
            σYes
            colorYes
            #Yes

            Location

            2nd, distr, DRAW, 1:ShadeNorm(

            Description

            ShadeNorm( is equivalent to normalcdf( in terms of the probability it calculates: if a random variable follows the normal distribution, you can use it to calculate the probability that the variable's value falls in a certain interval. However, in addition to calculating the probability, this command also draws the normal curve, and shades the interval whose area represents the probability you want.

            Note that this command does not actually return the value it calculates in Ans or anywhere else: it's merely displayed on the graph. If you're going to use the value in further calculations, you'll have to use normalcdf( as well.

            There are two ways to use ShadeNorm(. With two arguments (lower bound and upper bound), the calculator will assume you mean the standard normal distribution, and use that to find the probability corresponding to the interval between "lower bound" and "upper bound". You can also supply two additional arguments to use the normal distribution with a specified mean and standard deviation. For example:

            for the standard normal distribution
:ShadeNorm(-1,1

for the normal distribution with mean 10 and std. dev. 2.5
:ShadeNorm(5,15,10,2.5

            Advanced

            Often, you want to find a "tail probability" - a special case for which the interval has no lower or no upper bound. For example, "what is the probability x is greater than 2?". The TI-83+ has no special symbol for infinity, but you can use E99 to get a very large number that will work equally well in this case (E is the decimal exponent obtained by pressing [2nd] [EE]). Use E99 for positive infinity, and -E99 for negative infinity.

            It can be hard to find the best window for ShadeNorm( to work in, since it doesn't automatically zoom for you. For the standard curve, the graph doesn't go above y=.5 (a good value for Ymax); Ymin should probably be something small. Xmin and Xmax could be -3 to 3 (3 deviations out); change this around to see more or less of the graph.

            For nonstandard curves, increasing the standard deviation stretches and flattens the curve; by dividing Ymax and multiplying Xmin and Xmax by the standard deviation, you'll account for this effect. To account for the mean, add it to both Xmin and Xmax. You may also choose to standardize the lower and upper values instead by applying the formula (z-μ)/σ.

            Keep in mind that ShadeNorm is just a drawing command and not an actual graphed function, so resizing the window, ClrDraw, and a bunch of other things will simply get rid of it.

            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

            History

            Calculator OS Version Description
            TI-83 0.01013 Added
            Property Value
            Hex Value $BB36
            Categories
            Localizations
            • FR: Ombre_t(

            Shade_t(

            Overview

            Draws the density function for the Student-t distribution specified by degrees of freedom df, and shades or colors the area between lowerbound and upperbound.
            Color#: 10 - 24 or color name pasted from [vars] COLOR.

            Availability: Token available everywhere.

            Syntax

            Shade_t(lowerbound,upperbound,df[,color#])

            Arguments

            NameTypeOptional
            lowerbound
            upperbound
            df
            color#colorNumYes

            Location

            2nd, distr, DRAW, 2:Shade_t(

            Description

            Shade_t( is equivalent to tcdf( in terms of the probability it calculates: if a random variable follows the Student's t distribution, you can use it to calculate the probability that the variable's value falls in a certain interval. However, in addition to calculating the probability, this command also draws the distribution, and shades the interval whose area represents the probability you want.

            Note that this command does not actually return the value it calculates in Ans or anywhere else: it's merely displayed on the graph. If you're going to use the value in further calculations, you'll have to use tcdf( as well.

            Like tcdf(, Shade_t( takes three arguments: the lower bound, the upper bound, and the degrees of freedom.

            Advanced

            Often, you want to find a "tail probability" - a special case for which the interval has no lower or no upper bound. For example, "what is the probability x is greater than 2?". The TI-83+ has no special symbol for infinity, but you can use E99 to get a very large number that will work equally well in this case (E is the decimal exponent obtained by pressing [2nd] [EE]). Use E99 for positive infinity, and -E99 for negative infinity.

            The Shade_t( command's output is affected by the graphing window, and on many windows you won't be able to get a good idea of what the graph looks like. For best results, Ymin should be either 0 or a small negative number, and Ymax should be 0.5 or less. Xmin and Xmax should be opposites of each other (so the middle of the graph is 0), but how large they are depends on the degrees of freedom and on how much of the graph you want to see: -4 and 4 are good starting places.

            Keep in mind that Shade_t( is a drawing command and not the graph of an equation, so changing graph settings, the ClrDraw command, and a great deal of other things will erase its output.

            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

            History

            Calculator OS Version Description
            TI-83 0.01013 Added
            Property Value
            Hex Value $BB37
            Categories
            Localizations
            • FR: Ombreχ²(

            Shadeχ²(

            Overview

            Draws the density function for the χ² distribution specified by degrees of freedom df, and shades and colors the area between lowerbound and upperbound.
            Color#: 10 - 24 or color name pasted from [vars] COLOR.

            Availability: Token available everywhere.

            Syntax

            Shadeχ²(lowerbound,upperbound,df[,color#])

            Arguments

            NameTypeOptional
            χ²
            lowerbound
            upperbound
            dfYes
            color#colorNumYes

            Location

            2nd, distr, DRAW, 3:Shade, (

            Description

            Shadeχ²( is equivalent to χ²cdf( in terms of the probability it calculates: if a random variable follows the χ² distribution, you can use it to calculate the probability that the variable's value falls in a certain interval. However, in addition to calculating the probability, this command also draws the χ² curve, and shades the interval whose area represents the probability you want.

            Note that this command does not actually return the value it calculates in Ans or anywhere else: it's merely displayed on the graph. If you're going to use the value in further calculations, you'll have to use χ²cdf( as well.

            The Shadeχ²( command takes three arguments. lower and upper identify the interval you're interested in. df specifies the degrees of freedom (selecting from an infinite family of χ² distributions).

            Thus, the following code would find the probability of χ² between 0 and 1 on a χ² distribution with 2 degrees of freedom, and shade this interval:

            :Shadeχ²(0,1,2

            Advanced

            Often, you want to find a "tail probability" - a special case for which the interval has no lower or no upper bound. For example, "what is the probability x is greater than 2?". The TI-83+ has no special symbol for infinity, but you can use E99 to get a very large number that will work equally well in this case (E is the decimal exponent obtained by pressing [2nd] [EE]). Use E99 for positive infinity, and -E99 for negative infinity.

            It can be hard to find the best window for Shadeχ²( to work in, since it doesn't automatically zoom for you. For any number of degrees of freedom (except for 1), the graph doesn't go above y=.5 (a good value for Ymax); Ymin should probably be something small and negative. Xmin should be around 0 (possibly slightly less if you like seeing axes), while Xmax probably shouldn't go above 5.

            Keep in mind that Shadeχ²( is just a drawing command and not an actual graphed function, so resizing the window, ClrDraw, and other commands that refresh the graphscreen will remove it.

            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583.

            History

            Calculator OS Version Description
            TI-83 0.01013 Added
            Property Value
            Hex Value $BB38
            Categories
            Localizations
            • FR: Ombre𝐅(

            Shade𝐅(

            Overview

            Draws the density function for the 𝐅distribution specified by numerator df and denominator df and shades and colors the area between lowerbound and upperbound.
            Color#: 10 - 24 or color name pasted from [vars] COLOR.

            Availability: Token available everywhere.

            Syntax

            Shade𝐅(lowerbound,upperbound,numerator df,denominator df[,color#])

            Arguments

            NameTypeOptional
            𝐅
            lowerbound
            upperbound
            numerator df
            denominator dfYes
            color#colorNumYes

            Location

            2nd, distr, DRAW, 4:Shade, (

            Description

            Examples

            Explanation 1

            code 1

            Explanation 2

            code 2

            Error Conditions

            Advanced Notes

            History

            Calculator OS Version Description
            TI-83 0.01013 Added
            Property Value
            Hex Value $BB39
            Categories
            Localizations
            • FR: Matr►list(

            Matr►list(

            Overview

            Fills each listname with elements from each column in matrix.

            Availability: Token available everywhere.

            Syntax

            Matr►list(matrix,listnameA,...,listname n)

            Arguments

            NameTypeOptional
            matrixmatrix
            listnameAlist
            ...
            listname nlist

            Location

            2nd, list, OPS, A:Matr►list(

            Overview

            Fills a listname with elements from a specified column# in matrix.

            Availability: Token available everywhere.

            Syntax

            Matr►list(matrix,column#,listname)

            Arguments

            NameTypeOptional
            matrixmatrix
            column#
            listnamelist

            Location

            2nd, list, OPS, A:Matr►list(

            Description

            The Matr►list( command stores one or more columns of a matrix (or expression resulting in a matrix) to list variables. The syntax is simple: first enter the matrix, then enter the list or lists you want to store columns to. The first (leftmost) column will be stored to the first list entered, the second column will be stored to the second list, and so on. For example:

            [[11,12,13,14][21,22,23,24][31,32,33,34
        [[11 12 13 14]
         [21 22 23 24]
         [31 32 33 34]]
Matr►list(Ans,L1,L2
        Done
L1
        {11 21 31}
L2
        {12 22 32}

            If there are more lists than columns in the matrix when doing Matr►list(, the extra lists will be ignored.

            Matr►list( can also be used to extract a specific column of a matrix to a list. The order of the arguments is: matrix, column number, list name.

            [[11,12,13,14][21,22,23,24][31,32,33,34
        [[11 12 13 14]
         [21 22 23 24]
         [31 32 33 34]]
Matr►list(Ans,4,L1
        Done
L1
        {14 24 34}

            Advanced Uses

            While the command deals with columns, occasionally you might want to store the matrix to lists by rows. The T (transpose) command is your friend here: applying it to the matrix will flip it diagonally, so that all rows will become columns and vice-versa. For example:

            [[11,12,13,14][21,22,23,24][31,32,33,34
                     [[11 12 13 14]
                     [21 22 23 24]
                     [31 32 33 34]]
            Matr►list(AnsT,L1,L2
                     Done
            L1
                     {11 12 13 14}
            L2
                     {21 22 23 24}

            Optimizations

            When using Matr►list( to store to named lists, only the first list must have an ʟ in front of its name — it can be omitted for the rest. For example:

            :Matr►list([A],ʟCOL1,ʟCOL2,ʟCOL3
can be
:Matr►list([A],ʟCOL1,COL2,COL3

            On the other hand, when storing a specific column of a matrix to a named list, the list does not need to be preceded by an ʟ.

            :Matr►list([A],N,ʟCOL1
can be
:Matr►list([A],N,COL1

            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, thornahawk, Timothy Foster.

            History

            Calculator OS Version Description
            TI-83 0.01013 Added
            Property Value
            Hex Value $BB3A
            Categories
            Localizations
            • FR: List►matr(

            List►matr(

            Overview

            Fills matrixname column by column with the elements from each specified listname.

            Availability: Token available everywhere.

            Syntax

            List►matr(listname1,...,listname n,matrixname)

            Arguments

            NameTypeOptional
            listname1listName
            ...
            listname nlist
            matrixnamematrix

            Location

            2nd, list, OPS, 0:List, matr(

            Description

            The List►matr( builds a matrix by combining several list expressions, and stores it to the specified variable ([A] through [J]). Each list specifies a column of the matrix: the first list will be stored down the first (leftmost) column, the second list down the second column, and so on. For example:

            List►matr({1,2,3},{10,20,30},{100,200,300},[A]
        Done
[A]
        [[1 10 100]
         [2 20 200]
         [3 30 300]]

            Advanced Uses

            The calculator can actually handle lists that are not the same size. It will pad zeroes to the shorter lists, until they have the same length as the longest list.

            List►matr({1,2,3},{10},{100,200},[A]
        Done
[A]
        [[1 10 100]
         [2  0 200]
         [3  0   0]]

            Error Conditions

            • ERR:ARGUMENT is thrown if there are more than 99 lists (since a matrix can be at most 99x99)
            • ERR:INVALID DIM is thrown if one of the lists is longer than 99 elements (since a matrix can be at most 99x99)

            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, thornahawk, Timothy Foster.

            History

            Calculator OS Version Description
            TI-83 0.01013 Added
            Property Value
            Hex Value $BB3B
            Categories
            Localizations
            • FR: Z-Test(

            Z-Test(

            Overview

            Performs a z test with frequency freqlist. alternative= -1 is <; alternative=0 is ≠; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results.
            Color#: 10 - 24 or color name pasted from [vars] COLOR.

            Comment:Data list input

            Availability: Token only available from within the Basic editor.

            Syntax

            Z-Test(μ0,σ[,listname,freqlist,alternative,drawflag,color#])

            Arguments

            NameTypeOptional
            μ
            0
            σ
            listnamelist
            freqlistlist
            alternative
            drawflag
            color#colorNum

            Location

            stat, TESTS, 1:Z-Test(

            Overview

            Performs a z test. alternative=-1 is <; alternative=0 is ≠; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results.
            Color#: 10 - 24 or color name pasted from [vars] COLOR.

            Comment:Summary stats input

            Availability: Token only available from within the Basic editor.

            Syntax

            Z-Test(μ0,σ,x̄,n[,alternative,drawflag,color#])

            Arguments

            NameTypeOptional
            μ
            0
            σ
            x̄Yes
            nYes
            alternativeYes
            drawflagYes
            color#colorNumYes

            Location

            stat, TESTS, 1:Z-Test(

            Description

            Z-Test( performs a z significance test of a null hypothesis you supply. This test is valid for simple random samples from a population with a known standard deviation. In addition, either the population must be normally distributed, or the sample size has to be sufficiently large.

            The logic behind a Z-Test is as follows: we want to test the hypothesis that the true mean of a population is a certain value (μ0). To do this, we assume that this "null hypothesis" is true, and calculate the probability that the variation from this mean occurred, under this assumption. If this probability is sufficiently low (usually, 5% is the cutoff point), we conclude that since it's so unlikely that the data could have occurred under the null hypothesis, the null hypothesis must be false, and therefore the true mean μ is not equal to μ0. If, on the other hand, the probability is not too low, we conclude that the data may well have occurred under the null hypothesis, and therefore there's no reason to reject it.

            In addition to the null hypothesis, we must have an alternative hypothesis as well - usually this is simply that the true mean is not μ0. However, in certain cases when we have reason to suspect the true mean is less than or greater than μ0, we might use a "one-sided" alternative hypothesis, which will state that the true mean μ<μ0 or that μ>μ0.

            As for the Z-Test( command itself, there are two ways of calling it: you may give it a list of all the sample data, or the necessary statistics about the list - its size, and the mean. In either case, you can indicate what the alternate hypothesis is, by a value of 0, -1, or 1 for the alternative argument. 0 indicates a two-sided hypothesis of μ≠μ0, -1 indicates μ<μ0, and 1 indicates μ>μ0.

            Although you can access the Z-Test( command on the home screen, via the catalog, there's no need: the Z-Test… interactive solver, found in the statistics menu, is much more intuitive to use - you don't have to memorize the syntax.

            In either case, it's important to understand the output of Z-Test. Here are the meanings of each line:

            • The first line, involving μ, is the alternative hypothesis.
            • z is the test statistic, the standardized difference between the sample mean and μ0. If the null hypothesis is true, it should be close to 0.
            • p is the probability that the difference between the sample mean and μ0 would occur if the null hypothesis is true. When the value is sufficiently small, we reject the null hypothesis and conclude that the alternative hypothesis is true. You should have a cutoff value ready, such as 5% or 1%. If p is lower, you "reject the null hypothesis on a 5% (or 1%) level" in technical terms.
            • x-bar is the sample mean.
            • Sx is the sample standard deviation. This isn't actually used in any calculations, and will only be shown for data list input.
            • n is the sample size.

            Sample Problem

            According to M&M's advertising, each standard-size bag of M&M's contains an average of 10 blue M&M's with a standard deviation of 2 M&M's. You think that this estimate is low, and that the true average is higher. You decide to test this hypothesis by buying thirty bags of M&M's. You count the number of blue M&M's in each, and store this number to L1.

            The value of μ0 is 10, because you want to test the null hypothesis that there are on average 10 blue M&M's per bag. The value of σ is 2. We want to test the values in L1. Because we want to test if there's actually more than 10 blue M&M's per bag, we have a one-sided alternate hypothesis: μ>μ0, which corresponds to an argument of 1. To solve the problem, you'd use this code:

            :Z-Test(10,2,L1,1

            Alternatively, you could calculate the mean and sample size of your sample, and put those into the command instead. The sample size is 30; let's suppose that the mean was 11.2. The code you'd use is:

            :Z-Test(10,2,11.2,30,1

            You will see the following output:

            Z-Test
 μ>10
 z=3.286335345
 p=5.0755973e-4
 x=11.2
 n=30

            The most important part of this output is "p=5.0755973e-4". This value of p is much smaller than 1% or 0.01; it's in fact around 0.0005. This is significant on the 1% level, so we reject the null hypothesis and conclude that the alternative hypothesis is true: μ>10, that is, the average number of blue M&M's in a bag is more than 10.

            Advanced Uses

            The final argument of Z-Test(, draw?, will display the results in a graphical manner if you put in "1" for it. The calculator will draw the standard normal curve, and shade the area of the graph beyound the z statistic. In addition, the value of z and the value of p will be displayed (the value of p corresponds to the shaded area). You would make your conclusions in the same way as for the regular output.

            As with most other statistical commands, you may use a frequency list in your input (when using the data list syntax).

            Optimization

            Most of the arguments of the Z-Test( command have default values, and the argument can be omitted if this value is accepted.

            • The draw? argument can be omitted if you don't want graphical output, although you could put "0" in as well.
            • If the draw? argument is omitted, you can omit the alternative argument to use a two-sided test (μ≠μ0). If you include the draw? argument, you have to include this - otherwise there will be confusion as to what the 5th argument means.
            • With data list input, you can always omit the frequency list if you won't be using it.
            • With data list input, if the draw? and alternative arguments are omitted, and your data is in L1, you may omit L1 as well. However, if alternative or draw? is present, you have to include it, or else the syntax may be confused with the syntax for summary stats input.

            The code in the sample problem above can't be optimized, because the alternative argument is 1:

            ::Z-Test(10,2,L1,1

            However, if we were doing a two-sided test, we could omit the alternative and the list arguments (since we're testing L1):

            :Z-Test(10,2,L1,0
can be
:Z-Test(10,2

            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

            History

            Calculator OS Version Description
            TI-83 0.01013 Added
            Property Value
            Hex Value $BB3C
            Categories
            Localizations
            • FR: T-Test

            T-Test

            Overview

            Performs a t test with frequency freqlist. alternative=-1 is <; alternative=0 is ≠; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results.
            Color#: 10 - 24 or color name pasted from [vars] COLOR.

            Comment:Data list input

            Availability: Token only available from within the Basic editor.

            Syntax

            T-Test μ0[,listname,freqlist,alternative,drawflag,color#])

            Arguments

            NameTypeOptional
            μ
            0Yes
            listnamelistYes
            freqlistlistYes
            alternativeYes
            drawflagYes
            color#colorNumYes

            Location

            stat, TESTS, 2:T-Test

            Overview

            Performs a t test with frequency freqlist. alternative=-1 is < ; alternative=0 is ă; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results.
            Color#: 10 - 24 or color name pasted from [vars] COLOR.

            Availability: Token only available from within the Basic editor.

            Syntax

            T-Test μ0,x̄,Sx,n[,alternative,drawflag,color#])

            Arguments

            NameTypeOptional
            μ
            0
            x̄
            Sx
            nYes
            alternativeYes
            drawflagYes
            color#colorNumYes

            Location

            stat, TESTS, 2:T-Test

            Description

            T-Test performs a t significance test of a null hypothesis you supply. This test is valid for simple random samples from a population with an unknown standard deviation. In addition, either the population must be normally distributed, or the sample size has to be sufficiently large.

            The logic behind a T-Test is as follows: we want to test the hypothesis that the true mean of a population is a certain value (μ0). To do this, we assume that this "null hypothesis" is true, and calculate the probability that the variation from this mean occurred, under this assumption. If this probability is sufficiently low (usually, 5% is the cutoff point), we conclude that since it's so unlikely that the data could have occurred under the null hypothesis, the null hypothesis must be false, and therefore the true mean μ is not equal to μ0. If, on the other hand, the probability is not too low, we conclude that the data may well have occurred under the null hypothesis, and therefore there's no reason to reject it.

            In addition to the null hypothesis, we must have an alternative hypothesis as well - usually this is simply that the true mean is not μ0. However, in certain cases when we have reason to suspect the true mean is less than or greater than μ0, we might use a "one-sided" alternative hypothesis, which will state that the true mean μ<μ0 or that μ>μ0.

            As for the T-Test command itself, there are two ways of calling it: you may give it a list of all the sample data, or the necessary statistics about the list - its size, the mean, and the standard deviation. In either case, you can indicate what the alternate hypothesis is, by a value of 0, -1, or 1 for the alternative argument. 0 indicates a two-sided hypothesis of μ≠μ0, -1 indicates μ<μ0, and 1 indicates μ>μ0. (in fact, any negative argument will be treated as -1, and any positive argument as 1)

            Although you can access the T-Test command on the home screen, via the catalog, there's no need: the T-Test… interactive solver, found in the statistics menu, is much more intuitive to use - you don't have to memorize the syntax.

            In either case, it's important to understand the output of T-Test. Here are the meanings of each line:

            • The first line, involving μ, is the alternative hypothesis.
            • t is the test statistic, the standardized difference between the sample mean and μ0. If the null hypothesis is true, it should be close to 0.
            • p is the probability that the difference between the sample mean and μ0 would occur if the null hypothesis is true. When the value is sufficiently small, we reject the null hypothesis and conclude that the alternative hypothesis is true. You should have a cutoff value ready, such as 5% or 1%. If p is lower, you "reject the null hypothesis on a 5% (or 1%) level" in technical terms.
            • x-bar is the sample mean.
            • Sx is the sample standard deviation.
            • n is the sample size (not included, but also important, is df, the degrees of freedom, defined as n-1)

            Sample Problem

            According to M&M's advertising, each standard-size bag of M&M's contains an average of 10 blue M&M's. You think that this estimate is low, and that the true average is higher. You decide to test this hypothesis by buying thirty bags of M&M's. You count the number of blue M&M's in each, and store this number to L1.

            The value of μ0 is 10, because you want to test the null hypothesis that there are on average 10 blue M&M's per bag. We want to test the values in L1. Because we want to test if there's actually more than 10 blue M&M's per bag, we have a one-sided alternate hypothesis: μ>μ0, which corresponds to an argument of 1. To solve the problem, you'd use this code:

            :T-Test 10,L1,1

            Alternatively, you could calculate the mean, standard deviation, and size of your sample, and put those into the command instead. The sample size is 30; let's suppose that the mean was 11.2 and the standard deviation 1.3. The code you'd use is:

            :T-Test 10,11.2,1.3,30,1

            You will see the following output:

            T-Test
 μ>10
 z=5.055900531
 p=1.0857768e-5
 x=11.2
 Sx=1.3
 n=30

            The most important part of this output is "p=1.0857768e-5". This value of p is much smaller than 1% or 0.01; it's in fact around 0.00001. This is significant on the 1% level, so we reject the null hypothesis and conclude that the alternative hypothesis is true: μ>10, that is, the average number of blue M&M's in a bag is more than 10.

            Advanced Uses

            The final argument of T-Test, draw?, will display the results in a graphical manner if you put in "1" for it. The calculator will draw the Student's t distribution with the correct degrees of freedom, and shade the area of the graph beyond the t statistic. In addition, the value of t and the value of p will be displayed (the value of p corresponds to the shaded area). You would make your conclusions in the same way as for the regular output.

            As with most other statistical commands, you may use a frequency list in your input (when using the data list syntax).

            Optimization

            Most of the arguments of the T-Test command have default values, and the argument can be omitted if this value is accepted.

            • The draw? argument can be omitted if you don't want graphical output, although you could put "0" in as well.
            • If the draw? argument is omitted, you can omit the alternative argument to use a two-sided test (μ≠μ0). If you include the draw? argument, you have to include this - otherwise there will be confusion as to what the 5th argument means.
            • With data list input, you can always omit the frequency list if you won't be using it.
            • With data list input, if the draw? and alternative arguments are omitted, and your data is in L1, you may omit L1 as well. However, if alternative or draw? is present, you have to include it, or else the syntax may be confused with the syntax for summary stats input.

            The code in the sample problem above can't be optimized, because the alternative argument is 1:

            ::T-Test 10,L1,1

            However, if we were doing a two-sided test, we could omit the alternative and the list arguments (since we're testing L1):

            :T-Test 10,L1,0
can be
:T-Test 10

            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

            History

            Calculator OS Version Description
            TI-83 0.01013 Added
            Property Value
            Hex Value $BB3D
            Categories
            Localizations
            • FR: 2-CompZTest(

            2-SampZTest(

            Overview

            Computes a two-sample z test. alternative=-1 is <; alternative=0 is ≠; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results.
            Color#: 10 - 24 or color name pasted from [vars] COLOR.

            Availability: Token only available from within the Basic editor.

            Syntax

            2-SampZTest( σ1,σ2[,listname1,listname2,freqlist1,freqlist2,alternative,drawflag,color#])

            Arguments

            NameTypeOptional
            σ
            1Yes
            σYes
            2Yes
            listname1listNameYes
            listname2listNameYes
            freqlist1listYes
            freqlist2listYes
            alternativeYes
            drawflagYes
            color#colorNumYes

            Location

            stat, TESTS, 3:2-SampZTest(

            Overview

            Computes a two-sample z test. alternative=-1 is <; alternative=0 is ≠; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results.
            Color#: 10 - 24 or color name pasted from [vars] COLOR.

            Availability: Token only available from within the Basic editor.

            Syntax

            2-SampZTest(σ1,σ2,x̄1,n1,x̄2,n2[,alternative,drawflag,color#])

            Arguments

            NameTypeOptional
            σ
            1
            σ
            2
            x̄
            1
            n1Yes
            x̄Yes
            2Yes
            n2Yes
            alternativeYes
            drawflagYes
            color#colorNumYes

            Location

            stat, TESTS, 3:2-SampZTest(

            Description

            2-SampZTest( performs a z significance test to compare the means of two populations. This test is valid for simple random samples from populations with known standard deviations. In addition, either the populations must be normally distributed, or the sample sizes have to be sufficiently large (usually, greater than 10).

            The logic behind the test is as follows: we want to test the hypothesis that the true means of the two populations are equal (the null hypothesis). The letter μ is used for a population mean, so this is usually written as μ1=μ2. To do this, we assume that this "null hypothesis" is true, and calculate the probability that the difference between the two means occurred, under this assumption. If this probability is sufficiently low (usually, 5% is the cutoff point), we conclude that since it's so unlikely that the data could have occurred under the null hypothesis, the null hypothesis must be false, and therefore the means are not equal. If, on the other hand, the probability is not too low, we conclude that the data may well have occurred under the null hypothesis, and therefore there's no reason to reject it.

            In addition to the null hypothesis, we must have an alternative hypothesis as well - usually this is simply that the two means are not equal. However, in certain cases when we have reason to suspect that one mean is greater than the other (such as when we are trying to verify a claim that one mean is greater), our alternative hypothesis may be that the first mean is greater than the second (μ1>μ2) or less (μ1<μ2).

            As for the 2-SampZTest( command itself, there are two ways of calling it: after giving the two standard deviations, you may give it a list of all the sample data, or the necessary statistics about the list (x1 and x2 are the sample means, and n1 and n2 are the sample sizes). In either case, you can indicate what the alternate hypothesis is, by a value of 0, -1, or 1 for the alternative argument. 0 indicates a two-sided hypothesis of μ1≠μ2, -1 indicates μ1<μ2, and 1 indicates μ1>μ2. (In fact, the calculator will treat any negative value as -1, and any positive value as 1).

            Although you can access the 2-SampZTest( command on the home screen, via the catalog, there's no need: the 2-SampZTest… interactive solver, found in the statistics menu, is much more intuitive to use - you don't have to memorize the syntax.

            In either case, it's important to understand the output of 2-SampZTest. Here are the meanings of each line:

            • The first line, involving μ1 and μ2, is the alternative hypothesis.
            • z is the test statistic, the standardized difference between the means. If the null hypothesis is true, it should be close to 0.
            • p is the probability that the difference between μ1 and μ2 (the two means) would occur if the null hypothesis is true. When the value is sufficiently small, we reject the null hypothesis and conclude that the alternative hypothesis is true. You should have a cutoff value ready, such as 5% or 1%. If p is lower, you "reject the null hypothesis on a 5% (or 1%) level" in technical terms.
            • x-bar1 and x-bar2 are the two sample means.
            • n1 and n2 are the sample sizes.

            Sample Problem

            Your school claims that the average SAT score of students at the school is higher than at a rival school. You took samples of SAT scores from students at both schools (and stored them to L1 and L2). Although you didn't know the standard deviations, you decided to use the value 200 that you found online as an estimate.

            You now have all the data. You're assuming σ1 and σ2 are both 200; the two data lists are L1 and L2. Since the school's claim is that your school's score is higher, that will be your alternative hypothesis (μ1>μ2), which corresponds to a value of 1. The code you'd use is:

            :2-SampZTest(200,200,L1,L2,1

            Alternatively, you could calculate the mean and sample size of your sample, and put those into the command instead. Suppose you obtained SAT scores from 60 students at your school and 40 students at the rival school, and that the means were 1737 and 1623. Then your code is:

            :2-SampZTest(200,200,1737,60,1623,40,1

            You will see the following output:

            Z-Test
 μ1>μ2
 z=2.792418307
 p=.0026158434
 x1=1737
 x2=1623
 n1=60
 n2=40

            The most important part of this output is "p=.0026158434". This value of p is much smaller than 1% or 0.01. This is significant on the 1% level, so we reject the null hypothesis and conclude that the alternative hypothesis is true: μ1>μ2, that is, your school's average SAT score is indeed higher.

            Advanced Uses

            The final argument of 2-SampZTest(, draw?, will display the results in a graphical manner if you put in "1" for it. The calculator will draw the standard normal curve, and shade the area of the graph beyond the z statistic. In addition, the value of z and the value of p will be displayed (the value of p corresponds to the shaded area). You would make your conclusions in the same way as for the regular output.

            As with most other statistical commands, you may use a frequency list in your input (when using the data list syntax). If you do, then both lists must have frequencies, and the order of the arguments would be list1, list2, frequency1, frequency2.

            Optimization

            Most of the arguments of the 2-SampZTest( command have default values, and the argument can be omitted if this value is accepted.

            • The draw? argument can be omitted if you don't want graphical output, although you could put "0" in as well.
            • If the draw? argument is omitted, you can omit the alternative argument to use a two-sided test (μ1≠μ2). If you include the draw? argument, you have to include this - otherwise there will be confusion as to what the 5th argument means.
            • With data list input, you can always omit the frequency lists if you won't be using them.
            • With data list input, if the draw? and alternative arguments are omitted, and your data is in L1 and L2 (and you're not using frequency lists), you may omit L1 and L2 - those are default parameters. However, if alternative or draw? is present, you have to include it, or else the syntax may be confused with the syntax for summary stats input.

            The code in the sample problem above can't be optimized, because the alternative argument is 1:

            :2-SampZTest(200,200,L1,L2,1

            However, if we were doing a two-sided test, we could omit the alternative argument as well as the lists:

            :2-SampZTest(200,200,L1,L2,0
can be
:2-SampZTest(200,200

            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

            History

            Calculator OS Version Description
            TI-83 0.01013 Added
            Property Value
            Hex Value $BB3E
            Categories
            Localizations
            • FR: 1-PropZTest(

            1-PropZTest(

            Overview

            Computes a one-proportion z test. alternative=-1 is <; alternative=0 is ≠; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results.
            Color#: 10 - 24 or color name pasted from [vars] COLOR.

            Availability: Token only available from within the Basic editor.

            Syntax

            1-PropZTest(p0,x,n[,alternative,drawflag, color#])

            Arguments

            NameTypeOptional
            p0
            x
            n
            alternativeYes
            drawflagYes
            color#colorNumYes

            Location

            stat, TESTS, 5:1-PropZTest(

            Description

            1-PropZTest performs an z-test to compare a population proportion to a hypothesis value. This test is valid for sufficiently large samples: only when the number of successes (x in the command syntax) and the number of failures (n-x) are both >5.

            The logic behind the test is as follows: we want to test the hypothesis that the true proportion is equal to some value p0 (the null hypothesis). To do this, we assume that this "null hypothesis" is true, and calculate the probability that the (usually, somewhat different) actual proportion occurred, under this assumption. If this probability is sufficiently low (usually, 5% is the cutoff point), we conclude that since it's so unlikely that the data could have occurred under the null hypothesis, the null hypothesis must be false, and therefore the true proportion is not equal to p0. If, on the other hand, the probability is not too low, we conclude that the data may well have occurred under the null hypothesis, and therefore there's no reason to reject it.

            Commonly used notation has the letter π being used for the true population proportion (making the null hypothesis be π=p0). TI must have been afraid that this would be confused with the real number π, so on the calculator, "prop" is used everywhere instead.

            In addition to the null hypothesis, we must have an alternative hypothesis as well - usually this is simply that the proportion is not equal to p0. However, in certain cases, our alternative hypothesis may be that the proportion is greater or less than p0.

            The arguments to 1-PropZTest( are as follows:

            • p0 - the value for the null hypothesis (the proportion you're testing for)
            • x - the success count in the sample
            • n - the total size of the sample (so the sample proportion would be x__/n)
            • alternative (optional if you don't include draw?) - determines the alternative hypothesis
              • 0 (default value) - prop≠p0
              • -1 (or any negative value) - prop<p0
              • 1 (or any positive value) - prop>p0
            • draw? (optional) set this to 1 if you want a graphical rather than numeric result

            Although you can access the 1-PropZTest command on the home screen, via the catalog, there's no need: the 1-PropZTest… interactive solver, found in the statistics menu, is much more intuitive to use - you don't have to memorize the syntax.

            In either case, it's important to understand the output of 1-PropZTest. Here are the meanings of each line:

            • The first line, involving "prop" and p0, is the alternative hypothesis.
            • z is the test statistic. If the null hypothesis is true, it should be close to 0.
            • p is the probability that the difference between the proportion and p0 would occur if the null hypothesis is true. When the value is sufficiently small, we reject the null hypothesis and conclude that the alternative hypothesis is true. You should have a cutoff value ready, such as 5% or 1%. If p is lower, you "reject the null hypothesis on a 5% (or 1%) level" in technical terms.
            • p-hat is the sample proportion, x__/n.
            • n is the sample size.

            Advanced Uses

            The final optional argument of 1-PropZTest, draw?, will display the results in a graphical manner if you put in "1" for it. The calculator will draw the standard normal distribution, and shade the area of the graph that corresponds to the probability p. In addition, the value of z and the value of p will be displayed. You would make your conclusions in the same way as for the regular output.

            Optimization

            Some of the arguments of the 1-PropZTest command have default values, and the argument can be omitted if this value is used.

            • The draw? argument can be omitted if you don't want graphical output, although you could put "0" in as well.
            • If the above argument is omitted, and you're doing a two sided test, you may omit the alternative argument.

            Example:

            :1-PropZTest(.5,22,50,0,0
can be
:1-PropZTest(.5,22,50

            Error Conditions

            • ERR:DOMAIN is thrown if p0 or x__/n are not between 0 and 1, or x is negative or greater than n (however, any real value for alternative and draw? will work)

            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

            History

            Calculator OS Version Description
            TI-83 0.01013 Added
            Property Value
            Hex Value $BB3F
            Categories
            Localizations
            • FR: 2-PropZTest(

            2-PropZTest(

            Overview

            Computes a two-proportion z test. alternative=-1 is <; alternative=0 is ≠; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results.
            Color#: 10 - 24 or color name pasted from [vars] COLOR.

            Availability: Token only available from within the Basic editor.

            Syntax

            2-PropZTest(x1,n1,x2,n2[,alternative,drawflag, color#])

            Arguments

            NameTypeOptional
            x1
            n1
            x2
            n2
            alternativeYes
            drawflagYes
            color#colorNumYes

            Location

            stat, TESTS, 6:2-PropZTest(

            Description

            2-PropZTest( performs a_z_-test to compare two population proportions. This test is valid for sufficiently large samples: only when the number of successes (x in the command syntax) and the number of failures (n-x) are both >5, for both populations.

            The logic behind the test is as follows: we want to test the hypothesis that the proportions are equal (the null hypothesis). To do this, we assume that this "null hypothesis" is true, and calculate the probability that the differences between the two proportions occurred, under this assumption. If this probability is sufficiently low (usually, 5% is the cutoff point), we conclude that since it's so unlikely that the data could have occurred under the null hypothesis, the null hypothesis must be false, and therefore the proportions are not equal. If, on the other hand, the probability is not too low, we conclude that the data may well have occurred under the null hypothesis, and therefore there's no reason to reject it.

            Commonly used notation has the letters π1 and π2 being used for the true population proportions (making the null hypothesis be π1=π2). TI must have been afraid that this would be confused with the real number π, so on the calculator, "p1" and "p2" are used everywhere instead.

            In addition to the null hypothesis, we must have an alternative hypothesis as well - usually, this is simply that the proportions are not equal. However, in certain cases, our alternative hypothesis may be that one proportion is greater or less than the other.

            The arguments to 2-PropZTest( (which must be integers, or the calculator will generate a domain error) are as follows:

            • x1 - the success count in the first sample
            • n1 - the total size of the first sample (so the sample proportion would be x1__/n1)
            • x2 - the success count in the second sample
            • n2 - the total size of the second sample (so the sample proportion would be x2__/n2)
            • alternative (optional if you don't include draw?) - determines the alternative hypothesis
              • 0 (default value) - p1≠p2
              • -1 (or any negative value) - p1<p2
              • 1 (or any positive value) - p1>p2
            • draw? (optional) set this to 1 if you want a graphical rather than numeric result

            Although you can access the 2-PropZTest( command on the home screen, via the catalog, there's no need: the 2-PropZTest(… interactive solver, found in the statistics menu, is much more intuitive to use - you don't have to memorize the syntax.

            In either case, it's important to understand the output of 2-PropZTest(. Here are the meanings of each line:

            • The first line, involving p1 and p2, is the alternative hypothesis.
            • z is the test statistic. If the null hypothesis is true, it should be close to 0.
            • p is the probability that the difference between the two proportions would occur if the null hypothesis is true. When the value is sufficiently small, we reject the null hypothesis and conclude that the alternative hypothesis is true. You should have a cutoff value ready, such as 5% or 1%. If p is lower, you "reject the null hypothesis on a 5% (or 1%) level" in technical terms.
            • p-hat1 is the sample proportion x1__/n1.
            • p-hat2 is the sample proportion x2__/n2.
            • p-hat is the total sample proportion
            • n1 is the first sample size.
            • n2 is the second sample size.

            Advanced Uses

            The final optional argument of 2-PropZTest(, draw?, will display the results in a graphical manner if you put in "1" for it. The calculator will draw the standard normal distribution, and shade the area of the graph that corresponds to the probability p. In addition, the value of z and the value of p will be displayed. You would make your conclusions in the same way as for the regular output.

            Optimization

            Some of the arguments of the 2-PropZTest( command have default values, and the argument can be omitted if this value is used.

            • The draw? argument can be omitted if you don't want graphical output, although you could put "0" in as well.
            • If the above argument is omitted, and you're doing a two-sided test, you may omit the alternative argument.

            Example:

            :2-PropZTest(22,50,48,100,0,0
can be
:2-PropZTest(22,50,48,100

            Error Conditions

            • ERR:DOMAIN is thrown if the values of the arguments entered are not integers.

            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Myles_Zadok.

            History

            Calculator OS Version Description
            TI-83 0.01013 Added
            Property Value
            Hex Value $BB40
            Categories
            Localizations
            • FR: χ²-Test(

            χ²-Test(

            Overview

            Performs a chi-square test. drawflag=1 draws results; drawflag=0 calculates results.
            Color#: 10 - 24 or color name pasted from [vars] COLOR.

            Availability: Token only available from within the Basic editor.

            Syntax

            χ²-Test(observedmatrix,expectedmatrix[,drawflag,color#])

            Arguments

            NameTypeOptional
            χ²-
            observedmatrixmatrix
            expectedmatrixmatrixYes
            drawflagYes
            color#colorNumYes

            Location

            stat, TESTS, C:Test(

            Description

            This command performs a χ² test of independence. This test is used to assess the independence of two categorical variables with known frequencies. The test is only valid for a simple random sample from the population, and only if all the frequencies are sufficiently large (greater than 5).

            Note: this test is different from the χ² goodness of fit test, which the TI-83 calculators don't have a command for. For a program that will perform the χ² goodness-of-fit test, see the goodness-of-fit test routine.

            To use this test, you need a matrix containing a contingency table. This is a table in which every row corresponds to a value of the first variable, and every column to a value of the second. The number in each cell represents the frequency with which the corresponding values of the two variables occur together. For example: suppose that the two variables are sex (male and female) and eye color (blue, brown, and green). The contingency table would have two rows and three columns. The cell in the first row and column would be the number of blue-eyed men in the sample, the cell in the second row and first column would be the number of blue-eyed women, and so on.

            The χ²-Test( command takes two arguments: the observed matrix and expected matrix. The first of these should be the contingency table you've already completed, presumably in the Matrix editor. The expected matrix does not need to already exist: the χ²-Test( command will calculate and store the expected frequencies (under the assumption that the variables are independent) to this matrix.

            The command is primarily for use in a program. Although you can access the χ²-Test( command on the home screen, via the catalog, there's no need: you can use the χ²-Test… interactive solver found in the menu instead.

            In either case, it's important to understand the output of χ²-Test(. Here are the meanings of each line:

            • χ² is the test statistic, calculated from the differences between the observed and the expected matrices.
            • p is the probability associated with the test statistic. We use p to test the null hypothesis that the two variables are independent. If p is low (usually, if it's <0.05) this means there's little chance that two independent variables would have a contingency table so different from the expected, and we reject the null hypothesis (so we'd conclude that the two variables are not independent).
            • df is the degrees of freedom, defined as (# of rows - 1)*(# of columns - 1), important for calculating p.

            Sample Problem

            You want to compare the effectiveness of three treatments in curing a terminal disease. You have obtained data for 100 patients who had the disease, which contained information on the treatment used, and whether the patient lived or died. You put this information in a contingency table:

            Lived

            Died

            Treatment A

            40

            10

            Treatment B

            27

            6

            Treatment C

            11

            6

            To perform the test, you store this information to a matrix such as [A], either through the matrix editor or by hand:

            :[[40,10],[27,6],[11,6→[A]

            You submit this matrix as the first argument, and some other matrix (such as [B]) for the second:

            :χ²-Test([A],[B]

            The output looks something like this:

            χ²-Test
 χ²=2.14776311
 p=.3416796916
 df=2

            The most important part of this output is the line p=.3416796916 - the probability of getting such results under the hypothesis that the treatments and survival rate are independent. This value is greater than .05, so the data is not significant on a 5% level. There is not enough evidence to reject the null hypothesis, so treatment and survival rate may very well be independent. In non-mathematical language, this means that there's no reason to believe the treatments vary in effectiveness.

            Advanced Uses

            The final argument of χ²-Test(, draw?, will display the results in a graphical manner if you put in "1" for it. The calculator will draw the χ² distribution with the correct degrees of freedom, and shade the area of the graph beyond the χ² statistic. In addition, the same values as usually will be calculated and displayed. You would make your conclusions in the same way as for the regular output.

            See Also

            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Myles_Zadok.

            History

            Calculator OS Version Description
            TI-83 0.01013 Added
            Property Value
            Hex Value $BB41
            Categories
            Localizations
            • FR: ZintConf

            ZInterval

            Overview

            Computes a z confidence interval.

            Comment:Data list input

            Availability: Token only available from within the Basic editor.

            Syntax

            ZIntervalσ[,listname,freqlist,confidence level]

            Arguments

            NameTypeOptional
            σ
            listnamelist
            freqlistlist
            confidence level

            Location

            stat, TESTS, 7:ZInterval

            Overview

            Computes a z confidence interval.

            Comment:Summary stats input

            Availability: Token only available from within the Basic editor.

            Syntax

            ZIntervalσ,x̄,n[,confidence level]

            Arguments

            NameTypeOptional
            σ
            x̄
            nYes
            confidence levelYes

            Location

            stat, TESTS, 7:ZInterval

            Description

            The ZInterval command calculates a confidence interval for the mean value of a population, at a specific confidence level: for example, if the confidence level is 95%, you are 95% certain that the mean lies within the interval you get. Use ZInterval when you have a single variable to analyze, and you already know the standard deviation. The ZInterval assumes that your distribution is normal, but it will work for other distributions if the sample size is large enough.

            There are two ways to call the ZInterval command: by supplying it with needed sample statistics (mean and sample size), or by entering a list and letting the calculator work the statistics out. In either case, you will need to enter the standard deviation and desired confidence level as well.

            Sample Problem

            You want to know the average height of a student at your school. You haven't asked everyone, but you took a random sample of 30 people and found out their height (and stored it to L1). You've read in your textbook that the standard deviation of teenagers' heights is usually 6 inches. You've decided to use a 95% confidence interval.

            Since the syntax for entering a data list is ZInterval std. deviation, list, confidence level, the code would look like:

            :ZInterval 6,L1,95
you can also use
:ZInterval 6,L1,.95

            Alternatively, you could calculate the mean and sample size and enter those instead. The sample size in this case is 30; let's say the mean was 63 inches. The syntax for entering statistics is ZInterval std. deviation, mean, sample size, confidence level, so your code would look like:

            :ZInterval 6,63,30,95
you can also use
:ZInterval 6,63,30,.95

            Of course, the main use of the ZInterval command is in a program. While you can enter the ZInterval command on the home screen as well (just look in the catalog for it), it would probably be easier to select ZInterval… from the STAT>TEST menu (see the sidebar).

            Advanced Uses

            As with most other statistical commands, you can enter a second list after the data list, to add frequencies (only with the data list syntax, of course). The frequency list must contain non-negative real numbers, and can't be all 0.

            Optimization

            Using the data list syntax, all items but the standard deviation are optional: the calculator will assume you want to use L1 for your data unless another list is supplied, and that the confidence level you want is 95% unless you give another one. Using the summary stats syntax, the confidence level is also optional - again, the calculator will assume 95%. This means we can rewrite our code above in a simpler manner:

            :ZInterval 6,L1,95
can be
:ZInterval 6

            :ZInterval 6,63,30,95
can be
:ZInterval 6,63,30

            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

            History

            Calculator OS Version Description
            TI-83 0.01013 Added
            Property Value
            Hex Value $BB42
            Categories
            Localizations
            • FR: 2-CompZIntC(

            2-SampZInt(

            Overview

            Computes a two-sample z confidence interval.

            Comment:Data list input

            Availability: Token only available from within the Basic editor.

            Syntax

            2-SampZInt(σ1,σ2[,listname1,listname2,freqlist1,freqlist2,confidence level])

            Arguments

            NameTypeOptional
            σ
            1Yes
            σYes
            2Yes
            listname1listNameYes
            listname2listNameYes
            freqlist1listYes
            freqlist2listYes
            confidence levelYes

            Location

            stat, TESTS, 9:2-SampZInt(

            Overview

            Computes a two-sample z confidence interval.

            Comment:Summary stats input

            Availability: Token only available from within the Basic editor.

            Syntax

            2-SampZInt(σ1,σ2,x̄1,n1,x̄2,n2[,confidence level])

            Arguments

            NameTypeOptional
            σ
            1
            σ
            2
            x̄
            1
            n1Yes
            x̄Yes
            2Yes
            n2Yes
            confidence levelYes

            Location

            stat, TESTS, 9:2-SampZInt(

            Description

            The 2-SampZInt( command uses the techniques of Z Intervals to compute an interval for the difference between the means of two independent populations, at a specified confidence level. Use 2-SampZInt( when you have two independent variables to compare, and you already know their standard deviations. The 2-SampZInt( command assumes that both variables are distributed normally, but it will work for other distributions if the sample size is large enough.

            There are two ways to call this command: by supplying it with needed sample statistics (mean and sample size, for both data sets), or by entering two lists and letting the calculator work the statistics out. In either case, you will need to enter the standard deviation and desired confidence level as well.

            In the data list syntax, σ1 and σ2 are the two standard deviations.
            In the summary stats syntax, σ1 and σ2 are the two standard deviations, x1 and x2 the two sample means, and n1 and n2 the two sample sizes.

            The output will contain an open interval (a, b) that is your answer: the difference between the two means will lie in this interval. Specifically, it is the second mean subtracted from the first - μ1-μ2. If you're interested in the reverse difference, just flip the signs on the interval.

            Tip: don't use this command in a matched-pairs setting when you can match the two samples up by units or subjects. Instead, take the difference between the two samples in each matched pair, and use a regular ZInterval.

            Sample Problem

            You want to compare the average height of a freshman and a senior at your school. You haven't asked everyone, but you took a random sample of 40 people from each class and found out their heights (and stored them to L1 and L2). You've read in your textbook that the standard deviation of teenagers' heights is usually 6 inches. You've decided to use a 95% confidence interval.

            Based on the data list syntax for a 2-SampZInt(, here is your code:

            :2-SampZInt(6,6,L1,L2,95
you can also use
:2-SampZInt(6,6,L1,L2,.95

            Alternatively, you could calculate the mean and sample size and enter those instead. The sample size in this case is 40 for both data sets; let's say the means were 57 inches and 67 inches. You now have all the needed statistics:

            • σ1 is the standard deviation for freshmen: 6 inches
            • σ2 is the standard deviation for seniors: also 6 inches
            • x1 is the mean height of freshmen: 57 inches
            • n1 is the number of freshmen in the sample: 40
            • x2 is the mean height of seniors: 67 inches
            • n2 is the number of seniors in the sample: 40

            This means that the code is:

            :2-SampZInt(6,6,57,40,67,40,95
you can also use
:2-SampZInt(6,6,57,40,67,40,.95

            Of course, the main use of the 2-SampZInt( command is in a program. While you can enter the command on the home screen as well (just look in the catalog for it), it would probably be easier to select 2-SampZInt… from the STAT>TEST menu (see the sidebar), since you don't have to remember the syntax.

            Advanced Uses

            As with most other statistical commands, you can add frequencies to the lists (only with the data list syntax, of course); if you do, both lists must have frequencies, and the arguments go in the order first data list, second data list, first freq. list, second freq. list. Each frequency list must contain non-negative real numbers, which can't be all 0.

            Optimization

            Using the data list syntax, all items but the standard deviations are optional: the calculator will assume you want to use L1 and L2 for your data unless other lists are supplied, and that the confidence level you want is 95% unless you give another one. Using the summary stats syntax, the confidence level is also optional - again, the calculator will assume 95%. This means we can rewrite our code above in a simpler manner:

            :2-SampZInt(6,6,L1,L2,95
can be
:2-SampZInt(6,6

            :2-SampZInt(6,6,57,40,67,40,95
can be
:2-SampZInt(6,6,57,40,67,40

            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Timothy Foster.

            History

            Calculator OS Version Description
            TI-83 0.01013 Added
            Property Value
            Hex Value $BB43
            Categories
            Localizations
            • FR: 1-PropZInt(

            1-PropZInt(

            Overview

            Computes a one-proportion z confidence interval.

            Availability: Token only available from within the Basic editor.

            Syntax

            1-PropZInt(x,n[,confidence level])

            Arguments

            NameTypeOptional
            x
            n
            confidence levelYes

            Location

            stat, TESTS, A:1-PropZInt(

            Description

            The 1-PropZInt( command calculates a confidence interval for a proportion, at a specific confidence level: for example, if the confidence level is 95%, you are 95% certain that the proportion lies within the interval you get. The command assumes that the sample is large enough that the normal approximation to binomial distributions is valid: this is true if, in the sample you take, the positive and negative counts are both >5.

            The 1-PropZInt( command takes 3 arguments. The first, x, is the positive count in the sample. The second, n, is the total size of the sample. (So the sample proportion is equal to x out of n). The third argument is the confidence level, which defaults to 95.

            The output gives you a confidence interval of the form (a,b), meaning that the true proportion π is most likely in the range a<π<b, and the value of x__/n.

            Sample Problem

            You want to know the proportion of students at your school that support a particular political candidate. You take a random sample of 50 students, and find that 22 of them support that candidate. 22, the positive count, and 50-22=28, the negative count, are both >5, so the assumption is satisfied.

            Using 22 for x, and 50 for n, you decide to find a 95% confidence interval. The syntax for that is:

            :1-PropZInt(22,50,95
which can also be
:1-PropZInt(22,50,.95

            The output if you run the above code will look approximately like this:

            1-PropZInt
 (.30241,.57759)
 p=.44
 n=50

            This tells you that between about 30.2% and about 57.8% of the students at your school are in support of the political candidate.

            Optimization

            If the confidence level is 95%, you can omit the final 95, since that is the default value:

            :1-PropZInt(22,50,95
can be
:1-PropZInt(22,50

            Error Conditions

            • ERR:DOMAIN is thrown if the sample proportion is not between 0 and 1, any argument is negative, or the confidence level is 100 or more.

            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

            History

            Calculator OS Version Description
            TI-83 0.01013 Added
            Property Value
            Hex Value $BB44
            Categories
            Localizations
            • FR: 2-PropZInt(

            2-PropZInt(

            Overview

            Computes a two-proportion z confidence interval.

            Availability: Token only available from within the Basic editor.

            Syntax

            2-PropZInt(x1,n1,x2,n2[,confidence level])

            Arguments

            NameTypeOptional
            x1
            n1
            x2
            n2
            confidence levelYes

            Location

            stat, TESTS, B:2-PropZInt(

            Description

            The 2-PropZInt( command calculates a confidence interval for the difference between two proportions, at a specific confidence level: for example, if the confidence level is 95%, you are 95% certain that the difference lies within the interval you get. The command assumes that the sample is large enough that the normal approximation to binomial distributions is valid: this is true if, in both samples involved, the positive and negative counts are both >5.

            The 1-PropZInt( command takes 5 arguments. The first two, x1 and n1 are the positive count and total count in the first sample (so the estimated value of the first proportion is x1 out of n1. The next two arguments, x2 and n2, are the positive count and total count in the second sample.

            The output gives you a confidence interval of the form (a,b), which is the range of values for the difference π1-π2 (where π1 and π2 are the first and second proportions respectively). If you were looking for the difference π2-π1 all you have to do is switch two sides and negate the numbers in the interval.

            Sample Problem

            You want to compare the proportion of students at your school and at a friend's school. that support a particular political candidate. You take a random sample of 50 students, and find that 22 of them support that candidate. Your friend took a random sample of 75 students at his school, and found that 28 supported the candidate.

            The first proportion is the proportion of supporters at your school. 22 out of 50 students support the candidate, so x1=22 and n1=50.
            The second proportion is the proportion of supporters at your friend's school. 28 out of 75 students support the candidate, so x2=28 and n2=75.
            If you decided to do a 95% confidence interval, you would add the argument 95 after all these, so the syntax would be as follows:

            :2-PropZInt(22,50,28,75,95
which can also be
:2-PropZInt(22,50,28,75,.95

            The output if you run the above code will look approximately like this:

            1-PropZInt
 (-.1092,.24249)
 p1=.44
 p2=.3733333333
 n1=50
 n2=75

            This tells you that between about the difference betwen the proportions is between about -0.11 (your school's proportion being about 0.11 less than your friend's school's proportion) to about 0.24 (your school's proportion being about 0.24 greater than your friend's school's proportion).

            Optimization

            If the confidence level is 95%, you can omit the final 95, since that is the default value:

            :2-PropZInt(22,50,28,75,95
can be
:2-PropZInt(22,50,28,75

            Error Conditions

            • ERR:DOMAIN is thrown if either proportion is not between 0 and 1, or xi is negative or greater than ni, or the confidence level is negative or at least 100.

            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

            History

            Calculator OS Version Description
            TI-83 0.01013 Added
            Property Value
            Hex Value $BB45
            Categories
            Localizations
            • FR: GraphStyle(

            GraphStyle(

            Overview

            Sets a graphstyle for function#.

            Availability: Token only available from within the Basic editor.

            Syntax

            GraphStyle(function#,graphstyle#)

            Arguments

            NameTypeOptional
            function#
            graphstyle#

            Location

            prgm, CTL, H:GraphStyle(

            Description

            The GraphStyle( command allows you to set the graphing style of an equation (line, thick line, dotted line, etc.) from within a program.

            Its first argument, equation #, is the number of the equation whose graphing style you want to change - this depends on the mode you're in. For example, if you wanted to change the graphing style of Y1, you would need to be in function mode and use the value 1 for this argument. If you wanted to change the graphing style of r4, you would need to be in polar mode and use the value 4.

            The second argument is a number from 1 to 7, which translates to a graphing style as follows:

            • 1 - a normal line, usually the default graph style.
            • 2 - a thick line (three pixels wide).
            • 3 - a line, with everything above it shaded (only valid in function mode).
            • 4 - a line, with everything below it shaded (only valid in function mode).
            • 5 - a path: a line, with a ball moving along it as it is graphed (not valid in sequential mode).
            • 6 - animated: a ball moving along the graph (not valid in sequential mode).
            • 7 - a dotted line.

            Compare this to the effect of Connected or Dot mode. When either of these modes is set, all equations, from all graphing modes, are reverted to line style or dotted line style respectively; furthermore, it becomes the default graph style and clearing an equation will revert it to this graph style. The GraphStyle( command simply overrides these modes temporarily.

            Advanced

            In shading modes (3 and 4), the shading style cycles as follows:

            • The first function graphed shades using vertical lines one pixel apart
            • The second function shades using horizontal lines one pixel apart
            • The third function shades using negatively sloping diagonal lines, two pixels apart.
            • The fourth function shades using positively sloping diagonal lines, two pixels apart.
            • After that, functions will cycle through these four styles in that order.

            Error Conditions

            • ERR:DOMAIN if the equation # is not a valid equation number in this mode, or if style # is not an integer 1-7.
            • ERR:INVALID if the graphing style chosen is not valid for the current graphing mode.

            Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, kg583.

            History

            Calculator OS Version Description
            TI-83 0.01013 Added
            Property Value
            Hex Value $BB46
            Categories
            Localizations
            • FR: 2-CompTTest(

            2-SampTTest

            Overview

            Computes a two-sample t test. alternative=-1 is <; alternative=0 is ≠; alternative=1 is >. pooled=1 pools variances; pooled=0 does not pool variances. drawflag=1 draws results; drawflag=0 calculates results.
            Color#: 10 - 24 or color name pasted from [vars] COLOR.

            Availability: Token only available from within the Basic editor.

            Syntax

            2-SampTTest [listname1,listname2,freqlist1,freqlist2,alternative,pooled,drawflag,color#])

            Arguments

            NameTypeOptional
            listname1listNameYes
            listname2listNameYes
            freqlist1listYes
            freqlist2listYes
            alternativeYes
            pooledYes
            drawflagYes
            color#colorNumYes

            Location

            stat, TESTS, 4:2-SampTTest

            Overview

            Computes a two-sample t test. alternative=-1 is <; alternative=0 is ≠; alternative=1 is >. pooled=1 pools variances; pooled=0 does not pool variances. drawflag=1 draws results; drawflag=0 calculates results.
            Color#: 10 - 24 or color name pasted from [vars] COLOR.

            Availability: Token only available from within the Basic editor.

            Syntax

            2-SampTTestx̄1,Sx1,n1,v2,Sx2,n2[,alternative,pooled,drawflag,color#])

            Arguments

            NameTypeOptional
            x̄
            1
            Sx1
            n1
            v2
            Sx2
            n2Yes
            alternativeYes
            pooledYes
            drawflagYes
            color#colorNumYes

            Location

            stat, TESTS, 4:2-SampTTest

            Description

            2-SampTTest performs a t significance test to compare the means of two populations. This test is valid for simple random samples from populations with unknown standard deviations. In addition, either the populations must be normally distributed, or the sample sizes have to be sufficiently large (usually, greater than 10).

            The logic behind the test is as follows: we want to test the hypothesis that the true means of the two populations are equal (the null hypothesis). The letter μ is used for a population mean, so this is usually written as μ1=μ2. To do this, we assume that this "null hypothesis" is true, and calculate the probability that the difference between the two means occurred, under this assumption. If this probability is sufficiently low (usually, 5% is the cutoff point), we conclude that since it's so unlikely that the data could have occurred under the null hypothesis, the null hypothesis must be false, and therefore the means are not equal. If, on the other hand, the probability is not too low, we conclude that the data may well have occurred under the null hypothesis, and therefore there's no reason to reject it.

            In addition to the null hypothesis, we must have an alternative hypothesis as well - usually this is simply that the two means are not equal. However, in certain cases when we have reason to suspect that one mean is greater than the other (such as when we are trying to verify a claim that one mean is greater), our alternative hypothesis may be that the first mean is greater than the second (μ1>μ2) or less (μ1<μ2).

            As for the 2-SampTTest command itself, there are two ways of calling it: you may give it a list of all the sample data, or the necessary statistics about the list (x1 and x2 are the sample means, s1 and s2 the sample standard deviations, and n1 and n2 the sample sizes). In either case, you can indicate what the alternate hypothesis is, by a value of 0, -1, or 1 for the alternative argument. 0 indicates a two-sided hypothesis of μ1≠μ2, -1 indicates μ1<μ2, and 1 indicates μ1>μ2. (In fact, the calculator will treat any negative value as -1, and any positive value as 1).

            Although you can access the 2-SampTTest command on the home screen, via the catalog, there's no need: the 2-SampTTest… interactive solver, found in the statistics menu, is much more intuitive to use - you don't have to memorize the syntax.

            In either case, it's important to understand the output of 2-SampTTest. Here are the meanings of each line:

            • The first line, involving μ1 and μ2, is the alternative hypothesis.
            • t is the test statistic, the standardized difference between the means. If the null hypothesis is true, it should be close to 0.
            • p is the probability that the difference between μ1 and μ2 (the two means) would occur if the null hypothesis is true. When the value is sufficiently small, we reject the null hypothesis and conclude that the alternative hypothesis is true. You should have a cutoff value ready, such as 5% or 1%. If p is lower, you "reject the null hypothesis on a 5% (or 1%) level" in technical terms.
            • x-bar1 and x-bar2 are the two sample means.
            • Sx1 and Sx2 are the two sample standard deviations.
            • n1 and n2 are the sample sizes.

            Sample Problem

            Your school claims that the average SAT score of students at the school is higher than at a rival school. You took samples of SAT scores from students at both schools (and stored them to L1 and L2).
            Since the school's claim is that your school's score is higher, that will be your alternative hypothesis (μ1>μ2), which corresponds to a value of 1. The code you'd use is:

            :2-SampTTest L1,L2,1

            Alternatively, you could calculate the mean, standard deviation, and size of your samples, and put those into the command instead. Suppose you obtained SAT scores from 60 students at your school and 40 students at the rival school, the means were 1737 and 1623, and the standard deviation 211 and 218. Then your code is:

            :2-SampTTest 1737,211,60,1623,218,40,1

            You will see the following output:

            2-SampTTest
 μ1>μ2
 z=2.594854858
 p=.0056059824
 x1=1737
 x2=1623
 Sx1=211
 Sx2=218
 n1=60
 n2=40

            The most important part of this output is "p=.0056059824". This value of p is smaller than 1% or 0.01. This is significant on the 1% level, so we reject the null hypothesis and conclude that the alternative hypothesis is true: μ1>μ2, that is, your school's average SAT score is indeed higher.

            Advanced Uses

            The final optional argument of 2-SampTTest, draw?, will display the results in a graphical manner if you put in "1" for it. The calculator will draw the distribution, and shade the area of the graph beyound the t statistic. In addition, the value of t and the value of p will be displayed (the value of p corresponds to the shaded area). You would make your conclusions in the same way as for the regular output.

            The optional argument pooled?, if given a nonzero value, will pool the standard deviations to find a combined value which will then be used for both populations. Use this feature if you have reason to believe that the two populations have the same standard deviation.

            As with most other statistical commands, you may use a frequency list in your input (when using the data list syntax). If you do, then both lists must have frequencies, and the order of the arguments would be list1, list2, frequency1, frequency2.

            Optimization

            Some of the arguments of the 2-SampTTest command have default values, and the argument can be omitted if this value is accepted.

            • The draw? argument can be omitted if you don't want graphical output, although you could put "0" in as well.
            • If the draw? argument is omitted, you can omit the pooled? argument if you do not want your standard deviations pooled.
            • If both the above arguments are omitted, and you're doing a two sided test, you may omit the alternative argument.
            • With data list input, you can always omit the frequency lists if you won't be using them.
            • With data list input, if the flags that go at the end are omitted, and you're using the default lists L1 and L2, you may omit those as well.

            The code in the sample problem above can't be optimized, because the alternative argument is 1:

            :2-SampTTest L1,L2,1

            However, if we were doing a two-sided test, we could omit the alternative argument as well as the lists:

            :2-SampTTest L1,L2,0
can be just
:2-SampTTest

            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Timothy Foster.

            History

            Calculator OS Version Description
            TI-83 0.01013 Added
            Property Value
            Hex Value $BB47
            Categories
            Localizations
            • FR: 2-Comp𝐅Test(

            2-Samp𝐅Test

            Overview

            Performs a two-sample 𝐅 test. alternative=-1 is <; alternative=0 is ≠; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results.
            Color#: 10 - 24 or color name pasted from [vars] COLOR.

            Availability: Token only available from within the Basic editor.

            Syntax

            2-Samp𝐅Test[listname1,listname2,freqlist1,freqlist2,alternative,drawflag,color#]

            Arguments

            NameTypeOptional
            𝐅Yes
            listname1listNameYes
            listname2listNameYes
            freqlist1listYes
            freqlist2listYes
            alternativeYes
            drawflagYes
            color#colorNumYes

            Location

            stat, TESTS, E:2-Samp, Test

            Overview

            Performs a two-sample 𝐅 test. alternative=-1 is <; alternative=0 is ≠; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results.
            Color#: 10 - 24 or color name pasted from [vars] COLOR.

            Availability: Token only available from within the Basic editor.

            Syntax

            2-Samp𝐅TestSx1,n1,Sx2,n2[,alternative,drawflag,color#]

            Arguments

            NameTypeOptional
            𝐅
            Sx1
            n1
            Sx2
            n2Yes
            alternativeYes
            drawflagYes
            color#colorNumYes

            Location

            stat, TESTS, E:2-Samp, Test

            Description

            Examples

            Explanation 1

            code 1

            Explanation 2

            code 2

            Error Conditions

            Advanced Notes

            History

            Calculator OS Version Description
            TI-83 0.01013 Added
            Property Value
            Hex Value $BB48
            Categories
            Localizations
            • FR: TintConf

            TInterval

            Overview

            Computes a t confidence interval.

            Comment:Data list input

            Availability: Token only available from within the Basic editor.

            Syntax

            TInterval [listname,freqlist,confidence level]

            Arguments

            NameTypeOptional
            listnamelistYes
            freqlistlistYes
            confidence levelYes

            Location

            stat, TESTS, 8:TInterval

            Overview

            Computes a t confidence interval.

            Comment:Summary stats input

            Availability: Token only available from within the Basic editor.

            Syntax

            TInterval x̄,Sx,n[,confidence level]

            Arguments

            NameTypeOptional
            x̄
            Sx
            nYes
            confidence levelYes

            Location

            stat, TESTS, 8:TInterval

            Description

            The TInterval command calculates a confidence interval for the mean value of a population, at a specific confidence level: for example, if the confidence level is 95%, you are 95% certain that the mean lies within the interval you get. Use TInterval when you have a single variable to analyze, and don't know the standard deviation. The TInterval assumes that your distribution is normal, but it will work for other distributions if the sample size is large enough.

            There are two ways to call the TInterval command: by supplying it with needed sample statistics (mean, sample standard deviation, and sample size), or by entering a list and letting the calculator work the statistics out.

            Sample Problem

            You want to know the average height of a student at your school. You haven't asked everyone, but you took a random sample of 30 people and found out their heights (and stored it to L1). You've decided to use a 95% confidence interval.

            Since the syntax for entering a data list is TInterval list, confidence level, here is your code:

            :TInterval L1,95
you can also use
:TInterval L1,.95

            Alternatively, you could calculate the mean, sample size, and standard deviation, and enter those instead. The sample size is 30; let's say the mean was 63 inches and the standard deviation was 6.2 inches.

            The syntax for entering statistics is TInterval mean, std. deviation, sample size, confidence level, so your code would look like:

            :TInterval 63,6.2,30,95
you can also use
:TInterval 63,6.2,30,.95

            Of course, the main use of the TInterval command is in a program. While you can enter the TInterval command on the home screen as well (just look in the catalog for it), it would probably be easier to select TInterval… from the STAT>TEST menu (see the sidebar).

            One thing to note about using TInterval in a program is that it will not display data if there are lines of code after it. Either the command is on the last line of code, or it will not display anything. The way to work around this is to display the lower and upper variables, as that is where TInterval stores the results.

            :TInterval //some statistical data
:Disp lower,upper

            Advanced Uses

            As with most other statistical commands, you can enter a second list after the data list, to add frequencies (only with the data list syntax, of course). The frequency list must contain non-negative integers, and can't be all 0.

            Optimization

            Using the data list syntax, all the arguments are optional: the calculator will assume you want to use L1 for your data unless another list is supplied, and that the confidence level you want is 95% unless you give another one. Using the summary stats syntax, the confidence level is also optional - again, the calculator will assume 95%. This means we can rewrite our code above in a simpler manner:

            :TInterval L1,95
can be just
:TInterval

            :TInterval 63,6.2,30,95
can be
:TInterval 63,6.2,30

            Error Conditions

            • ERR:DATA TYPE occurs if complex numbers are used (in some cases, ERR:ARGUMENT is thrown instead).
            • ERR:DIM MISMATCH occurs if the data and frequency lists aren't the same size.
            • ERR:DOMAIN occurs in any of the following cases:
              • The confidence level isn't in the range (0 .. 100).
              • The standard deviation isn't positive.
              • The sample size isn't an integer greater than 1.
            • ERR:STAT occurs if the frequency list's elements aren't integers.

            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Myles_Zadok.

            History

            Calculator OS Version Description
            TI-83 0.01013 Added
            Property Value
            Hex Value $BB49
            Categories
            Localizations
            • FR: 2-CompTIntC(

            2-SampTInt

            Overview

            Computes a two-sample t confidence interval. pooled=1 pools variances; pooled=0 does not pool variances.

            Comment:Data list input

            Availability: Token only available from within the Basic editor.

            Syntax

            2-SampTInt[listname1,listname2,freqlist1,freqlist2,confidence level,pooled]

            Arguments

            NameTypeOptional
            listname1listNameYes
            listname2listNameYes
            freqlist1listYes
            freqlist2listYes
            confidence levelYes
            pooledYes

            Location

            stat, TESTS, 0:2-SampTInt

            Overview

            Computes a two-sample t confidence interval. pooled=1 pools variances; pooled=0 does not pool variances.

            Comment:Summary stats input

            Availability: Token only available from within the Basic editor.

            Syntax

            2-SampTIntx̄1,Sx1,n1,x̄2,Sx2,n2[,confidence  level,pooled]

            Arguments

            NameTypeOptional
            x̄
            1
            Sx1
            n1
            x̄
            2
            Sx2
            n2Yes
            confidenceYes
            levelYes
            pooledYes

            Location

            stat, TESTS, 0:2-SampTInt

            Description

            The 2-SampTInt command uses the techniques of T Intervals to compute an interval for the difference between the means of two independent populations, at a specified confidence level. Use 2-SampTInt( when you have two independent variables to compare, and you don't know their standard deviations. The 2-SampTInt command assumes that both your variables are normally distributed, but it will work for other distributions if the sample size is large enough.

            There are two ways to call this command: by supplying it with needed sample statistics (mean, standard deviation, and sample size, for both data sets), or by entering two lists and letting the calculator work the statistics out. In either case, you will need to enter the desired confidence level as well.

            In the summary stats syntax, x1 and x2 the two sample means, s1 and s2 are the two sample standard deviations, and n1 and n2 the two sample sizes.

            The output will contain an open interval (a, b) that is your answer: the difference between the two means will lie in this interval. Specifically, it is the second mean subtracted from the first - μ1-μ2. If you're interested in the reverse difference, just flip the signs on the interval.

            Tip: don't use this command in a matched-pairs setting when you can match the two samples up by units or subjects. Instead, take the difference between the two samples in each matched pair, and use a regular TInterval.

            Sample Problem

            You want to compare the average height of a freshman and a senior at your school. You haven't asked everyone, but you took a random sample of 40 people from each class and found out their heights (and stored them to L1 and L2). You've decided to use a 95% confidence interval.

            Based on the data list syntax for a 2-SampTInt, here is your code:

            :2-SampTInt L1,L2,95
you can also use
:2-SampTInt L1,L2,.95

            Alternatively, you could calculate the mean and sample size and enter those instead. The sample size in this case is 40 for both data sets; let's say the means were 57 inches and 67 inches and the standard deviations 5.2 and 7.1 inches. You now have all the needed statistics:

            • x1 is the mean height of freshmen: 57 inches
            • s1 is the sample standard deviation for freshmen: 5.2 inches
            • n1 is the number of freshmen in the sample: 40
            • x2 is the mean height of seniors: 67 inches
            • s2 is the sample standard deviation for seniors: 7.1 inches
            • n2 is the number of seniors in the sample: 40

            This means that the code is:

            :2-SampTInt 57,5.2,40,67,7.1,40,95
you can also use
:2-SampTInt 57,5.2,40,67,7.1,40,.95

            Of course, the main use of the 2-SampTInt command is in a program. While you can enter the command on the home screen as well (just look in the catalog for it), it would probably be easier to select 2-SampTInt… from the STAT>TEST menu (see the sidebar), since you don't have to remember the syntax.

            Advanced Uses

            As with most other statistical commands, you can add frequencies to the lists (only with the data list syntax, of course); if you do, both lists must have frequencies, and the arguments go in the order first data list, second data list, first freq. list, second freq. list. Each frequency list must contain non-negative real numbers, which can't be all 0.

            There is a final argument to 2-SampTInt: pooled. It can be either 0 or 1 (although any argument that isn't 0 will get treated as a 1); the default value is 0. If the value is 1, then then the variances will be pooled: that is, the calculator will assume that the variances of the two populations are equal, and use a combined form of the two standard deviations in place of each population's individual standard deviation. Set this flag if you have reason to believe that the standard deviations are equal.

            Optimization

            Using the data list syntax, all items are optional: the calculator will assume you want to use L1 and L2 for your data unless other lists are supplied, and that the confidence level you want is 95% unless you give another one. Using the summary stats syntax, the confidence level is also optional - again, the calculator will assume 95%. This means we can rewrite our code above in a simpler manner:

            :2-SampTInt L1,L2,95
can be
:2-SampTInt

            :2-SampTInt 57,5.2,40,67,7.1,40,95
can be
:2-SampTInt 57,5.2,40,67,7.1,40

            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

            History

            Calculator OS Version Description
            TI-83 0.01013 Added
            Property Value
            Hex Value $BB4A
            Categories
            Localizations
            • FR: ListesDéfaut

            SetUpEditor

            Overview

            Removes all list names from the stat list editor, and then restores list names L1 through L6 to columns 1 through 6.

            Availability: Token available everywhere.

            Syntax

            SetUpEditor

            Location

            stat, EDIT, 5:SetUpEditor

            Overview

            Removes all list names from the stat list editor, then sets it up to display one or more listnames in the specified order, starting with column 1.

            Availability: Token available everywhere.

            Syntax

            SetUpEditor listname1[,listname2,...,listname20]

            Arguments

            NameTypeOptional
            listname1listName
            listname2listNameYes
            ...Yes
            listname20listNameYes

            Location

            stat, EDIT, 5:SetUpEditor

            Description

            The SetUpEditor command is used to define which lists are shown in the List Editor (which can be accessed by pressing [STAT] [ENTER] [Edit…]). The list editor provides a convenient interface for viewing and editing items inside lists (especially when the elements of two lists are connected to each other, such as a list for X-coordinates and one for Y-coordinates, since they will be shown in the same row).

            If the command is called without any arguments, it uses the default six lists: L1, L2, L3, L4, L5, and L6.

            :SetUpEditor

            However, you can use it to select any lists that you have defined, or even lists that are archived or not yet defined. To do this, simply put the lists you want as arguments to the command. For example, if you want to edit the lists FOO and BAR, do:

            :SetUpEditor FOO,BAR

            Both the list editor itself and the SetUpEditor command support up to 20 lists. If you specify more than 20, the 21st and beyond will be ignored.

            The List Editor doesn't do anything when you are running a program, so it may seem as though SetUpEditor is nearly useless in programs. This is not the case, however, because of SetUpEditor's powerful side effect: if the lists it is given as arguments are archived, it will unarchive them. If they don't exist, it will create empty lists with zero items. If the lists exist, the items stored inside are not modified.

            Advanced Uses

            Due to this side effect, SetUpEditor can be used for lists with external data such as saved games or high scores. When the user first runs the program, the assumption is you don't know anything about the state of those lists: they may be archived, or they may not even exist. You can deal with both of those individually: storing to the dimension will create the list if it didn't exist, and the UnArchive command will move the list to RAM if it wasn't there.

            However, if you're wrong about the list, both of these commands will cause an error. If the list exists but is archived, storing to its dimension will cause an ERR:ARCHIVE error. If the list doesn't exist, unarchiving it will cause an ERR:UNDEFINED error. Sounds like a vicious circle.

            The SetUpEditor command allows you to deal with both of these problems at once. Say the program saves its data in LSAVE. Use the SetUpEditor command on it, and from then on you know that the list exists AND that it is unarchived.

            :SetUpEditor SAVE

            At the end of the program, you should clean up after yourself, though. You don't want the user to see the list SAVE in the editor (he might be tempted to edit it and give himself a huge high score, for one thing). So you should use the SetUpEditor command again, this time without arguments, to reset the editor to its default state.

            For more information about using SetUpEditor in the context of saving data, see the page on saving.

            Similar Commands

            See Also

            Source: parts of this page were written by the following TI|BD contributors: 2Tie, burr, DarkerLine, GoVegan, Timothy Foster.

            History

            Calculator OS Version Description
            TI-83 0.01013 Added
            Property Value
            Hex Value $BB4B
            Categories
            Localizations
            • FR: Pmt_Fin

            Pmt_End

            Overview

            Specifies an ordinary annuity, where payments occur at the end of each payment period.

            Availability: Token available everywhere.

            Syntax

            Pmt_End

            Location

            apps, 1:Finance, CALC, E:Pmt_End

            Description

            The Pmt_End and Pmt_Bgn commands toggle a setting with the finance solver. In Pmt_End mode, the calculator assumes that the payments are made at the end of each time period, rather than at the beginning.

            Make sure to set the calculator to one of the modes before using the finance solving commands in a program, since otherwise the result is unpredictable.

            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

            History

            Calculator OS Version Description
            TI-83 0.01013 Added
            Property Value
            Hex Value $BB4C
            Categories
            Localizations
            • FR: Pmt_Déb

            Pmt_Bgn

            Overview

            Specifies an annuity due, where payments occur at the beginning of each payment period.

            Availability: Token available everywhere.

            Syntax

            Pmt_Bgn

            Location

            apps, 1:Finance, CALC, F:Pmt_Bgn

            Description

            The Pmt_Bgn and Pmt_End commands toggle a setting with the finance solver. In Pmt_Bgn mode, the calculator assumes that the payments are made at the beginning of each time period, rather than at the end.

            Make sure to set the calculator to one of the modes before using the finance solving commands in a program, since otherwise the result is unpredictable.

            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

            History

            Calculator OS Version Description
            TI-83 0.01013 Added
            Property Value
            Hex Value $BB4D
            Categories
            Localizations
            • FR: Réel

            Real

            Overview

            Sets mode to display complex results only when you enter complex numbers.

            Availability: Token only available from within the Basic editor.

            Syntax

            Real

            Location

            mode, Real

            Description

            The Real command puts the calculator in real number-only mode. This shouldn't be taken quite literally, as you can still type in 𝑖 to get complex numbers, and do operations with them (they will be displayed as in a+b𝑖 mode, in that case). However, any operation done with real numbers that comes out to a complex result, such as taking the square root of a negative number, will throw a ERR:NONREAL ANS error.

            There is no real advantage to using Real mode over a+b𝑖 mode — it just adds another error condition that wouldn't be triggered otherwise. However, it is the default setting, and so there's a good chance that the calculator will be in Real mode when someone runs your program. Thus, when using complex numbers implicitly (such as in a quadratic equation solver) you should do something about this.

            Advanced Uses

            Rather than switch to a+b𝑖 mode, you might want to force the calculations to use complex numbers by making the original argument complex. The general way to do this is by adding +0i to the number. However, there may be an optimization in any particular case. See the quadratic formula routine for a good example of this.

            Real
        Done
√(-1)    
        (causes an error)
√(-1+0i)        
        i

            See Also

            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

            History

            Calculator OS Version Description
            TI-83 0.01013 Added
            Property Value
            Hex Value $BB4E
            Categories
            Localizations
            • FR: r𝑒^θ𝑖

            r𝑒^θ𝑖

            Overview

            Sets the mode to polar complex number mode (re``^θi).

            Availability: Token only available from within the Basic editor.

            Syntax

            re^θi

            Arguments

            NameTypeOptional
            e
            θ
            i

            Location

            mode

            Description

            The re^θ𝑖 command puts the calculator into polar complex number mode. This means that:

            • Taking square roots of negative numbers, and similar operations, no longer returns an error.
            • Complex results are displayed in the form re^(θ𝑖) (hence the name of the command)

            The mathematical underpinning of this complex number format is due to the fact that if (x,y) is a point in the plane using the normal coordinates, it can also be represented using coordinates (r,θ) where r is the distance from the origin and θ is the angle that the line segment to the point from the origin makes to the positive x-axis (see Polar and PolarGC for more information on polar coordinates and graphing). What does this have to do with complex numbers? Simple: if x+y𝑖 is a complex number in normal (rectangular) form, and re^(θ𝑖) is the same number in polar form, then (x,y) and (r,θ) represent the same point in the plane.

            Of course, that has a lot to do with how you define imaginary exponents, which isn't that obvious.

            An equivalent form to polar form is the form r[cos(θ)+𝑖sin(θ)].

            Unfortunately, the calculator seems to have some confusion about the use of degree and radian angle measures for θ in this mode (the answer is: you can only use radians — degrees make no sense with complex exponents). When calculating a value re^(θ𝑖) by using the e^( command and plugging in numbers, the calculator assumes θ is a radian angle, whether it's in Degree or Radian mode. However, when displaying a complex number as re^(θ𝑖), the calculator will display θ in radian or degree measure, whichever is enabled. This may lead to such pathological output as:

            Degree:r𝑒^θ𝑖
        Done
𝑒^(πi)
        1𝑒^(180i)
Ans=𝑒^(180𝑖)
        0 (false)

            It's recommended, then, to use Radian mode whenever you're in re^θ𝑖 mode.

            Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan.

            History

            Calculator OS Version Description
            TI-83 0.01013 Added
            Property Value
            Hex Value $BB4F
            Categories
            Localizations
            • FR: a+b𝑖

            a+b𝑖

            Overview

            Sets the mode to rectangular complex number format (a+bi).

            Availability: Token only available from within the Basic editor.

            Syntax

            a+bi

            Arguments

            NameTypeOptional
            i

            Location

            mode, a+b, 𝑖

            Description

            The a+b𝑖 command puts the calculator into rectangular complex number mode. This means that:

            • Taking square roots of negative numbers, and similar operations, no longer returns an error.
            • Complex results are displayed in the form a+b𝑖 (hence the name of the command)

            This is the standard way of displaying complex numbers, though they can also be displayed in polar form (see r𝑒^θ𝑖 for more details). To extract the coefficients a and b, use the real( and imag( commands.

            Advanced Uses

            Rather than switch to a+b𝑖 mode, you might want to force the calculations to use complex numbers by making the original argument complex. The general way to do this is by adding +0𝑖 to the number. However, there may be an optimization in any particular case. See the quadratic formula routine for a good example of this.

            Real
        Done
√(-1)    
        (causes an error)
√(-1+0i)        
        i

            See Also

            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Myles_Zadok, Trenly.

            History

            Calculator OS Version Description
            TI-83 0.01013 Added
            Property Value
            Hex Value $BB50
            Categories
            Localizations
            • FR: ExpAff

            ExprOn

            Overview

            Turns on the expression display during TRACE.

            Availability: Token only available from within the Basic editor.

            Syntax

            ExprOn

            Location

            2nd, format, ExprOn

            Description

            The ExprOn command enables a "long" form of displaying the equation or plot being traced.

            In this mode, when tracing an equation, the equation's name and its formula are written in small font at the top of the screen. For example, when tracing Y1 which is equal to 2X, "Y1=2X" will be displayed.

            When tracing a plot, the plot number is written, followed by the list or lists that it describes. For example, when tracing Plot1, which is a scatter plot of ʟX and ʟY, "P1:X,Y" will be displayed.

            Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Myles_Zadok.

            History

            Calculator OS Version Description
            TI-83 0.01013 Added
            Property Value
            Hex Value $BB51
            Categories
            Localizations
            • FR: ExpNAff

            ExprOff

            Overview

            Turns off the expression display during TRACE.

            Availability: Token only available from within the Basic editor.

            Syntax

            ExprOff

            Location

            2nd, format, ExprOff

            Description

            The ExprOff command enables a "short" form of displaying the equation or plot being traced. That is, only the number of the equation or plot will be displayed, in the top right corner of the screen. When tracing a plot, the number will be prefixed with a P to distinguish it from an equation.

            Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Myles_Zadok.

            History

            Calculator OS Version Description
            TI-83 0.01013 Added
            Property Value
            Hex Value $BB52
            Categories
            Localizations
            • FR: EffToutListes

            ClrAllLists

            Overview

            Sets to 0 the dimension of all lists in memory.

            Availability: Token available everywhere.

            Syntax

            ClrAllLists

            Location

            2nd, mem, MEMORY, 4:ClrAllLists

            Description

            The ClrAllLists command sets the dimension (length) of all lists to zero. This is virtually equivalent to deleting the lists, except for two differences:

            • The lists still exist and will show up in the list menu and the memory management menu.
            • The dim( command will return 0 for a cleared list, rather than an error.

            However, accessing a cleared list in any other way will return an error, just as for a deleted list.

            The ClrAllLists command should never be used in a program you give to someone else or upload - unless the user is aware of this effect, they might lose important data stored in one of their lists. There is no way to limit the effect of ClrAllLists, so a program should use ClrList instead to avoid affecting unrelated lists (this is assuming you already want to use this questionably-useful effect).

            Outside a program (or in a program for personal use), you might use this command to clear the contents of your lists to free up memory, while still not deleting the lists. This might possibly be convenient. Maybe.

            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Myles_Zadok.

            History

            Calculator OS Version Description
            TI-83 0.01013 Added
            Property Value
            Hex Value $BB53
            Categories
            Localizations
            • FR: GetCalc(

            GetCalc(

            Overview

            Gets contents of variable on another TI-84 Plus CE and stores it to variable on the receiving TI-84 Plus CE. By default, the TI-84 Plus CE uses the USB port if it is connected. If the USB cable is not connected, it uses the I/O port.portflag=0 use USB port if connected;portflag=1 use USB port;portflag=2 use I/O port.(Ignored when program runs on the TI-84 Plus CE.)

            Availability: Token only available from within the Basic editor.

            Syntax

            GetCalc(variable[,portflag])

            Arguments

            NameTypeOptional
            variable
            portflagYes

            Location

            prgm, I/O, 0:GetCalc(

            Description

            The GetCalc( command allows you to make multiplayer games, where two calculators communicate with each other across a link cable that is connected between them. The GetCalc( command can only receive one variable from another calculator, and the variable can be any variable (a real, list, matrix, string, etc.). The calculator doesn't exchange variable values when the variable is received, but instead replace the variable of the same name on the receiving calculator.

            For the GetCalc( command to work correctly, the sending calculator must be in a preemptible state and it cannot be executing an assembly program. (The sending calculator is the one which is not executing the GetCalc( command.) The two main commands that you should use to ensure this are Pause and Menu(; however, any command that is waiting for user input will also work perfectly fine (such as Prompt and Input).

            The GetCalc( command behaves a little differently in the older TI-83 models. If the sending calculator is idle with the Pause or Menu( command, it will automatically "press enter" when the receiving calculator executes GetCalc(. This can be frustrating when in a menu, because it prevents the user's opportunity to make a selection.

            However, this can make real-time gaming more possible if used in conjunction with the Pause command. When the receiving calculator receives the variable, it could then execute the Pause command, while the sending calculator automatically exits the power-saving state and could then perform the GetCalc( command. All models after the TI-83 do not automatically exit their power-saving states.

            Advanced Uses

            The TI-84+ and TI-84+SE will use the USB port if it is connected to a USB cable, otherwise they will use the I/O port. However, you can specify which port you want to use by putting a number after the variable as GetCalc('s second argument: zero to use the USB port if connected to a USB cable, one to use the USB port without checking to see if it's connected, and two to use the I/O port.

            See Also

            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, jonbush, kg583, Myles_Zadok, Timtech.

            History

            Calculator OS Version Description
            TI-83 0.01013 Added
            Property Value
            Hex Value $BB54
            Categories
            Localizations
            • FR: EffVar

            DelVar

            Overview

            Deletes from memory the contents of variable.

            Availability: Token only available from within the Basic editor.

            Syntax

            DelVar variable

            Arguments

            NameTypeOptional
            variable

            Location

            prgm, CTL, G:DelVar

            Description

            The DelVar command deletes the contents of a variable (and thus the variable itself) from memory. You can use the DelVar command with any variable: reals, lists, matrices, strings, pictures, etc. However, you cannot use DelVar on specific elements of a matrix or string; it will actually throw a ERR:SYNTAX error. (It also does not work on programs, unfortunately.)

            If the DelVar command is used with a real variable, the variable is not only deleted from memory but automatically set to zero the next time it is used. This is equivalent to using store (→) to manually set the variable yourself. Because the DelVar command is two bytes instead of one, there is no size difference between the two.

            :0→A
same as
:DelVar A

            While there is no size difference between the two, DelVar does have some problems that go along with using it. If used in a For loop to delete the counter variable or used to delete the variable and/or value in the IS>( or DS<( commands before using them, it will cause an ERR:UNDEFINED error.

            This is a result of the way that the interpreter in TI-Basic is designed, so there is nothing you can do about it. You just need to be cognizant of it when using DelVar in a For( loop or together with IS>( or DS<(.

            Advanced Uses

            When you are done using variables, you should delete them at the end of the program with the DelVar command to cleanup. Each variable takes up a set amount of space (for example, a real variable is 15 bytes), and the more variables you can delete the more free memory is available. Free memory helps your programs run faster and allows you to pack more things on your calculator.

            Because the DelVar command doesn't update the Ans variable, you can use DelVar and the current value in Ans will still be preserved for later use.

            Optimizations

            The DelVar command does not need a line break or colon (which indicates a new line of code) following the variable name. This allows you to make chains of variables (organized in whatever order you want), and it saves a byte for each line break or colon removed.

            :DelVar A
:DelVar B
can be
:DelVar ADelVar B

            Besides making chains of variables, the DelVar command also allows you to take the command from the next line and put it immediately after the DelVar command.

            :DelVar A
:Disp "Hello
can be
:DelVar ADisp "Hello

            There are, however, two cases in which the following statement will be ignored, so you should add a newline:

            DelVar also does not count as a line with respect to IS>(, DS<(, and single-line If statements.

            :If B
:Then
:DelVar A
:Disp "Hello
:End
can be
:If B
:DelVar ADisp "Hello

            Command Timings

            The speed of the DelVar command depends on the circumstance where it is used. When the variable already exists, DelVar is slower because it has to deallocate the variable from the RAM. DelVar is also significantly slower for zeroing real variables when compared to using → to set the variable to 0. The speed difference becomes apparent when the value is reset many times but is not a major factor if only used sparingly.

            Error Conditions

            • ERR:SYNTAX is thrown when trying to delete a system variable (e.g. DelVar Xmin) or a program, even though this is syntactically correct.
            • ERR:UNDEFINED is thrown if you delete the loop variable while inside the loop, or delete the variable used in IS>( or DS<(.
            • ERR:ARCHIVED is thrown if you use DelVar on an archived variable.

            See Also

            Source: parts of this page were written by the following TI|BD contributors: AntKou, basickevin, burr, DarkerLine, GoVegan, jonbush, kg583, Myles_Zadok.

            History

            Calculator OS Version Description
            TI-83 1.010 Renamed DelVar to DelVar
            Property Value
            Hex Value $BB55
            Categories
            Localizations
            • FR: Equ►Chaine(

            Equ►String(

            Overview

            Converts the contents of a Y= var to a string and stores it in Str``n

            Availability: Token available everywhere.

            Syntax

            Equ►String(Y= var,Strn)

            Arguments

            NameTypeOptional
            var
            n

            Location

            2nd, catalog, Equ►String(

            Description

            This command stores the contents of an equation variable (such as Y1 or X1T) to a string (one of Str0, Str1, … Str9). This can be used when you want to display the equation as text (either using the Text( command on the graph screen, or the Output( or Disp commands on the home screen). For example:

            :Equ►String(Y1,Str1
:Text(0,0,"Y1(X)=",Str1

            Apart from cases in which the user has already stored to the equation variable prior to running the program, about the only situation in which you would use Equ►String( is for the output of a regression.

            Advanced

            You can use Equ►String( (outside a program) to get the → or " symbols in a string:

            1. Type them on the home screen and press [ENTER]
            2. Select 2:Quit when the ERR:SYNTAX comes up.
            3. Press [Y=] to go to the equation editor.
            4. Press [2nd] [ENTRY] to recall the symbols to Y1
            5. Now, use Equ►String(Y1,Str1) to store the symbols to a string.

            See Also

            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Myles_Zadok.

            History

            Calculator OS Version Description
            TI-83 0.01013 Added
            Property Value
            Hex Value $BB56
            Categories
            Localizations
            • FR: Chaine►Equ(

            String►Equ(

            Overview

            Converts string into an equation and stores it in Y= var.
            string can be a string or string variable.
            String►Equ( is the inverse of Equ►String(.

            Availability: Token only available from within the Basic editor.

            Syntax

            String►Equ(string,Y= var)

            Arguments

            NameTypeOptional
            stringstring
            var

            Location

            prgm, I/O, D:String>Equ(, F:String>Equ(

            Description

            This command stores the contents of a string to an equation variable (such as Y1 or X1T). This command can, in theory, be used whenever you need to set any equation variable.

            In practice, however, this command is useless. This is because the → (store) operation can be used for the same purpose:

            :String►Equ(Str1,Y1
can be
:Str1→Y1

            This replacement is universal, takes the same time to run (because it actually uses the same routines), is more convenient to type since you don't have to go through the command catalog, and is two bytes smaller.

            Advanced

            Unlike any normal use of the → (store) operation, this situation is different because it doesn't modify Ans. For example:

            :125
:"sin(X→Y1
:Disp Ans

            Because this use of → does not modify Ans, '125' will be displayed rather than 'sin(X'. However, if we were to replace Y1 with Str1, then the → operation would work normally, and 'sin(X' would be displayed.

            It's also important to realize the difference between the String►Equ( command and the related Equ►String(, aside from the fact that the latter is actually useful. The main difference is that while Equ►String('s arguments both have to be variables, String►Equ('s first argument can either be a variable (Str0 through Str9), a constant string (e.g., "sin(X)"), or an expression that returns a string (e.g., sub(Str1,1,5)). This applies to the → operation as well.

            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Myles_Zadok, Timtech.

            History

            Calculator OS Version Description
            TI-83 0.01013 Added
            Property Value
            Hex Value $BB57
            Categories
            Localizations
            • FR: Efface entrées

            Clear Entries

            Overview

            Clears the contents of the Last Entry storage area.

            Availability: Token available everywhere.

            Syntax

            Clear Entries

            Location

            2nd, mem, MEMORY, 3:Clear Entries

            Description

            Normally, by pressing 2nd ENTER repeatedly, you can cycle through some of the recent entries on the home screen. With the Clear Entries command, this history is cleared (only Clear Entries remains in the history).

            This can be used to free some memory, although it's recommended not to do this in a program (because clearing things without asking first isn't nice). Aside from that, maybe the only reason to use Clear Entries is to protect your privacy — although someone looking at your entries will know you cleared something, so it's not that effective.

            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Myles_Zadok.

            History

            Calculator OS Version Description
            TI-83 0.01013 Added
            Property Value
            Hex Value $BB58
            Categories
            Localizations
            • FR: Sélect(

            Select(

            Overview

            Selects one or more specific data points from a scatter plot or xyLine plot (only), and then store's the selected data points to two new lists, Xlistname and Ylistname.

            Availability: Token available everywhere.

            Syntax

            Select(Xlistname,Ylistname)

            Arguments

            NameTypeOptional
            Xlistnamelist
            Ylistnamelist

            Location

            2nd, list, OPS, 8:Select(

            Description

            When Select( is called, if it has any Scatter or xyLine plots to work with, it displays the graph screen and allows the user to pick a left bound and then a right bound on one of the plots (the left and right keys move from point to point, while the up and down keys switch plots). Then, it stores all the points between those bounds to x-list name and y-list name. Finally, it sets the chosen plot to use x-list name and y-list name as its X and Y lists.

            Optimization

            It isn't necessary to add the ʟ symbol before list names:

            :Select(ʟX,ʟY)
can be
:Select(X,Y)

            Error Conditions

            • ERR:INVALID is thrown if there are no enabled Scatter or xyLine plots for the command to work with.

            Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan.

            History

            Calculator OS Version Description
            TI-83 0.01013 Added
            Property Value
            Hex Value $BB59
            Categories
            Localizations
            • FR: ANUVA(

            ANOVA(

            Overview

            Performs a one-way analysis of variance for comparing the means of two to 20 populations.

            Availability: Token available everywhere.

            Syntax

            ANOVA(list1,list2[,list3,...,list20])

            Arguments

            NameTypeOptional
            list1list
            list2list
            list3listYes
            ...Yes
            list20listYes

            Location

            stat, TESTS, H:ANOVA(

            Description

            The ANOVA (analysis of variance) command is used to test if there is a significant difference between the means of several populations (this is an extension of the two-sample t-test which compares only two populations). The calculator assumes the null hypothesis, that all means are equal, and returns a probability value, p, of the differences in the data occurring if the null hypothesis were true. If p is small (usually, if it's less than .05), then it's unlikely we'd get such differences just by chance if the null hypothesis were true, so we reject it and conclude that at least one of the means is different.

            There are two reasons why we don't test the means in pairs using a simpler test. First of all, it would take a long time: there's so many pairs to compare. Second of all, when you're doing many tests, there's a high probability you'll get a low p-value by chance. Imagine that you're doing 10 tests. If the probability of getting a low p-value on one test is .05, then the probability that at least one test will return one is 1-.9510: about 0.4 - this is quite likely to happen. The ANOVA test avoids this by having only one null hypothesis to test.

            If you're only interested in the result of the test, the only thing you'll need in the output is the second line: "p=…" This is your p-value, and determines whether you should reject the null hypothesis or not. If you need more detail, here are the meanings of the other variables:

            • F is the test statistic. If the null hypothesis is true, it should follow Snedecor's F distribution, and Fcdf( can be used to determine the p-value.
            • For both Factor and Error:
              • MS is the mean squares (SS/df). If the null hypothesis is true, Factor MS should be roughly equal to Error MS
              • SS is the sum of squares - see the TI-83+ Manual for formulas
              • df is the number of degrees of freedom - for Factor, it's the df between the categorical variables, and for Error, it's the sum of df between each variable.
            • Sxp is the pooled variation.

            Advanced Uses

            The statistics F, p, and Sxp will be stored to the appropriate variables after this test. The other six statistics do not have a normal variable associated with them. However, the two-byte tokens 0x6237 through 0x623C are, in fact, used to store the values of Factor MS, Factor SS, Factor df, Error MS, Error SS, and Error df respectively. They can't be accessed through a menu, but if you use a hex editor to paste them into your program, you will be able to use them just like any other variable.

            However, be careful because the Factor and Error tokens look exactly alike (even though they refer to different variables), and can be confused. Also, there is a chance that future OS versions will change the behavior of ANOVA(, though this is unlikely, and this trick will no longer work.

            Error Conditions

            • ERR:ARGUMENT is thrown if one of the lists is blank, only one list is used, or the function is completely blank.
            • ERR:SYNTAX is thrown if you do not use lists (Matrixes, numbers,etc)
              • ERR:INVALID DIM is thrown if you use a list that has 0 or a negative number.
              • ERR:DATA TYPE is thrown by using "l" or a list with a different set of data.

            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583, Myles_Zadok, nap386, Trenly.

            History

            Calculator OS Version Description
            TI-83 0.01013 Added
            Property Value
            Hex Value $BB5A
            Categories
            Localizations
            • FR: GraphBoitMoust

            ModBoxplot

            Overview

            Used as the "type" argument in the command.
            Where # gives Plot1, Plot2 or Plot3.

            Availability: Token only available from within the Basic editor.

            Syntax

            Plot#(type,Xlist[,freqlist,color#])

            Arguments

            NameTypeOptional
            typeModBoxplot token
            Xlistlist
            freqlistlist
            color#colorNum

            Location

            2nd, stat plot, TYPE

            Description

            The commands Plot1(, Plot2(, and Plot3(, which are identical except for which stat plot (1, 2, or 3) they affect, define their corresponding stat plot. When the stat plot is defined, it is also turned on so no PlotsOn command is necessary.

            The first argument of the commands is always the type of plot, and is one of Scatter, xyLine, Histogram, Boxplot, ModBoxplot, and NormProbPlot - these types are found in the TYPE submenu of the stat plot menu. The other arguments vary. For all but Histogram and Boxplot, there is a mark argument - this is a dot, a cross, or a box, symbols that can be found in the MARK submenu of the stat plot menu. On color calculators, there is an optional final argument to specify the color of the plot.

            Scatter plot

            Plot#(Scatter, x-list, y-list, mark) defines a scatter plot. The points defined by x-list and y-list are plotted using mark on the graph screen.

            x-list and y-list must be the same length.

            xyLine plot

            Plot#(xyLine, x-list, y-list, mark) defines an xyLine plot. Similarly to a scatter plot, the points defined by x-list and y-list are plotted using mark on the graph screen, but with an xyLine plot they are also connected by a line, in the order that they occur in the lists.

            x-list and y-list must be the same length.

            Histogram plot

            Plot#(Histogram, x-list, freq list) defines a Histogram plot. The x-axis is divided into intervals that are Xscl wide. A bar is drawn in in each interval whose height corresponds to the number of points in the interval. Points that are not between Xmin and Xmax are not tallied.

            Xscl must not be too small - it can divide the screen into no more than 47 different bars.

            Box plot

            Plot#(Boxplot, x-list, freq list) defines a box plot. A rectangular box is drawn whose left edge is Q1 (the first quartile) of the data, and whose right edge is Q3 (the third quartile). A vertical segment is drawn within the box at the median, and 'whiskers' are drawn from the box to the minimum and maximum data points.

            The box plot ignores the Ymax and Ymin dimensions of the screen, and any plots that aren't box plots or modified box plots. Each box plot takes approximately 1/3 of the screen in height, and if more than one are plotted, they will take up different areas of the screen.

            Modified box plot

            Plot#(ModBoxplot, x-list, freq list, mark) defines a modified box plot. This is almost entirely like the normal box plot, except that it also draws outliers. Whiskers are only drawn to the furthers point within 1.5 times the interquartile range (Q3-Q1) of the box. Beyond this point, data points are drawn individually, using mark.

            The box plot ignores the Ymax and Ymin dimensions of the screen, and any plots that aren't box plots or modified box plots. Each box plot takes approximately 1/3 of the screen in height, and if more than one are plotted, they will take up different areas of the screen.

            Normal probability plot

            Plot#(NormProbPlot, data list, data axis, mark) defines a normal probability plot. The mean and standard deviation of the data are calculated. Then for each point, the number of standard deviations it is from the mean is calculated, and the point is plotted against this number using mark. data axis can be either X or Y: it determines whether the value of a point determines it's x-coordinate or y-coordinate.

            The point behind this rather convoluted process is to test the extent to which the data is normally distributed. If it follows the normal distribution closely, then the result will be close to a straight line - otherwise it will be curved.

            Advanced Uses

            After doing a regression, a scatter plot of ʟRESID against the x-list is a useful measure of the effectiveness of the regression. If the plot appears random, this is a good sign; if there is a pattern to the plot, this means it's likely that a better regression model exists.

            Optimization

            The ʟ symbol at the beginning of list names can be omitted everywhere in this command.

            In addition, every element except the plot type and the data list or data lists are optional, and take on the following default values:

            • freq list is 1 by default, meaning that all frequencies are 1.
            • mark is the box by default.
            • data axis is X by default.

            Error Conditions

            • ERR:DIM MISMATCH is thrown if the x and y lists, or the data and frequency lists, have different dimensions.
            • ERR:STAT is thrown if Xscl is too small in the case of a Histogram.

            All errors are thrown when plotting the stat plot, as opposed to when the command is executed, and do not provide a 2:Goto option.

            Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Myles_Zadok.

            History

            Calculator OS Version Description
            TI-83 0.01013 Added
            Property Value
            Hex Value $BB5B
            Categories
            Localizations
            • FR: GraphProbNorm

            NormProbPlot

            Overview

            Used as the "type" argument in the command
            Where # gives Plot1, Plot2 or Plot3.

            Availability: Token only available from within the Basic editor.

            Syntax

            Plot#(type,Xlist[,freqlist,color#])

            Arguments

            NameTypeOptional
            typeNormProbPlot token
            Xlistlist
            freqlistlist
            color#colorNum

            Location

            2nd, stat plot, TYPE

            Description

            The commands Plot1(, Plot2(, and Plot3(, which are identical except for which stat plot (1, 2, or 3) they affect, define their corresponding stat plot. When the stat plot is defined, it is also turned on so no PlotsOn command is necessary.

            The first argument of the commands is always the type of plot, and is one of Scatter, xyLine, Histogram, Boxplot, ModBoxplot, and NormProbPlot - these types are found in the TYPE submenu of the stat plot menu. The other arguments vary. For all but Histogram and Boxplot, there is a mark argument - this is a dot, a cross, or a box, symbols that can be found in the MARK submenu of the stat plot menu. On color calculators, there is an optional final argument to specify the color of the plot.

            Scatter plot

            Plot#(Scatter, x-list, y-list, mark) defines a scatter plot. The points defined by x-list and y-list are plotted using mark on the graph screen.

            x-list and y-list must be the same length.

            xyLine plot

            Plot#(xyLine, x-list, y-list, mark) defines an xyLine plot. Similarly to a scatter plot, the points defined by x-list and y-list are plotted using mark on the graph screen, but with an xyLine plot they are also connected by a line, in the order that they occur in the lists.

            x-list and y-list must be the same length.

            Histogram plot

            Plot#(Histogram, x-list, freq list) defines a Histogram plot. The x-axis is divided into intervals that are Xscl wide. A bar is drawn in in each interval whose height corresponds to the number of points in the interval. Points that are not between Xmin and Xmax are not tallied.

            Xscl must not be too small - it can divide the screen into no more than 47 different bars.

            Box plot

            Plot#(Boxplot, x-list, freq list) defines a box plot. A rectangular box is drawn whose left edge is Q1 (the first quartile) of the data, and whose right edge is Q3 (the third quartile). A vertical segment is drawn within the box at the median, and 'whiskers' are drawn from the box to the minimum and maximum data points.

            The box plot ignores the Ymax and Ymin dimensions of the screen, and any plots that aren't box plots or modified box plots. Each box plot takes approximately 1/3 of the screen in height, and if more than one are plotted, they will take up different areas of the screen.

            Modified box plot

            Plot#(ModBoxplot, x-list, freq list, mark) defines a modified box plot. This is almost entirely like the normal box plot, except that it also draws outliers. Whiskers are only drawn to the furthers point within 1.5 times the interquartile range (Q3-Q1) of the box. Beyond this point, data points are drawn individually, using mark.

            The box plot ignores the Ymax and Ymin dimensions of the screen, and any plots that aren't box plots or modified box plots. Each box plot takes approximately 1/3 of the screen in height, and if more than one are plotted, they will take up different areas of the screen.

            Normal probability plot

            Plot#(NormProbPlot, data list, data axis, mark) defines a normal probability plot. The mean and standard deviation of the data are calculated. Then for each point, the number of standard deviations it is from the mean is calculated, and the point is plotted against this number using mark. data axis can be either X or Y: it determines whether the value of a point determines it's x-coordinate or y-coordinate.

            The point behind this rather convoluted process is to test the extent to which the data is normally distributed. If it follows the normal distribution closely, then the result will be close to a straight line - otherwise it will be curved.

            Advanced Uses

            After doing a regression, a scatter plot of ʟRESID against the x-list is a useful measure of the effectiveness of the regression. If the plot appears random, this is a good sign; if there is a pattern to the plot, this means it's likely that a better regression model exists.

            Optimization

            The ʟ symbol at the beginning of list names can be omitted everywhere in this command.

            In addition, every element except the plot type and the data list or data lists are optional, and take on the following default values:

            • freq list is 1 by default, meaning that all frequencies are 1.
            • mark is the box by default.
            • data axis is X by default.

            Error Conditions

            • ERR:DIM MISMATCH is thrown if the x and y lists, or the data and frequency lists, have different dimensions.
            • ERR:STAT is thrown if Xscl is too small in the case of a Histogram.

            All errors are thrown when plotting the stat plot, as opposed to when the command is executed, and do not provide a 2:Goto option.

            Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Myles_Zadok.

            History

            Calculator OS Version Description
            TI-83 0.01013 Added
            Property Value
            Hex Value $BB64
            Categories
              Localizations
              • FR: G-T

              G-T

              Overview

              Sets graph-table vertical split-screen mode.

              Availability: Token only available from within the Basic editor.

              Syntax

              G-T

              Location

              mode, GRAPH-TABLE

              Description

              G-T puts the calculator into "Graph-Table" mode: this mode shows the home screen at full size, but the graph screen and table will be displayed together, each taking up half the screen (divided vertically).

              G-T is usually used at the beginning of a program to ensure that the screen mode is G-T , for programs such as math programs that want to demonstrate the thinking step-by-step.

              :G-T

              With OS version 2.30 (on the TI-84+ and TI-84+ SE calculators), G-T mode can be used with stat plots as well.

              Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583, mattyjraps, Xphoenix.

              History

              Calculator OS Version Description
              TI-83 1.010 Added
              Property Value
              Hex Value $BB65
              Categories
              Localizations
              • FR: ZminMax

              ZoomFit

              Overview

              Recalculates Ymin and Ymax to include the minimum and maximum Y values, between Xmin and Xmax, of the selected functions and replots the functions.

              Availability: Token only available from within the Basic editor.

              Syntax

              ZoomFit

              Location

              zoom, ZOOM, 0:ZoomFit

              Description

              The ZoomFit zooms to the smallest window that contains all points of the currently graphed equations. In Func mode, this means that it calculates the minimum and maximum Y-value for the current Xmin to Xmax range, and sets Ymin and Ymax to those values (Xmin and Xmax remain unchanged). In other graphing modes, this process is done for both X and Y over the range of T, θ, or n.

              Optimization

              When graphing an equation with ZoomFit, the calculator will first calculate all points to find the minimum and maximum, then calculate all the points again to graph it. This can be time consuming if the equation is very complicated, and in that case doing part of the process manually might be faster if you reuse the points.

              Error Conditions

              • ERR:INVALID is thrown if this command is using outside a program (although the menu option, of course, is fine).
              • ERR:WINDOW RANGE is thrown when the window ends up being empty (if the function is constant, for example)

              Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, HJTP.

              History

              Calculator OS Version Description
              TI-83 1.010 Added
              Property Value
              Hex Value $BB66
              Categories
              Localizations
              • FR: CorrelAff

              DiagnosticOn

              Overview

              Sets diagnostics-on mode; r, r², and R² are displayed as regression model results.

              Availability: Token available everywhere.

              Syntax

              DiagnosticOn

              Location

              2nd, catalog, DiagnosticOn

              Description

              After the DiagnosticOn command is executed, all regression commands found in the STAT>CALC menu, as well as LinRegTTest, will display the correlation statistics r and r² (or R2 for regressions that are not linear). This is turned off by default, but there is no disadvantage whatsoever to turning it on. To reverse this command, execute the DiagnosticOff command.

              The statistic r, known as the Pearson correlation coefficient, measures the strength and direction of any linear relationship in the data. If r is close to 1, then the relationship is strong and positive (that is, the variables increase and decrease together). If r is close to -1, then the relationship is strong and negative (that is, as one variable increases, the other decreases). If r is close to 0, there is no linear relationship.

              The statistic r² or R², known as the coefficient of determination, is equal to the square of the above value (when it exists) and is also a measure of the strength of a relationship. Specifically, it represents the proportion of variance in the dependent variable that is accounted for by the regression model. If this value is close to 1, there is a strong relationship; if it's close to 0, there is either no relationship or the regression model is not appropriate for the data.

              Advanced

              Although these statistics are a good indication of whether a regression curve is good or not, they are not infallible. For example, the initial portion of data that actually correlates exponentially may well appear linear and have a high correlation coefficient with a linear fit.

              Another good way to check a regression curve is to look at the plot of the residuals vs. the x-values. If the regression curve is a good fit, then this plot should appear random in going from positive to negative. However, should you see a distinct pattern - say, if you tried a linear fit but the residual plot looks vaguely parabolic - you know you should try a different regression curve.

              You should also consider what your regression line implies about the nature of the data and vice versa. For example, if you're comparing the height of release of a ball to the time it takes to fall, a natural assumption is that the regression curve should pass through (0,0), and a curve that doesn't do that may be incorrect. However, take this advice with a grain of salt: if your curve fits the data points you put in but not such natural-assumption points, that may simply mean that the curve works on a limited domain. Or, it may mean your assumptions are wrong.

              Command Timings

              Although the correlation statistics are displayed with DiagnosticOn, they are calculated in either case. This means that DiagnosticOn and DiagnosticOff will not change how fast regressions are calculated.

              Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Myles_Zadok, thornahawk.

              History

              Calculator OS Version Description
              TI-83 1.010 Added
              Property Value
              Hex Value $BB67
              Categories
              Localizations
              • FR: CorrelNAff

              DiagnosticOff

              Overview

              Sets diagnostics-off mode; r, r², and R² are not displayed as regression model results.

              Availability: Token available everywhere.

              Syntax

              DiagnosticOff

              Location

              2nd, catalog, DiagnosticOff

              Description

              After the DiagnosticOff command is executed, all regression commands found in the STAT>CALC menu, as well as LinRegTTest, will not display the correlation statistics r and r2 (or just R2 in some cases). This is already turned off by default, although there is no disadvantage whatsoever to turning it on. To reverse this command, execute the DiagnosticOn command.

              The statistic r, known as the correlation coefficient, measures the strength and direction of any linear relationship in the data (therefore if your regression model isn't linear, it may not exist, unless the calculator performed a transformation on the data). If r is close to 1, then the relationship is strong and positive (that is, the variables increase and decrease together). If r is close to -1, then the relationship is strong and negative (that is, as one variable increases, the other decreases). If r is close to 0, there is no linear relationship.

              The statistic r2 or R2 is equal to the square of the above value (when it exists) and is also a measure of the strength of a relationship. Specifically, it represents the proportion of variance in the dependent variable that is accounted for by the regression model. If this value is close to 1, there is a strong relationship; if it's close to 0, there is either no relationship or the regression model doesn't fit the data.

              Advanced

              Although these statistics are a good indication of whether a regression curve is good or not, they are not infallible. For example, the initial portion of data that actually correlates exponentially may well appear linear and have a high correlation coefficient with a linear fit.

              Another good way to check a regression curve is to look at the plot of the residuals vs. the x-values. If the regression curve is a good fit, then this plot should appear random in going from positive to negative. However, should you see a distinct pattern - say, if you tried a linear fit but the residual plot looks vaguely parabolic - you know you should try a different regression curve.

              You should also consider what your regression line implies about the nature of the data and vice versa. For example, if you're comparing the height of release of a ball to the time it takes to fall, a natural assumption is that the regression curve should pass through (0,0), and a curve that doesn't do that may be incorrect. However, take this advice with a grain of salt: if your curve fits the data points you put in but not such natural-assumption points, that may simply mean that the curve works on a limited domain. Or, it may mean your assumptions are wrong.

              Command Timings

              Although the correlation statistics are not displayed with DiagnosticOff, they are calculated in either case. This means that DiagnosticOn and DiagnosticOff will not change how fast regressions are calculated.

              Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Myles_Zadok.

              History

              Calculator OS Version Description
              TI-83 1.010 Added
              Property Value
              Hex Value $BB68
              Categories
              Localizations
              • FR: Archive

              Archive

              Overview

              Moves the specified variable from RAM to the user data archive memory.

              Availability: Token available everywhere.

              Syntax

              Archive variables

              Arguments

              NameTypeOptional
              variables

              Location

              2nd, mem, 5:Archive

              Description

              The Archive command moves a variable from RAM to the archive (also known as ROM). A quick synopsis of the difference between the two:

              • Data in the archive cannot be accessed, but it's protected from RAM clears (which may occur during battery removal if not done carefully); also, the archive can hold much more data.
              • Data in RAM can be accessed for calculations, but it can also be deleted during a RAM clear or accidentally overwritten by another program.

              Nothing happens if the variable in question is already archived.

              You might want to use this command to protect data such as saved games from being accidentally deleted. It's not, in general, a good idea to archive commonly used variables, such as the real variables A-Z, since programs usually expect to be able to access these variables without problems, and won't check if they're archived.

              Also, some variables cannot be archived. These include:

              • The real variables R, T, X, Y, θ, and n (due to their use in graphing)
              • The equation variables Yn, XnT, YnT, rn, u, v, and w
              • The stat plots Plot_#_
              • Window, table, and zoom variables such as TblInput or Xmin
              • Statistical variables and the list ʟRESID
              • Finance variables

              Finally, the Archive command does not work on programs when using it from a program (it does, however, archive programs from the home screen). However, an assembly program can be executed as a subroutine so that Archive and UnArchive can be used within a program. The program should however be run again afterwards.

              Advanced Uses

              As archived variables (and programs) can not be accessed by the calculator's inbuilt OS, archiving programs can be quite problematic when trying to execute them. However; by enabling your programs to be viewable in assembly shells, you can execute your programs without needing to unarchive them first. This is because the assembly shell copies the program to the RAM automatically, and is then executed. Closing the program will automatically remove the copy from the RAM, so no RAM is lost in the end.

              Error Conditions

              • ERR:ARCHIVE FULL is thrown when there isn't enough space in the archive for the variable.
              • ERR:INVALID is thrown when trying to archive a program from within a program.
              • ERR:VARIABLE is thrown when trying to archive a variable that cannot be archived.

              Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Myles_Zadok, thornahawk, Trenly.

              History

              Calculator OS Version Description
              TI-83+ 0.103 Added
              Property Value
              Hex Value $BB69
              Categories
              Localizations
              • FR: DésArchive

              UnArchive

              Overview

              Moves the specified variables from the user data archive memory to RAM.
              To archive variables, use Archive.

              Availability: Token available everywhere.

              Syntax

              UnArchive variable

              Arguments

              NameTypeOptional
              variable

              Location

              2nd, mem, 6:UnArchive

              Description

              The UnArchive command moves a variable from the archive (also known as ROM) to RAM. A quick synopsis of the difference between the two:

              • Data in the archive cannot be accessed, but it's protected from RAM clears (which may occur during battery removal if not done carefully); also, the archive can hold much more data.
              • Data in RAM can be accessed for calculations, but it can also be deleted during a RAM clear or accidentally overwritten by another program.

              It is, in general, not recommended to place real variables in the archive (since so many programs use them); also, some variables cannot be archived (see the Archive command for details). Although programs can be archived and unarchived, the Archive and UnArchive commands will not archive or unarchive programs from within a program. For the most part, lists are the only type of variable it makes sense to archive and unarchive in a program.

              The UnArchive command doesn't do anything if the variable in question is already in RAM. However, there is no way to test if a variable is in RAM or archive, short of trying to access it and potentially getting an error.

              Advanced Uses

              The Archive and UnArchive commands can be used in conjunction for saving data as a program exits.

              Optimization

              The SetUpEditor command is often used in place of the UnArchive command when dealing with lists, for several reasons:

              • using SetUpEditor will not prevent the program from working on a TI-83, like UnArchive will
              • SetUpEditor will create a list with length 0 if it doesn't exist; UnArchive will throw an error
              • SetUpEditor saves space in the program, since it can unarchive more than one list at a time, and doesn't require the little L in front

              Error Conditions

              • ERR:MEMORY is thrown if there isn't enough memory available in RAM for the variable.
              • ERR:VARIABLE is thrown when unarchiving a system variable or a application even if there is enough space.

              See Also

              Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, nap386.

              History

              Calculator OS Version Description
              TI-83+ 0.103 Added
              Property Value
              Hex Value $BB6A
              Categories
              Localizations
              • FR: Asm(

              Asm(

              Overview

              Availability: Token available everywhere.

              Syntax

              Asm(

              Description

              The Asm( command is used for running an assembly program. Unlike TI-Basic programs, assembly programs are written in the calculator's machine code directly, which makes them more powerful in both speed and functionality. However, it also means that if they crash, they crash hard — there is no built-in error menu to protect you.

              Keep in mind that many assembly programs these days are written for a shell such as Ion or MirageOS. If you're dealing with one of those programs, calling Asm( on it will do nothing; you need to get the appropriate shell and run that instead.

              With the AsmPrgm and AsmComp( commands, you can create small assembly programs yourself, directly on the calculator. If you are using at TI-84+CE with OS 5.3, the Asm( is unnecessary to run such programs.

              Error Conditions

              • ERR:INVALID is thrown if the program isn't an assembly program.

              See Also

              Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583, Myles_Zadok, Trenly.

              History

              Calculator OS Version Description
              TI-83+ 0.103 Added
              Property Value
              Hex Value $BB6B
              Categories
              Localizations
              • FR: AsmComp(

              AsmComp(

              Overview

              Availability: Token available everywhere.

              Syntax

              AsmComp(

              Description

              This command is used to compress an assembly program written using AsmPrgm into an "assembled" assembly program. This will make the program about twice as small, and protect it from being edited, in addition to making execution faster.

              To use AsmComp(, give it the ASCII represented assembly program, followed by the name you want the assembled program to have. That name can't be already taken. Since it's not easy to rename an assembled assembly program, if you want to write a program called prgmGAME, you type the ASCII represented code in a program with a different name (e.g. GAMEA) and then do AsmComp((prgmGAMEA,prgmGAME).

              Assembly programs can be run with Asm(.

              Error Conditions

              • ERR:DUPLICATE is thrown if prgm_RESULT_ is an already used program name;
              • ERR:INVALID is thrown if prgm_ORIGINAL_ doesn't start with AsmPrgm;
              • ERR:SYNTAX is thrown if prgm_ORIGINAL_ is not an assembly program.

              Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, MateoConLechuga, Myles_Zadok, Trenly.

              History

              Calculator OS Version Description
              TI-83+ 0.103 Added
              Property Value
              Hex Value $BB6C
              Categories
              Localizations
              • FR: AsmPrgm

              AsmPrgm

              Overview

              Availability: Token available everywhere.

              Syntax

              AsmPrgm

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 0.103 Added
              Property Value
              Hex Value $BB6D
              Categories
              Localizations
              • FR: [CompiledAsm83P]

              [CompiledAsm83P]

              Overview

              Syntax

              [CompiledAsm83P]

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              Property Value
              Hex Value $BB6E
              Categories
              Localizations
              • FR: Á

              Á

              Overview

              Availability: Token available everywhere.

              Syntax

              Á

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BB6F
              Categories
              Localizations
              • FR: À

              À

              Overview

              Availability: Token available everywhere.

              Syntax

              À

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BB70
              Categories
              Localizations
              • FR: Â

              Â

              Overview

              Availability: Token available everywhere.

              Syntax

              Â

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BB71
              Categories
              Localizations
              • FR: Ä

              Ä

              Overview

              Availability: Token available everywhere.

              Syntax

              Ä

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BB72
              Categories
              Localizations
              • FR: á

              á

              Overview

              Availability: Token available everywhere.

              Syntax

              á

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BB73
              Categories
              Localizations
              • FR: à

              à

              Overview

              Availability: Token available everywhere.

              Syntax

              à

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BB74
              Categories
              Localizations
              • FR: â

              â

              Overview

              Availability: Token available everywhere.

              Syntax

              â

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BB75
              Categories
              Localizations
              • FR: ä

              ä

              Overview

              Availability: Token available everywhere.

              Syntax

              ä

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BB76
              Categories
              Localizations
              • FR: É

              É

              Overview

              Availability: Token available everywhere.

              Syntax

              É

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BB77
              Categories
              Localizations
              • FR: È

              È

              Overview

              Availability: Token available everywhere.

              Syntax

              È

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BB78
              Categories
              Localizations
              • FR: Ê

              Ê

              Overview

              Availability: Token available everywhere.

              Syntax

              Ê

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BB79
              Categories
              Localizations
              • FR: Ë

              Ë

              Overview

              Availability: Token available everywhere.

              Syntax

              Ë

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BB7A
              Categories
              Localizations
              • FR: é

              é

              Overview

              Availability: Token available everywhere.

              Syntax

              é

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BB7B
              Categories
              Localizations
              • FR: è

              è

              Overview

              Availability: Token available everywhere.

              Syntax

              è

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BB7C
              Categories
              Localizations
              • FR: ê

              ê

              Overview

              Availability: Token available everywhere.

              Syntax

              ê

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BB7D
              Categories
              Localizations
              • FR: ë

              ë

              Overview

              Availability: Token available everywhere.

              Syntax

              ë

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BB7F
              Categories
              Localizations
              • FR: Ì

              Ì

              Overview

              Availability: Token available everywhere.

              Syntax

              Ì

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BB80
              Categories
              Localizations
              • FR: Î

              Î

              Overview

              Availability: Token available everywhere.

              Syntax

              Î

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BB81
              Categories
              Localizations
              • FR: Ï

              Ï

              Overview

              Availability: Token available everywhere.

              Syntax

              Ï

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BB82
              Categories
              Localizations
              • FR: í

              í

              Overview

              Availability: Token available everywhere.

              Syntax

              í

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BB83
              Categories
              Localizations
              • FR: ì

              ì

              Overview

              Availability: Token available everywhere.

              Syntax

              ì

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BB84
              Categories
              Localizations
              • FR: î

              î

              Overview

              Availability: Token available everywhere.

              Syntax

              î

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BB85
              Categories
              Localizations
              • FR: ï

              ï

              Overview

              Availability: Token available everywhere.

              Syntax

              ï

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BB86
              Categories
              Localizations
              • FR: Ó

              Ó

              Overview

              Availability: Token available everywhere.

              Syntax

              Ó

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BB87
              Categories
              Localizations
              • FR: Ò

              Ò

              Overview

              Availability: Token available everywhere.

              Syntax

              Ò

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BB88
              Categories
              Localizations
              • FR: Ô

              Ô

              Overview

              Availability: Token available everywhere.

              Syntax

              Ô

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BB89
              Categories
              Localizations
              • FR: Ö

              Ö

              Overview

              Availability: Token available everywhere.

              Syntax

              Ö

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BB8A
              Categories
              Localizations
              • FR: ó

              ó

              Overview

              Availability: Token available everywhere.

              Syntax

              ó

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BB8B
              Categories
              Localizations
              • FR: ò

              ò

              Overview

              Availability: Token available everywhere.

              Syntax

              ò

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BB8C
              Categories
              Localizations
              • FR: ô

              ô

              Overview

              Availability: Token available everywhere.

              Syntax

              ô

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BB8D
              Categories
              Localizations
              • FR: ö

              ö

              Overview

              Availability: Token available everywhere.

              Syntax

              ö

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BB8E
              Categories
              Localizations
              • FR: Ú

              Ú

              Overview

              Availability: Token available everywhere.

              Syntax

              Ú

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BB8F
              Categories
              Localizations
              • FR: Ù

              Ù

              Overview

              Availability: Token available everywhere.

              Syntax

              Ù

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BB90
              Categories
              Localizations
              • FR: Û

              Û

              Overview

              Availability: Token available everywhere.

              Syntax

              Û

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BB91
              Categories
              Localizations
              • FR: Ü

              Ü

              Overview

              Availability: Token available everywhere.

              Syntax

              Ü

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BB92
              Categories
              Localizations
              • FR: ú

              ú

              Overview

              Availability: Token available everywhere.

              Syntax

              ú

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BB93
              Categories
              Localizations
              • FR: ù

              ù

              Overview

              Availability: Token available everywhere.

              Syntax

              ù

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BB94
              Categories
              Localizations
              • FR: û

              û

              Overview

              Availability: Token available everywhere.

              Syntax

              û

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BB95
              Categories
              Localizations
              • FR: ü

              ü

              Overview

              Availability: Token available everywhere.

              Syntax

              ü

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BB96
              Categories
              Localizations
              • FR: Ç

              Ç

              Overview

              Availability: Token available everywhere.

              Syntax

              Ç

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BB97
              Categories
              Localizations
              • FR: ç

              ç

              Overview

              Availability: Token available everywhere.

              Syntax

              ç

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BB98
              Categories
              Localizations
              • FR: Ñ

              Ñ

              Overview

              Availability: Token available everywhere.

              Syntax

              Ñ

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BB99
              Categories
              Localizations
              • FR: ñ

              ñ

              Overview

              Availability: Token available everywhere.

              Syntax

              ñ

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BB9A
              Categories
              Localizations
              • FR: ´

              ´

              Overview

              Availability: Token available everywhere.

              Syntax

              ´

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BB9B
              Categories
              Localizations
              • FR: ```

              ```

              Overview

              Availability: Token available everywhere.

              Syntax

              ```

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BB9C
              Categories
              Localizations
              • FR: ¨

              ¨

              Overview

              Availability: Token available everywhere.

              Syntax

              ¨

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BB9D
              Categories
              Localizations
              • FR: ¿

              ¿

              Overview

              Availability: Token available everywhere.

              Syntax

              ¿

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BB9E
              Categories
              Localizations
              • FR: ¡

              ¡

              Overview

              Availability: Token available everywhere.

              Syntax

              ¡

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BB9F
              Categories
              Localizations
              • FR: α

              α

              Overview

              Availability: Token available everywhere.

              Syntax

              α

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BBA0
              Categories
              Localizations
              • FR: β

              β

              Overview

              Availability: Token available everywhere.

              Syntax

              β

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BBA1
              Categories
              Localizations
              • FR: γ

              γ

              Overview

              Availability: Token available everywhere.

              Syntax

              γ

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BBA2
              Categories
              Localizations
              • FR: Δ

              Δ

              Overview

              Availability: Token available everywhere.

              Syntax

              Δ

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BBA3
              Categories
              Localizations
              • FR: δ

              δ

              Overview

              Availability: Token available everywhere.

              Syntax

              δ

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BBA4
              Categories
              Localizations
              • FR: ε

              ε

              Overview

              Availability: Token available everywhere.

              Syntax

              ε

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BBA5
              Categories
              Localizations
              • FR: λ

              λ

              Overview

              Availability: Token available everywhere.

              Syntax

              λ

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BBA6
              Categories
              Localizations
              • FR: μ

              μ

              Overview

              Availability: Token available everywhere.

              Syntax

              μ

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BBA7
              Categories
              Localizations
              • FR: |π

              |π

              Overview

              Syntax

              |π

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BBA8
              Categories
              Localizations
              • FR: ρ

              ρ

              Overview

              Availability: Token available everywhere.

              Syntax

              ρ

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BBA9
              Categories
              Localizations
              • FR: Σ

              Σ

              Overview

              Availability: Token available everywhere.

              Syntax

              Σ

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BBAB
              Categories
              Localizations
              • FR: Φ

              Φ

              Overview

              Availability: Token available everywhere.

              Syntax

              Φ

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BBAC
              Categories
              Localizations
              • FR: Ω

              Ω

              Overview

              Availability: Token available everywhere.

              Syntax

              Ω

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BBAD
              Categories
              Localizations
              • FR: ṗ

              ṗ

              Overview

              Syntax

              ṗ

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BBAE
              Categories
              Localizations
              • FR: χ

              χ

              Overview

              Availability: Token available everywhere.

              Syntax

              χ

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BBAF
              Categories
              Localizations
              • FR: 𝐅

              𝐅

              Overview

              Syntax

              𝐅

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BBB0
              Categories
              Localizations
              • FR: a

              a

              Overview

              Availability: Token available everywhere.

              Syntax

              a

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BBB1
              Categories
              Localizations
              • FR: b

              b

              Overview

              Availability: Token available everywhere.

              Syntax

              b

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BBB2
              Categories
              Localizations
              • FR: c

              c

              Overview

              Availability: Token available everywhere.

              Syntax

              c

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BBB3
              Categories
              Localizations
              • FR: d

              d

              Overview

              Availability: Token available everywhere.

              Syntax

              d

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BBB4
              Categories
              Localizations
              • FR: e

              e

              Overview

              Availability: Token available everywhere.

              Syntax

              e

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BBB5
              Categories
              Localizations
              • FR: f

              f

              Overview

              Availability: Token available everywhere.

              Syntax

              f

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BBB6
              Categories
              Localizations
              • FR: g

              g

              Overview

              Availability: Token available everywhere.

              Syntax

              g

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BBB7
              Categories
              Localizations
              • FR: h
              h

              Overview

              Availability: Token available everywhere.

              Syntax

              h

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BBB8
              Categories
              Localizations
              • FR: i

              i

              Overview

              Availability: Token available everywhere.

              Syntax

              i

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BBB9
              Categories
              Localizations
              • FR: j

              j

              Overview

              Availability: Token available everywhere.

              Syntax

              j

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BBBA
              Categories
              Localizations
              • FR: k

              k

              Overview

              Availability: Token available everywhere.

              Syntax

              k

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BBBC
              Categories
              Localizations
              • FR: l

              l

              Overview

              Availability: Token available everywhere.

              Syntax

              l

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BBBD
              Categories
              Localizations
              • FR: m

              m

              Overview

              Availability: Token available everywhere.

              Syntax

              m

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BBBE
              Categories
              Localizations
              • FR: n

              n

              Overview

              Availability: Token available everywhere.

              Syntax

              n

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BBBF
              Categories
              Localizations
              • FR: o

              o

              Overview

              Availability: Token available everywhere.

              Syntax

              o

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BBC0
              Categories
              Localizations
              • FR: p

              p

              Overview

              Availability: Token available everywhere.

              Syntax

              p

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BBC1
              Categories
              Localizations
              • FR: q

              q

              Overview

              Availability: Token available everywhere.

              Syntax

              q

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BBC2
              Categories
              Localizations
              • FR: r

              r

              Overview

              Availability: Token available everywhere.

              Syntax

              r

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BBC3
              Categories
              Localizations
              • FR: s

              s

              Overview

              Availability: Token available everywhere.

              Syntax

              s

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BBC4
              Categories
              Localizations
              • FR: t

              t

              Overview

              Availability: Token available everywhere.

              Syntax

              t

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BBC5
              Categories
              Localizations
              • FR: u

              u

              Overview

              Availability: Token available everywhere.

              Syntax

              u

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BBC6
              Categories
              Localizations
              • FR: v

              v

              Overview

              Availability: Token available everywhere.

              Syntax

              v

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BBC7
              Categories
              Localizations
              • FR: w

              w

              Overview

              Availability: Token available everywhere.

              Syntax

              w

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BBC8
              Categories
              Localizations
              • FR: x

              x

              Overview

              Availability: Token available everywhere.

              Syntax

              x

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BBC9
              Categories
              Localizations
              • FR: y

              y

              Overview

              Availability: Token available everywhere.

              Syntax

              y

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BBCA
              Categories
              Localizations
              • FR: z

              z

              Overview

              Availability: Token available everywhere.

              Syntax

              z

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BBCB
              Categories
              Localizations
              • FR: σ

              σ

              Overview

              Availability: Token available everywhere.

              Syntax

              σ

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BBCC
              Categories
              Localizations
              • FR: τ

              τ

              Overview

              Availability: Token available everywhere.

              Syntax

              τ

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BBCD
              Categories
              Localizations
              • FR: Í

              Í

              Overview

              Syntax

              Í

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BBCE
              Categories
              Localizations
              • FR: RéorganiserMém

              GarbageCollect

              Overview

              Displays the garbage collection menu to allow cleanup of unused archive memory.

              Availability: Token available everywhere.

              Syntax

              GarbageCollect

              Location

              2nd, catalog, GarbageCollect

              Description

              A bit of a preamble: unlike RAM, which is the easy-to-access memory, Flash ROM (the archive), used for long-term storage on the 83+ and higher, can't be written to easily. Skipping over technicalities, what's written in the archive once is semi-permanent, and can't be written to again unless an entire 64KB sector of memory is erased.

              As a result, when you delete a variable from archive, the calculator doesn't delete it immediately (there may be other, good variables in the same block that would get erased as well), it just marks it as deleted. Similarly, when you unarchive a variable, its data is copied to RAM and the original is marked as deleted.

              Naturally, this can't be done forever: sooner or later you'll run out of space in the archive because all of it is taken up by these "garbage variables". At this point, the calculator does something known as "garbage collecting". It copies the actually-used variables in each sector to a backup sector (set aside just for this purpose), then erases it; the process is repeated for the other sectors. Additionally, the variables are rearranged so that they aren't spread out all over the place; this makes it more likely that a spot will be found for large variables.

              While "garbage collecting" will be done automatically when it's absolutely necessary, this may be a time-consuming process at that stage. Instead, you can call the GarbageCollect command yourself periodically (how often depends on your calculator habits, but generally once a month or so could work) to keep the Flash ROM in a semi-neat state, and then it will be a fairly quick process.

              During garbage collection, a menu will appear that asks you "Garbage Collect?", giving you the options No and Yes. If you didn't select the GarbageCollect command yourself, it's highly recommended to select Yes. If you did select it, you probably want to garbage collect, so you should also select Yes. At that point, the message "Garbage collecting…" will be displayed for some time, and then the process will end.

              Advanced Uses

              To avoid garbage collecting often, reduce the amount of times you archive and unarchive variables. There's also the consideration that too many writes to the Flash ROM (which are directly related to the number of GarbageCollects you do) can, in theory, wear it out. This probably would take much longer than anyone's used a TI-83+ calculator so far, though, and in all probability you don't really have to worry about this.

              Source: parts of this page were written by the following TI|BD contributors: burr, CloudVariable, DarkerLine, GoVegan, kg583, Trenly.

              History

              Calculator OS Version Description
              TI-83+ 1.03 Added
              Property Value
              Hex Value $BBCF
              Categories
              Localizations
              • FR: ~

              ~

              Overview

              Comment:CF-DA: 83+ 1.15 or later

              Syntax

              ~

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.15 Added
              Property Value
              Hex Value $BBD0
              Categories
              Localizations
              • FR: '

              '

              Overview

              Syntax

              '

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              Property Value
              Hex Value $BBD1
              Categories
              Localizations
              • FR: @

              @

              Overview

              Availability: Token available everywhere.

              Syntax

              @

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.15 Added
              Property Value
              Hex Value $BBD2
              Categories
              Localizations
              • FR: #

              #

              Overview

              Availability: Token available everywhere.

              Syntax

              #

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.15 Added
              Property Value
              Hex Value $BBD3
              Categories
              Localizations
              • FR: $

              $

              Overview

              Availability: Token available everywhere.

              Syntax

              $

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.15 Added
              Property Value
              Hex Value $BBD4
              Categories
              Localizations
              • FR: &

              &

              Overview

              Availability: Token available everywhere.

              Syntax

              &

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.15 Added
              Property Value
              Hex Value $BBD5
              Categories
              Localizations
              • FR: ‛

              ‛

              Overview

              Syntax

              ‛

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.15 Added
              Property Value
              Hex Value $BBD6
              Categories
              Localizations
              • FR: ;

              ;

              Overview

              Availability: Token available everywhere.

              Syntax

              ;

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.15 Added
              Property Value
              Hex Value $BBD7
              Categories
              Localizations
              • FR: \

              \

              Overview

              Availability: Token available everywhere.

              Syntax

              \

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.15 Added
              Property Value
              Hex Value $BBD8
              Categories
              Localizations
              • FR: |

              |

              Overview

              Syntax

              |

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.15 Added
              Property Value
              Hex Value $BBD9
              Categories
              Localizations
              • FR: _

              _

              Overview

              Syntax

              _

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.15 Added
              Property Value
              Hex Value $BBDA
              Categories
              Localizations
              • FR: %

              %

              Overview

              Availability: Token available everywhere.

              Syntax

              %

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.15 Added
              Property Value
              Hex Value $BBDB
              Categories
              Localizations
              • FR: …

              …

              Overview

              Comment:DB-F5: 83+ 1.16 or later

              Syntax

              …

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.16 Added
              Property Value
              Hex Value $BBDC
              Categories
              Localizations
              • FR: ∠

              ∠

              Overview

              Syntax

              ∠

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.16 Added
              Property Value
              Hex Value $BBDD
              Categories
              Localizations
              • FR: ß

              ß

              Overview

              Syntax

              ß

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.16 Added
              Property Value
              Hex Value $BBDE
              Categories
              Localizations
              • FR: ˣ

              ˣ

              Overview

              Syntax

              ˣ

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.16 Added
              Property Value
              Hex Value $BBDF
              Categories
              Localizations
              • FR: ᴛ

              ᴛ

              Overview

              Syntax

              ᴛ

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.16 Added
              Property Value
              Hex Value $BBE0
              Categories
              Localizations
              • FR: ₀

              ₀

              Overview

              Availability: Token available everywhere.

              Syntax

              ₀

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.16 Added
              Property Value
              Hex Value $BBE1
              Categories
              Localizations
              • FR: ₁
              ₁

              Overview

              Availability: Token available everywhere.

              Syntax

              ₁

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.16 Added
              Property Value
              Hex Value $BBE2
              Categories
              Localizations
              • FR: ₂

              ₂

              Overview

              Availability: Token available everywhere.

              Syntax

              ₂

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.16 Added
              Property Value
              Hex Value $BBE3
              Categories
              Localizations
              • FR: ₃

              ₃

              Overview

              Availability: Token available everywhere.

              Syntax

              ₃

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.16 Added
              Property Value
              Hex Value $BBE4
              Categories
              Localizations
              • FR: ₄

              ₄

              Overview

              Availability: Token available everywhere.

              Syntax

              ₄

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.16 Added
              Property Value
              Hex Value $BBE5
              Categories
              Localizations
              • FR: ₅

              ₅

              Overview

              Availability: Token available everywhere.

              Syntax

              ₅

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.16 Added
              Property Value
              Hex Value $BBE6
              Categories
              Localizations
              • FR: ₆

              ₆

              Overview

              Availability: Token available everywhere.

              Syntax

              ₆

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.16 Added
              Property Value
              Hex Value $BBE7
              Categories
              Localizations
              • FR: ₇

              ₇

              Overview

              Availability: Token available everywhere.

              Syntax

              ₇

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.16 Added
              Property Value
              Hex Value $BBE8
              Categories
              Localizations
              • FR: ₈

              ₈

              Overview

              Availability: Token available everywhere.

              Syntax

              ₈

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.16 Added
              Property Value
              Hex Value $BBE9
              Categories
              Localizations
              • FR: ₉

              ₉

              Overview

              Availability: Token available everywhere.

              Syntax

              ₉

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.16 Added
              Property Value
              Hex Value $BBEA
              Categories
              Localizations
              • FR: ₁₀

              ₁₀

              Overview

              Syntax

              ₁₀

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.16 Added
              Property Value
              Hex Value $BBEB
              Categories
              Localizations
              • FR: ◄

              ◄

              Overview

              Syntax

              ◄

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.16 Added
              Property Value
              Hex Value $BBEC
              Categories
              Localizations
              • FR: ►

              ►

              Overview

              Syntax

              ►

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.16 Added
              Property Value
              Hex Value $BBED
              Categories
              Localizations
              • FR: ↑

              ↑

              Overview

              Syntax

              ↑

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.16 Added
              Property Value
              Hex Value $BBEE
              Categories
              Localizations
              • FR: ↓

              ↓

              Overview

              Syntax

              ↓

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.16 Added
              Property Value
              Hex Value $BBF0
              Categories
              Localizations
              • FR: ×

              ×

              Overview

              Syntax

              ×

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.16 Added
              Property Value
              Hex Value $BBF1
              Categories
              Localizations
              • FR: ∫

              ∫

              Overview

              Syntax

              ∫

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.16 Added
              Property Value
              Hex Value $BBF2
              Categories
              Localizations
              • FR: 🡅

              🡅

              Overview

              Syntax

              🡅

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.16 Added
              Property Value
              Hex Value $BBF3
              Categories
              Localizations
              • FR: 🡇

              🡇

              Overview

              Syntax

              🡇

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.16 Added
              Property Value
              Hex Value $BBF4
              Categories
              Localizations
              • FR: √

              √

              Overview

              Syntax

              √

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.16 Added
              Property Value
              Hex Value $BBF5
              Categories
              Localizations
              • FR: ⌸

              ⌸

              Overview

              Comment:inverted equal

              Syntax

              ⌸

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-83+ 1.16 Added
              Property Value
              Hex Value $BC
              Categories
              Localizations
              • FR: √(

              √(

              Overview

              Availability: Token available everywhere.

              Syntax

              √(

              Description

              Takes the square root of a positive or negative number. It works exactly the same as 2×√ or ^(1/2) but is smaller and uses an ending parenthesis. If used on a list, it will return a list with the square root of each element.

              √(4)
        2
√(2)
        1.414213562

√({1,-1})
        {1 i}

              This may return a complex number or throw ERR:NONREAL ANS (depending on mode settings) if taking the square root of a negative number.

              Optimization

              Never raise something to the one-half power explicitly; use this command instead.

              :X^(1/2)→X
can be
:√(X→X

              Error Conditions

              Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, thornahawk.

              History

              Calculator OS Version Description
              TI-82 1.0 √ added
              TI-83 0.01013 Renamed √ to √(
              Property Value
              Hex Value $BD
              Categories
              Localizations
              • FR: ³√(

              ³√(

              Overview

              Availability: Token available everywhere.

              Syntax

              ³√(

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-82 1.0 ³√ added
              TI-83 0.01013 Renamed ³√ to ³√(
              Property Value
              Hex Value $BE
              Categories
              Localizations
              • FR: ln(

              ln(

              Overview

              Returns the natural logarithm of a real or complex number, expression, or list.

              Availability: Token available everywhere.

              Syntax

              ln(value)

              Arguments

              NameTypeOptional
              value

              Location

              ln

              Description

              The ln( command computes the natural logarithm of a value — the exponent to which the constant e must be raised, to get that value. This makes it the inverse of the e^( command.

              ln( is a real number for all positive real values. For negative numbers, ln( is an imaginary number (so taking ln( of a negative number will cause ERR:NONREAL ANS to be thrown in Real mode), and of course it's a complex number for complex values. ln( is not defined at 0, even if you're in a complex mode.

              Advanced Uses

              Using either the ln( or the log( command, logarithms of any base can be calculated, using the identity:

              (1) \(\begin{align} \log_b{x} = \frac{\ln{x}}{\ln{b}} = \frac{\log{x}}{\log{b}} \end{align}\)

              So, to take the base B log of a number X, you could use either of the following equivalent ways:

              :log(X)/log(B)

              :ln(X)/ln(B)

              This is the exponent to which B must be raised, to get X.

              Error Conditions

              Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Timothy Foster.

              History

              Calculator OS Version Description
              TI-82 1.0 ln added
              TI-83 0.01013 Renamed ln to ln(
              Property Value
              Hex Value $BF
              Categories
              Localizations
              • FR: 𝑒^(

              𝑒^(

              Overview

              Returns e raised to power.

              Availability: Token available everywhere.

              Syntax

              𝑒^(power)

              Arguments

              NameTypeOptional
              power

              Location

              2nd, eˣ

              Overview

              Returns a list of e raised to a list of powers.

              Availability: Token available everywhere.

              Syntax

              𝑒^(list)

              Arguments

              NameTypeOptional
              listlist

              Location

              2nd, eˣ

              Description

              The e^( command raises the constant e to a power. Since it's possible to just type out e, ^, and (, the reason for having a separate function isn't immediately obvious but in fact most of the time you need to use e, it's to raise it to a power.

              The trigonometric and hyperbolic functions can be expressed, and in fact are usually defined, in terms of e^(.

              e^( accepts numbers and lists (but unfortunately not matrices) as arguments. It also works, and is often used for, complex numbers (in fact, one of the standard forms of complex numbers on TI-83 series calculators is r𝑒^θ𝑖, which uses the e^( function)

              e^(2)
        7.389056099
𝑒^(πi)
        -1
𝑒^({-1,0,1})
        {.3678794412 1 2.718281828}

              Formulas

              The e^( is usually defined by an infinite series:

              (1) \(\begin{align} e^x=\sum_{n=0}^\infty{\frac{x^n}{n!}} \end{align}\)

              This is then used to define exponentiation in general (for all real and even complex numbers), rather than using some sort of definition of exponents that involves multiplying a number by itself many times (which only works for integers).

              Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Myles_Zadok, Timothy Foster.

              History

              Calculator OS Version Description
              TI-82 1.0 𝑒^ added
              TI-83 0.01013 Renamed 𝑒^ to 𝑒^(
              Property Value
              Hex Value $C0
              Categories
              Localizations
              • FR: log(

              log(

              Overview

              Returns logarithm of a real or complex number, expression, or list.

              Availability: Token available everywhere.

              Syntax

              log(value)

              Arguments

              NameTypeOptional
              value

              Location

              log

              Description

              The log( command computes the base 10 logarithm of a value — the exponent to which 10 must be raised, to get that value. This makes it the inverse of the 10^( command.

              log( is a real number for all positive real values. For negative numbers, log( is an imaginary number (so taking log( of a negative number will cause ERR:NONREAL ANS to be thrown in Real mode), and of course it's a complex number for complex values. log( is not defined at 0, even if you're in a complex mode.

              Advanced Uses

              Using either the ln( or the log( command, logarithms of any base can be calculated, using the identity:

              (1) \(\begin{align} \log_b{x} = \frac{\ln{x}}{\ln{b}} = \frac{\log{x}}{\log{b}} \end{align}\)

              So, to take the base B log of a number X, you could use either of the following equivalent ways:

              :log(X)/log(B)

              :ln(X)/ln(B)

              This is the exponent to which B must be raised, to get X. If using OS 2.53 MP or higher, this formula can be circumvented entirely with an optional second argument:

              :log(X,B)

              This form is functionally identical to the logBASE command with the same arguments available with the same OS, but unlike its counterpart does not have any special visual rendering when in MATHPRINT mode. Both logBASE and the second argument of log( are disabled in exam mode.

              The base 10 logarithm specifically can also be used to calculate the number of digits a whole number has:

              :1+int(log(N))

              This will return the number of digits N has, if N is a whole number. If N is a decimal, it will ignore the decimal digits of N.

              Error Conditions

              Source: parts of this page were written by the following TI|BD contributors: DarkerLine, Deflect, GoVegan, kg583, Timothy Foster.

              History

              Calculator OS Version Description
              TI-82 1.0 log added
              TI-83 0.01013 Renamed log to log(
              Property Value
              Hex Value $C1
              Categories
              Localizations
              • FR: ₁₀^(

              ₁₀^(

              Overview

              Availability: Token available everywhere.

              Syntax

              ₁₀^(

              Description

              Examples

              Explanation 1

              code 1

              Explanation 2

              code 2

              Error Conditions

              Advanced Notes

              History

              Calculator OS Version Description
              TI-82 1.0 ₁₀^ added
              TI-83 0.01013 Renamed ₁₀^ to ₁₀^(
              Property Value
              Hex Value $C2
              Categories
              Localizations
              • FR: sin(

              sin(

              Overview

              Returns the sine of a real number, expression, or list.

              Availability: Token available everywhere.

              Syntax

              sin(value)

              Arguments

              NameTypeOptional
              valuereal|expression|real[]

              Location

              sin

              Description

              sin(θ) returns the sine of θ, which is defined as the y-value of the point of intersection of the unit circle and a line containing the origin that makes an angle θ with the positive x-axis

              The value returned depends on whether the calculator is in Radian or Degree mode. A full rotation around a circle is 2π radians, which is equal to 360°. The conversion from radians to degrees is angle180/π and from degrees to radians is angleπ/180. The sin( command also works on a list of real numbers.

              In radians:

              sin(π/6)
    .5

              In degrees:

              sin(30)
    .5

              Advanced Uses

              You can bypass the mode setting by using the ° (degree) and ʳ (radian) symbols. These next two commands will return the same values no matter if your calculator is in degrees or radians:

              sin(30°)
    .5

              sin(π/6ֿ¹)
    .5

              Error Conditions

              • ERR:DATA TYPE is thrown if you supply a matrix or a complex argument.
              • ERR:DOMAIN is thrown if you supply an input ≥1E12.

              See Also

              Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, simplethinker, Xeda Elnara.

              History

              Calculator OS Version Description
              TI-82 1.0 sin added
              TI-83 0.01013 Renamed sin to sin(
              Property Value
              Hex Value $C3
              Categories
              Localizations
              • FR: Arcsin(

              sin⁻¹(

              Overview

              Returns the arcsine of a real number, expression, or list.

              Availability: Token available everywhere.

              Syntax

              sin⁻¹(value)

              Arguments

              NameTypeOptional
              ⁻¹real|expression|real[]
              valuereal|expression|real[]

              Location

              2nd, sin⁻¹

              Description

              sinֿ¹( returns the arcsine of its argument. It is the inverse of sin(, which means that sinֿ¹(z) produces an angle θ such that sin(θ)=z.

              Like sin(, the result of sinֿ¹( depends on whether the calculator is in Radian or Degree mode. However, unlike sine, the result is in degrees or radians, not the argument. A full rotation around a circle is 2π radians, which is equal to 360°. The conversion of θ=sinֿ¹(n) from radians to degrees is θ180/π and from degrees to radians is θπ/180. The sinֿ¹( command also works on lists.

              The sinֿ¹( function can be defined for all real and complex numbers; however, the function assumes real values only in the closed interval [-1,1]. Because the trigonometric functions and their inverses in the Z80 calculators are restricted only to real values, the calculator will throw ERR:DOMAIN if the argument is outside of this interval, no matter what the mode setting may be.

              In radians:

              :sinֿ¹(1)
    1.570796327

              In degrees:

              :sinֿ¹(1)
    90

              Advanced Uses

              Since the function sine itself doesn't have the restrictions that arcsine does, and since arcsine is the inverse of sine, you can use sinֿ¹(sin( to keep a variable within a certain range (most useful on the graph screen). Here is an example for a game like pong. The ball travels between -6 and 6.

              You could use a flag like this:

              :If 6=abs(X        \\ X is the position
:-D→D        \\ D is the direction
:X+D→X        \\ new position
:Pt-On(-54,X,"=")

              An easier way to do this, without needing a flag or even an If statement, is using sinֿ¹(sin(

              :X+1→X        \\ Note: the calculator is in degree mode
:Pt-On(-54,sinֿ¹(sin(15X))/15,"=")    \\ 15 is used because sinֿ¹ ranges from [-90,90]
                                        and X from [-6,6],  so 90/6=15

              Error Conditions

              • ERR:DATA TYPE is thrown if you input a complex value or a matrix.
              • ERR:DOMAIN is thrown if you supplied an argument outside the interval [-1,1]

              Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, simplethinker, thornahawk.

              History

              Calculator OS Version Description
              TI-82 1.0 sin⁻¹ added
              TI-83 0.01013 Renamed sin⁻¹ to sin⁻¹(
              Property Value
              Hex Value $C4
              Categories
              Localizations
              • FR: cos(

              cos(

              Overview

              Returns cosine of a real number, expression, or list.

              Availability: Token available everywhere.

              Syntax

              cos(value)

              Arguments

              NameTypeOptional
              valuereal|expression|real[]

              Location

              cos

              Description

              cos(θ) returns the cosine of θ, which is defined as the x-value of the point of intersection of the unit circle and a line containing the origin that makes an angle θ with the positive x-axis

              The value returned depends on whether the calculator is in Radian or Degree mode. A full rotation around a circle is 2π radians, which is equal to 360°. The conversion from radians to degrees is angle180/π and from degrees to radians is angleπ/180. The cos( command also works on a list of real numbers.

              In radians:

              cos(π/3)
    .5

              In degrees:

              cos(60)
    .5

              Advanced Uses

              You can bypass the mode setting by using the ° (degree) and ʳ (radian) symbols. These next two commands will return the same values no matter if your calculator is in degrees or radians:

              cos(60°)
    .5

              cos(π/3ֿ¹ )
    .5

              Error Conditions

              • ERR:DATA TYPE is thrown if you supply a matrix or a complex argument.
              • ERR:ARGUMENT is thrown if you use more than one number.
              • ERR:DOMAIN is thrown if you supply an input ≥1E12.

              See Also

              Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Myles_Zadok, nap386, simplethinker, Xeda Elnara.

              History

              Calculator OS Version Description
              TI-82 1.0 cos added
              TI-83 0.01013 Renamed cos to cos(
              Property Value
              Hex Value $C5
              Categories
              Localizations
              • FR: Arccos(

              cos⁻¹(

              Overview

              Returns arccosine of a real number, expression, or list.

              Availability: Token available everywhere.

              Syntax

              cos⁻¹(value)

              Arguments

              NameTypeOptional
              ⁻¹real|expression|real[]
              valuereal|expression|real[]

              Location

              2nd, cos⁻¹

              Description

              cosֿ¹( returns the arccosine of its argument. It is the inverse of cos(, which means that cosֿ¹(n) produces an angle θ such that cos(θ)=n.

              Like cos(, the result of cosֿ¹( depends on whether the calculator is in Radian or Degree mode. However, unlike cosine, the result is in degrees or radians, not the argument. A full rotation around a circle is 2π radians, which is equal to 360°. The conversion of θ=cosֿ¹(n) from radians to degrees is θ180/π and from degrees to radians is θπ/180. The cosֿ¹( command also works on a list.

              The cosֿ¹( function can be defined for all real and complex numbers, but assumes real values only in the closed interval [-1,1]. Because Z80 calculators have their trigonometric functions and inverses restricted only to real values, the calculator will throw ERR:DOMAIN if the argument is outside of this interval, no matter what the mode setting may be.

              In radians:

              :cosֿ¹(-1)
    3.141592654

              In degrees:

              :cosֿ¹(-1)
    180

              Advanced Uses

              Since the function cosine itself doesn't have the restrictions that arccosine does, and since arccosine is the inverse of cosine, you can use cosֿ¹(cos( to keep a variable within a certain range (most useful for the home screen). Here is an example for a game like pong. The ball travels between 0 and 12.

              You could use a flag like this:

              :If X=12 or not(X     \\ X is the position
:-D→D        \\ D is the direction
:X+D→X        \\ new position
:Output(8,X,"=

              An easier way to do this, without needing a flag or even an If statement, is using cosֿ¹(cos(

              :X+1→X        \\ Note: the calculator is in Degree mode
:Output(8,cosֿ¹(cos(15X))/15,"=")    \\ I used 15 because cosֿ¹ ranges from [0,180]
                                        and X from [0,12],  so 180/12=15

              Error Conditions

              • ERR:DOMAIN is thrown if you supplied an argument outside the interval [-1,1]
              • ERR:DATA TYPE is thrown if you input a complex value or a matrix.

              Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Myles_Zadok, simplethinker, thornahawk.

              History

              Calculator OS Version Description
              TI-82 1.0 cos⁻¹ added
              TI-83 0.01013 Renamed cos⁻¹ to cos⁻¹(
              Property Value
              Hex Value $C6
              Categories
              Localizations
              • FR: tan(

              tan(

              Overview

              Returns the tangent of a real number, expression, or list.

              Availability: Token available everywhere.

              Syntax

              tan(value)

              Arguments

              NameTypeOptional
              valuereal|expression|real[]

              Location

              tan

              Description

              tan(θ) calculates the tangent of the angle θ, which is defined by \(\tan \theta=\frac{\sin \theta}{\cos \theta}\)

              The value returned depends on whether the calculator is in Radian or Degree mode. A full rotation around a circle is 2π radians, which is equal to 360°. The conversion from radians to degrees is angle180/π and from degrees to radians is angleπ/180. The tan( command also works on a list of real numbers.

              Since tangent is defined as the quotient of sine divided by cosine, it is undefined for any angle such that cos(θ)=0.

              In radians:

              tan(π/4)
    1

              In degrees:

              tan(45)
    1

              Advanced Uses

              You can bypass the mode setting by using the ° (degree) and ʳ (radian) symbols. These next two commands will return the same values no matter if your calculator is in degrees or radians:

              tan(45°)
    1

              tan(π/4¹ )
    1

              Error Conditions

              • ERR:DATA TYPE is thrown if you supply a matrix or a complex argument.
              • ERR:DOMAIN is thrown if you supply an angle of π/2±nπ (in radians, where n is an integer) or 90±180n (in degrees, where n is an integer), or when the input is ≥1E12.

              Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Mr Dino, simplethinker, Timothy Foster, Weregoose, Xeda Elnara.

              History

              Calculator OS Version Description
              TI-82 1.0 tan added
              TI-83 0.01013 Renamed tan to tan(
              Property Value
              Hex Value $C7
              Categories
              Localizations
              • FR: Arctan(

              tan⁻¹(

              Overview

              Returns the arctangent of a real number, expression, or list.

              Availability: Token available everywhere.

              Syntax

              tan⁻¹(value)

              Arguments

              NameTypeOptional
              ⁻¹real|expression|real[]
              valuereal|expression|real[]

              Location

              2nd, tan⁻¹

              Description

              tanֿ¹( returns the arctangent of its argument. It is the inverse of tan(, which means that tanֿ¹(n) produces an angle θ such that tan(θ)=n.

              Like tan(, the result of tanֿ¹( depends on whether the calculator is in Radian or Degree mode. However, unlike tangent, the result is in degrees or radians, not the argument. A full rotation around a circle is 2π radians, which is equal to 360°. The conversion of θ=tanֿ¹(n) from radians to degrees is θ180/π and from degrees to radians is θπ/180. The tanֿ¹( command also works on a list.

              tanֿ¹( will always return a value between -π/2 and π/2 (or -90° and 90°).

              In radians:

              :tanֿ¹(1)
    .7853981634

              In degrees:

              :tanֿ¹(1)
    45

              Optimization

              Expressions of the form tanֿ¹(y__/x) are usually better recast as R►Pθ(x,y); the latter will not fail even if x should happen to be equal to zero.

              Error Conditions

              • ERR:DATA TYPE is thrown if you input a complex value or a matrix.

              Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, thornahawk.

              History

              Calculator OS Version Description
              TI-82 1.0 tan⁻¹ added
              TI-83 0.01013 Renamed tan⁻¹ to tan⁻¹(
              Property Value
              Hex Value $C8
              Categories
              Localizations
              • FR: sh(

              sinh(

              Overview

              Returns the hyperbolic sine of a real number, expression, or list.

              Availability: Token available everywhere.

              Syntax

              sinh(value)

              Arguments

              NameTypeOptional
              valuereal|expression|real[]

              Location

              2nd, catalog, sinh(

              Description

              Calculates the hyperbolic sine of a value. The hyperbolic trig functions sinh(, cosh(, and tanh( are an analog of normal trig functions, but for a hyperbola, rather than a circle. They can be expressed in terms of real powers of e, and don't depend on the Degree or Radian mode setting.

              sinh(0)
    0
sinh(1)
    1.175201194

              Like normal trig commands, sinh( works on lists as well, but not on complex numbers, even though the function is often extended to the complex numbers in mathematics.

              Formulas

              The definition of hyperbolic sine is:

              (1) \(\begin{align} \sinh{x}=\frac{e^x-e^{-x}}{2} \end{align}\)

              Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, thornahawk, Timothy Foster.

              History

              Calculator OS Version Description
              TI-82 1.0 sinh added
              TI-83 0.01013 Renamed sinh to sinh(
              Property Value
              Hex Value $C9
              Categories
              Localizations
              • FR: Argsh(

              sinh⁻¹(

              Overview

              Returns the hyperbolic arcsine of a real number, expression, or list.

              Availability: Token available everywhere.

              Syntax

              sinh⁻¹ (value)

              Arguments

              NameTypeOptional
              ⁻¹real|expression|real[]
              valuereal|expression|real[]

              Location

              2nd, catalog, sinh

              Description

              The sinhֿ¹( command calculates the inverse hyperbolic sine of a value. sinhֿ¹(x) is the number y such that x = sinh(y). Unlike for the standard trig functions, this uniquely determines the inverse hyperbolic sine of any real number.

              The sinhֿ¹( command also works for lists.

              sinhֿ¹(0)
    0
sinhֿ¹({1,2,3})
    {.881373587 1.443635475 1.818446459}

              Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, thornahawk.

              History

              Calculator OS Version Description
              TI-82 1.0 sinh⁻¹ added
              TI-83 0.01013 Renamed sinh⁻¹ to sinh⁻¹(
              Property Value
              Hex Value $CA
              Categories
              Localizations
              • FR: ch(

              cosh(

              Overview

              Returns hyperbolic cosine of a real number, expression, or list.

              Availability: Token available everywhere.

              Syntax

              cosh(value)

              Arguments

              NameTypeOptional
              valuereal|expression|real[]

              Location

              2nd, catalog, cosh(

              Description

              Calculates the hyperbolic cosine of a value. The hyperbolic trig functions sinh(, cosh(, and tanh( are an analog of normal trig functions, but for a hyperbola, rather than a circle. They can be expressed in terms of real powers of e, and don't depend on the Degree or Radian mode setting.

              cosh(0)
    1
cosh(1)
    1.543080635

              Like normal trig commands, cosh( works on lists as well, but not on complex numbers, even though the function is often extended to the complex numbers in mathematics.

              Formulas

              The definition of hyperbolic cosine is:

              (1) \(\begin{align} \cosh{x}=\frac{e^x+e^{-x}}{2} \end{align}\)

              Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Myles_Zadok, thornahawk, Timothy Foster.

              History

              Calculator OS Version Description
              TI-82 1.0 cosh added
              TI-83 0.01013 Renamed cosh to cosh(
              Property Value
              Hex Value $CB
              Categories
              Localizations
              • FR: Argch(

              cosh⁻¹(

              Overview

              Returns hyperbolic arccosine of a real number, expression, or list.

              Availability: Token available everywhere.

              Syntax

              cosh⁻¹ (value)

              Arguments

              NameTypeOptional
              ⁻¹real|expression|real[]
              valuereal|expression|real[]

              Location

              2nd, catalog, cosh

              Description

              The coshֿ¹( function gives the inverse hyperbolic cosine of a value. coshֿ¹(x) is the number y such that x = cosh(y).

              Although coshֿ¹(x) can be defined for all real and complex numbers, it assumes real values only for x≥1. Since hyperbolic functions in the Z80 calculators are restricted only to real values, ERR:DOMAIN is thrown when x<1.

              The coshֿ¹( command also works for lists.

              coshֿ¹(1)
    0
coshֿ¹({2,3})
    {1.316957897 1.762747174}

              Error Conditions

              • ERR:DOMAIN when taking the inverse cosh of a number less than 1.

              Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Myles_Zadok, thornahawk.

              History

              Calculator OS Version Description
              TI-82 1.0 cosh⁻¹ added
              TI-83 0.01013 Renamed cosh⁻¹ to cosh⁻¹(
              Property Value
              Hex Value $CC
              Categories
              Localizations
              • FR: th(

              tanh(

              Overview

              Returns hyperbolic tangent of a real number, expression, or list.

              Availability: Token available everywhere.

              Syntax

              tanh(value)

              Arguments

              NameTypeOptional
              valuereal|expression|real[]

              Location

              2nd, catalog, tanh(

              Description

              Calculates the hyperbolic tangent of a value. The hyperbolic trig functions sinh(, cosh(, and tanh( are an analog of normal trig functions, but for a hyperbola, rather than a circle. They can be expressed in terms of real powers of e, and don't depend on the Degree or Radian mode setting.

              tanh(0)
    0
tanh(1)
    .761594156

              Like normal trig commands, tanh( works on lists as well, but not on complex numbers, even though the function is often extended to the complex numbers in mathematics.

              Advanced Uses

              The tanh( command can be used to approximate the sign function:

              (1) \(\begin{align} \texttt{sgn} x=\begin{cases}-1&\text{if }x<0,\\0&\text{if }x=0,\\1&\text{if }x>0.\end{cases} \end{align}\)

              As the absolute value of the input becomes large, the convergence is achieved at a point closer to zero. For the function to work as intended generally, numbers having lesser orders of magnitude need to be multiplied by a factor large enough for the argument to arrive at ±16.720082053122, which is the smallest input to produce ±1 (respectively) to fourteen digits of accuracy.

              5/12→X
    .4166666667
tanh(E9X)
    1
tanh(-E9X)
    -1

              Formulas

              The definition of the hyperbolic tangent is:

              (2) \(\begin{align} \tanh{x}=\frac{e^x-e^{-x}}{e^x+e^{-x}}=\frac{e^{2x}-1}{e^{2x}+1} \end{align}\)

              Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, Edward H, GoVegan, thornahawk, Timothy Foster, Weregoose.

              History

              Calculator OS Version Description
              TI-82 1.0 tanh added
              TI-83 0.01013 Renamed tanh to tanh(
              Property Value
              Hex Value $CD
              Categories
              Localizations
              • FR: Argth(

              tanh⁻¹(

              Overview

              Returns the hyperbolic arctangent of a real number, expression, or list.

              Availability: Token available everywhere.

              Syntax

              tanh⁻¹(value)

              Arguments

              NameTypeOptional
              ⁻¹real|expression|real[]
              valuereal|expression|real[]

              Location

              2nd, catalog, tanh

              Description

              The tanhֿ¹( command calculates the inverse hyperbolic tangent of a value. tanhֿ¹(x) is the number y such that x = tanh(y).

              tanhֿ¹(x), although it can be defined for all real and complex numbers, is real-valued only for x in the open interval (-1,1). Since Z80 calculators have their hyperbolic functions and inverses restricted to real values, ERR:DOMAIN is thrown when x is outside the interval (-1,1).

              The tanhֿ¹( command also works for lists.

              tanhֿ¹(0)
    0
tanhֿ¹({-.5,.5})
    {-.5493061443 .5493061443}

              Error Conditions

              • ERR:DOMAIN when taking the inverse tanh of a number not between -1 and 1.

              Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, thornahawk.

              History

              Calculator OS Version Description
              TI-82 1.0 tanh⁻¹ added
              TI-83 0.01013 Renamed tanh⁻¹ to tanh⁻¹(
              Property Value
              Hex Value $CE
              Categories
              Localizations
              • FR: If

              If

              Overview

              If condition = 0 (false), skips commandA.

              Availability: Token only available from within the Basic editor.

              Syntax

              If condition:commandA:commands

              Arguments

              NameTypeOptional
              condition
              commandA
              commands

              Location

              prgm, CTL, 1:If

              If Then End

              Overview

              Executes commands from Then to End if condition = 1 (true).

              Availability: Token only available from within the Basic editor.

              Syntax

              If:conditionThen:commandsEnd:commands

              Arguments

              NameTypeOptional
              :
              condition
              commands
              commands

              Location

              prgm, CTL, 2:Then

              If Then Else End

              Overview

              Executes commands from Then to Else if condition = 1 (true); from Else to End if condition = 0 (false).

              Availability: Token only available from within the Basic editor.

              Syntax

              If:conditionThen:commandsElse:commandsEnd:commands

              Arguments

              NameTypeOptional
              condition
              commands
              commands
              commands

              Location

              prgm, CTL, 3:Else

              Description

              The If command is crucial to most programs. It allows you to execute code if and only if an expression is not equal to zero. Advanced uses of the If command allow you to execute a different block of code if the check turns out to be false. The simplest form of the command is quite easy to understand:

              :If (condition)
:statement

              When the calculator gets to that point in your program, it will check to see if the condition is nonzero. Most expressions you will use with If are called conditional expressions; that is, they return 1 if the condition is true and 0 if it is false. Examples include 2+2=4, A=5, and pxl-Test(R,C). Therefore, when the condition is true, the expression evaluates to 1 and the statement is run. When the condition is false, the expression evaluates to 0, and the statement is skipped.

              Using Then, Else, and End

              When you want more than one line of code to depend on the same condition, use an If-Then block.

              :If (condition)
:Then
code to execute if true
:End

              An If-Then block also has an optional Else clause, which is used to execute different code when the condition is false.

              :If (condition)
:Then
code to execute if true
:Else
code to execute if false
:End

              Advanced Uses

              If statements can execute and skip other If statements. This leads to odd yet effective constructs like these:

              :If A
:If B
//Executes if A is false or B is true

              If A:Then
//Executes if A is true
If B:Else
//Executes if A is false or B is false
End

              Memory Leaks

              Each time the program enters an If-Then block, the calculator uses 35+(size of the condition) bytes of memory to keep track of the block. This memory is given back to you as soon as the program reaches an End statement. This isn't really a problem unless you're low on RAM, or have a lot of nested If-Then statements. However, if you use Goto to jump out of such a statement, you lose those bytes for as long as the program is running — and if you keep doing this, you might easily run out of memory, resulting in ERR:MEMORY.

              Optimization

              As far as the TI-BASIC interpreter is concerned, a value of 0 is false, and any other value is true. We can use a numerical expression rather than a conditional one in the condition of the If statement in a case like the following:

              :If A≠0
:Disp "A IS NOT 0

can be
:If A
:Disp "A IS NOT 0

              When code in a single-line If statement simply changes a variable, it can often be replaced with an equivalent piecewise expression, which will be smaller and faster.

              :If A=B
:C+2→C

can be
:C+2(A=B→C

              Code Timings

              Single-line If statements are greatly slowed when they are the first line in For( loops without a closing parenthesis. For example,

              Very slow
:For(I,1,2000
:If 0:
:End

19 times faster (!)
:For(I,1,2000)
:If 0:
:End

              Error Conditions

              • ERR:DATA TYPE occurs if the parameter is complex, even if it's complex in a silly way like 0i.
              • ERR:INVALID occurs if this statement is used outside a program.
              • ERR:SYNTAX occurs if an If is the last statement in the program, or the last except for one empty line.

              Source: parts of this page were written by the following TI|BD contributors: burr, CloudVariable, DarkerLine, GoVegan, kg583, lirtosiast, Trenly.

              History

              Calculator OS Version Description
              TI-82 1.0 Added
              Property Value
              Hex Value $CF
              Categories
              Localizations
              • FR: Then

              Then

              Overview

              Availability: Token available everywhere.

              Syntax

              ThenSee If:Then

              Arguments

              NameTypeOptional
              See

              Location

              Then

              Description

              The If command is crucial to most programs. It allows you to execute code if and only if an expression is not equal to zero. Advanced uses of the If command allow you to execute a different block of code if the check turns out to be false. The simplest form of the command is quite easy to understand:

              :If (condition)
:statement

              When the calculator gets to that point in your program, it will check to see if the condition is nonzero. Most expressions you will use with If are called conditional expressions; that is, they return 1 if the condition is true and 0 if it is false. Examples include 2+2=4, A=5, and pxl-Test(R,C). Therefore, when the condition is true, the expression evaluates to 1 and the statement is run. When the condition is false, the expression evaluates to 0, and the statement is skipped.

              Using Then, Else, and End

              When you want more than one line of code to depend on the same condition, use an If-Then block.

              :If (condition)
:Then
code to execute if true
:End

              An If-Then block also has an optional Else clause, which is used to execute different code when the condition is false.

              :If (condition)
:Then
code to execute if true
:Else
code to execute if false
:End

              Advanced Uses

              If statements can execute and skip other If statements. This leads to odd yet effective constructs like these:

              :If A
:If B
//Executes if A is false or B is true

              If A:Then
//Executes if A is true
If B:Else
//Executes if A is false or B is false
End

              Memory Leaks

              Each time the program enters an If-Then block, the calculator uses 35+(size of the condition) bytes of memory to keep track of the block. This memory is given back to you as soon as the program reaches an End statement. This isn't really a problem unless you're low on RAM, or have a lot of nested If-Then statements. However, if you use Goto to jump out of such a statement, you lose those bytes for as long as the program is running — and if you keep doing this, you might easily run out of memory, resulting in ERR:MEMORY.

              Optimization

              As far as the TI-BASIC interpreter is concerned, a value of 0 is false, and any other value is true. We can use a numerical expression rather than a conditional one in the condition of the If statement in a case like the following:

              :If A≠0
:Disp "A IS NOT 0

can be
:If A
:Disp "A IS NOT 0

              When code in a single-line If statement simply changes a variable, it can often be replaced with an equivalent piecewise expression, which will be smaller and faster.

              :If A=B
:C+2→C

can be
:C+2(A=B→C

              Code Timings

              Single-line If statements are greatly slowed when they are the first line in For( loops without a closing parenthesis. For example,

              Very slow
:For(I,1,2000
:If 0:
:End

19 times faster (!)
:For(I,1,2000)
:If 0:
:End

              Error Conditions

              • ERR:DATA TYPE occurs if the parameter is complex, even if it's complex in a silly way like 0i.
              • ERR:INVALID occurs if this statement is used outside a program.
              • ERR:SYNTAX occurs if an If is the last statement in the program, or the last except for one empty line.

              Source: parts of this page were written by the following TI|BD contributors: burr, CloudVariable, DarkerLine, GoVegan, kg583, lirtosiast, Trenly.

              History

              Calculator OS Version Description
              TI-82 1.0 Added
              Property Value
              Hex Value $D0
              Categories
              Localizations
              • FR: Else

              Else

              Overview

              SeeIf:Then:Else

              Availability: Token available everywhere.

              Syntax

              Else

              Location

              Else

              Description

              The If command is crucial to most programs. It allows you to execute code if and only if an expression is not equal to zero. Advanced uses of the If command allow you to execute a different block of code if the check turns out to be false. The simplest form of the command is quite easy to understand:

              :If (condition)
:statement

              When the calculator gets to that point in your program, it will check to see if the condition is nonzero. Most expressions you will use with If are called conditional expressions; that is, they return 1 if the condition is true and 0 if it is false. Examples include 2+2=4, A=5, and pxl-Test(R,C). Therefore, when the condition is true, the expression evaluates to 1 and the statement is run. When the condition is false, the expression evaluates to 0, and the statement is skipped.

              Using Then, Else, and End

              When you want more than one line of code to depend on the same condition, use an If-Then block.

              :If (condition)
:Then
code to execute if true
:End

              An If-Then block also has an optional Else clause, which is used to execute different code when the condition is false.

              :If (condition)
:Then
code to execute if true
:Else
code to execute if false
:End

              Advanced Uses

              If statements can execute and skip other If statements. This leads to odd yet effective constructs like these:

              :If A
:If B
//Executes if A is false or B is true

              If A:Then
//Executes if A is true
If B:Else
//Executes if A is false or B is false
End

              Memory Leaks

              Each time the program enters an If-Then block, the calculator uses 35+(size of the condition) bytes of memory to keep track of the block. This memory is given back to you as soon as the program reaches an End statement. This isn't really a problem unless you're low on RAM, or have a lot of nested If-Then statements. However, if you use Goto to jump out of such a statement, you lose those bytes for as long as the program is running — and if you keep doing this, you might easily run out of memory, resulting in ERR:MEMORY.

              Optimization

              As far as the TI-BASIC interpreter is concerned, a value of 0 is false, and any other value is true. We can use a numerical expression rather than a conditional one in the condition of the If statement in a case like the following:

              :If A≠0
:Disp "A IS NOT 0

can be
:If A
:Disp "A IS NOT 0

              When code in a single-line If statement simply changes a variable, it can often be replaced with an equivalent piecewise expression, which will be smaller and faster.

              :If A=B
:C+2→C

can be
:C+2(A=B→C

              Code Timings

              Single-line If statements are greatly slowed when they are the first line in For( loops without a closing parenthesis. For example,

              Very slow
:For(I,1,2000
:If 0:
:End

19 times faster (!)
:For(I,1,2000)
:If 0:
:End

              Error Conditions

              • ERR:DATA TYPE occurs if the parameter is complex, even if it's complex in a silly way like 0i.
              • ERR:INVALID occurs if this statement is used outside a program.
              • ERR:SYNTAX occurs if an If is the last statement in the program, or the last except for one empty line.

              Source: parts of this page were written by the following TI|BD contributors: burr, CloudVariable, DarkerLine, GoVegan, kg583, lirtosiast, Trenly.

              History

              Calculator OS Version Description
              TI-82 1.0 Added
              Property Value
              Hex Value $D1
              Categories
              Localizations
              • FR: While

              While

              Overview

              Executes commands while condition is true.

              Availability: Token only available from within the Basic editor.

              Syntax

              :Whilecondition:commands :End:command

              Arguments

              NameTypeOptional
              condition
              commands
              command

              Location

              prgm, CTL, 5:While

              Description

              A While loop executes a block of commands between the While and End commands as long as the specified condition is true. The condition is tested at the beginning of the loop (when the End command is encountered), so if the condition is initially false, the block of commands will never get executed. This distinguishes it from the Repeat command.

              After each time the While loop is executed, the condition is checked to see if it is still true. If it is, the block of commands is executed again, otherwise the program resumes after the End statement.

              Advanced Uses

              When using While loops, you have to provide the code to break out of the loop (it isn't built into the loop). If there is no code that ends the loop, then you will have an infinite loop. An infinite loop just keeps executing, until you have to manually exit the loop (by pressing the ON key). In the case that you actually want an infinite loop, you can just use 1 as the condition. Because 1 is always true (based on Boolean logic), the way the calculator sees it, the condition will always be true, and the loop will never end.

              :While 1
:statement(s)
:End

              Each time the program enters an While block, the calculator uses 35+(size of the condition) bytes of memory to keep track of this. This memory is given back to you as soon as the program reaches End. This isn't really a problem unless you're low on RAM, or have a lot of nested While statements. However, if you use Goto to jump out of a While block, you lose those bytes for as long as the program is running — and if you keep doing this, you might easily run out of memory, resulting in ERR:MEMORY.

              Optimization

              Because the While and Repeat commands are so similar, either one can be used in the same situation, but using one usually results in simpler code than the other. To decide which to use, answer some simple questions about the purpose of the code.

              1. Should the code inside the loop be executed at least once? (Alternatively, does the condition use some variable that we first use inside the loop?) If it should, use a Repeat loop. Otherwise, use a While loop.
              2. (Only if the previous question doesn't help) Think of the condition based on which the loop keeps going. Is this condition best phrased as "run the loop as long as this is true?" If so, use a While loop. Or is it more like "run the loop until this is true?" If so, Repeat is best.

              Example: we want the user to pick a number, but it has to be positive, so we'll keep asking until it is.

              1. Yes, we should run the loop once. Otherwise, where will we get the number from? So, we should use the Repeat loop.
              :Repeat N>0
:Prompt N
:End

              Another example: we want to wait for the user to press a key.

              1. We're not going to have any code in the loop, all that the loop will have is a condition. So the answer to question 1 is irrelevant.
              2. We can phrase the problem as "run the loop until a key is pressed" or as "run the loop while no key is pressed." However, we have a good way of testing for the former (getKey), while the latter can only be checked with not(getKey). Therefore, it's better to use a Repeat command:
              :Repeat getKey
:End

              Command Timings

              While and Repeat loops are identical regarding speed, so that shouldn't be a factor in deciding between them. However, For( loops are much faster at what they do, that is, at going through consecutive values for one variable. You should consider if a For( loop is more appropriate to your situation. If not, choose between a Repeat loop and a While loop.

              Error Conditions

              • ERR:INVALID occurs if this statement is used outside a program.

              Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, eibmoz_, GoVegan, Weregoose.

              History

              Calculator OS Version Description
              TI-82 1.0 Added
              Property Value
              Hex Value $D2
              Categories
              Localizations
              • FR: Repeat

              Repeat

              Overview

              Executes commands until condition is true.

              Availability: Token only available from within the Basic editor.

              Syntax

              Repeatcondition:commands:End:commands

              Arguments

              NameTypeOptional
              condition
              commands
              commands

              Location

              prgm, CTL, 6:Repeat

              Description

              A Repeat loop executes a block of commands between the Repeat and End commands until the specified condition is true. The condition is tested at the end of the loop (when the End command is encountered), so the loop will always be executed at least once. This means that you sometimes don't have to declare or initialize the variables in the condition before the loop.

              After each time the Repeat loop is executed, the condition is checked to see if it is true. If it is true, then the loop is exited and program execution continues after the End command. If the condition is false, the loop is executed again.

              Advanced Uses

              When using Repeat loops, you have to provide the code to break out of the loop (it isn't built into the loop). If there is no code that ends the loop, then you will have an infinite loop. An infinite loop just keeps executing, until you have to manually exit the loop (by pressing the ON key). In the case that you actually want an infinite loop, you can just use 0 as the condition. Because 0 is always false (based on Boolean Logic), the loop will never end.

              :Repeat 0
:statement(s)
:End

              Each time the program enters a Repeat block, the calculator uses 35+(size of the condition) bytes of memory to keep track of this. This memory is given back to you as soon as the program reaches End. This isn't really a problem unless you're low on RAM, or have a lot of nested Repeat statements. However, if you use Goto to jump out of a Repeat block, you lose those bytes for as long as the program is running — and if you keep doing this, you might easily run out of memory, resulting in ERR:MEMORY.

              Optimization

              The Ans variable (last answer) is a temporary variable that can hold any variable. Ans is changed when there is an expression or variable storage or when pausing with the Pause command. It is mostly useful when you are just manipulating one variable. To use Ans just put an expression on a line by itself; it will automatically be stored to Ans. You can then change the expressions on the next line where the variable was called and put Ans there instead.

              Because Repeat loops are executed at least once, you can sometimes put Ans in the condition instead of the variable.

              :Repeat A
:getKey→A
:End
can be
:Repeat Ans
:getKey→A
:End

              Command Timings

              When deciding whether to use a Repeat loop, as opposed to a For or While loop, it's good to know how Repeat loops stack up against them. This comparison comes from the Code Timings page showing the speeds of the three different kinds of loops:

              Format

              Bars

              Pixels

              For(A,0,2000
              End

              4 bars + 4 pixels

              36

              Delvar A
              While A≤2000
              A+1→A
              End

              23 bars

              184

              Delvar A
              Repeat A>2000
              A+1→A
              End

              22 bars + 7 pixels

              183

              The general conclusion you can take away from this table is that For( loops should be used when speed is a priority, and then you should use Repeat or While loops when the appropriate circumstance comes up. Each kind of loop has its own place, so it's still good to know how to use all three of them.

              Error Conditions

              • ERR:INVALID occurs if this statement is used outside a program.

              Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

              History

              Calculator OS Version Description
              TI-82 1.0 Added
              Property Value
              Hex Value $D3
              Categories
              Localizations
              • FR: For(

              For(

              Overview

              Executes commands through End, incrementing variable from begin by increment until variable>end.

              Availability: Token only available from within the Basic editor.

              Syntax

              :For(variable,begin,end[,increment]):commands:End:commands

              Arguments

              NameTypeOptional
              variable
              begin
              end
              incrementYes
              commandsYes
              commandsYes

              Location

              prgm, CTL, 4:For(

              Description

              A For( loop is generally used to do something a specific number of times or to go through each one of a bunch of things (such as elements of a list, or the pixels of your screen). Of all the loops, it's the most complicated. The syntax:

              For(variable,start,end[,step]
statement(s)
End

              What the loop does:

              1. Stores start to variable.
              2. If variable is greater than end (or less than, if step is negative), then the For( loop ends immediately.
              3. Runs the statement(s).
              4. Adds step to variable and returns to Step 2.

              If no value for step is given, step is assumed to be 1.

              In other words: a For( loop repeats its contents once for every value of variable between start and end.

              This is perhaps best explained with an example. The following code will display the numbers 1 to 10, in order:

              :For(A,1,10)
:Disp A
:End

              Now, all of this could be done with a Repeat or While command and some manipulation, except that this is faster because it's a single command. Still, why have a separate command for something that seems so specific and arbitrary? Well, it's because For( has so many uses!

              • Do something to each element of a list, matrix, or string.
              • Draw several similar objects on the graph screen.
              • Create animations.
              • Easily add the possibility of levels to many games.
              • Any number of other things…

              An advanced note: each time the program enters a For( loop, the calculator uses 43 bytes of memory to keep track of this. This memory is given back to you as soon as the program reaches End. This isn't really a problem unless you're low on RAM, or have a lot of nested For( statements. However, if you use Goto to jump out of a For( loop, you lose those bytes for as long as the program is running—and if you keep doing this, you might easily run out of memory, resulting in ERR:MEMORY.

              Advanced Uses

              Sometimes you want to exit out of a For( loop when it hasn't finished. You can do this by storing the end value to the variable you used in the For( loop. For example:

              :For(A,1,100)
<some code>
:If <condition for exiting out>
:100→A
:End

              For( can also be used to create a delay:

              //delays for about 0.5 second (83+) or 0.2 second (83+SE/84+/SE/CSE)
:For(A,1,200)
:End

              If X is end, the delay will be about X/1000 seconds for the TI-83/83+, and X/400 for other calculators.

              Unlike delays that use rand, a For( loop delay can execute an animation or other code during the delay.

              For( loops can be nested to execute code once for every combination of values of several variables. For example:

              :For(A,1,50)
:For(B,1,50)
:(some code)
:End
:End

              This will run (some code) 2500 times—once for every combination of a value of A from 1 to 50 and a value of B from 1 to 50.

              There's a standard way to exclude repetitions if the order of the variables doesn't matter (for example, if A=30, B=40 is the same situation as A=40, B=30 in the example above). In this case, the beginning of the loop should be changed to:

              :For(A,1,50)
:For(B,1,A)

              On the CSE, a list index can be used as the variable in a For( loop. When this is done, the loop will operate and exit normally, but the list will not be affected. For instance, this program

              :{1,2,3→L₁
:For(L₁(1),2,5
:Disp "X
:End
:Disp L₁

              will output:

              X
X
X
X
  {1,2,3}

              For( loops can also be used to exceed the normal overflow limit of \(10^{100}\) for variables and computations. For example, utilizing the optional step argument,

              :For(A,9E99,9E99,9E99
:End

              the value of A will be 1.8E100, which is otherwise impossible to assign to a variable by normal means. One could then use A as the step value for a For( command,

              :For(A,A,A,A
:End

              which doubles the value of A (so 1.8E100 becomes 3.6E100). This process can be repeated until the "true" overflow limit is reached at \(10^{128}\) (since the calculator stores the exponent as a signed 8-bit integer, ranging from -128 to 127).

              Optimization

              The seq( command, or simple math, can often be used in place of the For( command when dealing with lists. For example:

              :For(A,1,dim(L1
:cos(A)→L1(A
:End
//can be
:seq(cos(A),A,1,dim(L1→L1

              and

              :For(A,1,dim(L1
:1+L1(A→L1(A
:End
//can be
:1+L1→L1

              One rather strange optimization when using For( loops is actually leaving on the ending parenthesis of the For( loop in certain cases. If you don't do this, the following cases will be processed much slower when they are the first line of code in the loop:

              • IS>( and DS<( (no matter if the following command is skipped or not).
              • A lone If without an accompanying Then, but only when the condition is false (If with a true condition is unchanged).

              If the condition of the If command can be false (as in most actual cases), you should add a closing parenthesis because the difference is so great.

              An example use of this optimization:

              :For(I,1,1200
:If 0
:1
:End

//should be
:For(I,1,1200)
:If 0
:1
:End

              Command Timings

              Using a For( loop when it fits your purpose is much faster than adapting a While or Repeat loop to do so. Conclusion: For( loops are good!

              Error Conditions

              • ERR:INCREMENT is thrown if the increment of the For( loop is 0.
              • ERR:INVALID occurs if this statement is used outside a program.
              • ERR:UNDEFINED is thrown if you DelVar the loop variable while inside the loop.

              Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, Edward H, Electromagnet8, GoVegan, kg583, lirtosiast, MI Wright, muffinzrock, Myles_Zadok, Weregoose.

              History

              Calculator OS Version Description
              TI-82 1.0 Added
              Property Value
              Hex Value $D4
              Categories
              Localizations
              • FR: End

              End

              Overview

              Identifies end ofFor(, If-Then-Else, Repeat, or While loop.

              Availability: Token only available from within the Basic editor.

              Syntax

              End

              Location

              prgm, CTL, 7:End

              Description

              The End command is used together with the different control structures, including the If conditional, While loop, Repeat loop, and For( loop, to indicate the end of the code block for the respective control structure. In the case of the If conditional, you also need to add a Then command, which is used to indicate the beginning of the control structure.

              Advanced Uses

              You can prematurely end a control structure by using a single If conditional and then having End be its executed command. Because the calculator stores the positions of the End commands, it will take this End command to be the End command of the control structure.

              :If <condition>
:End

              One of the most important features of the End command is putting multiple control structures inside of each other (known as nesting). While you typically nest If conditionals inside of loops, you can actually nest any control structure inside of any other control structure — this even works when using the same control structure, such as a While loop inside of another While loop.

              When nesting control structures, you need to remember to put the appropriate number of End commands to close the appropriate structure. The easiest way to keep track of lots of nested control structures is to code the first part, add an End immediately after the beginning, and then hit 2nd DEL on the line with the End, then hit ENTER a lot of times.

              Error Conditions

              • ERR:INVALID occurs if this statement is used outside a program.
              • ERR:SYNTAX occurs if this statement is used before a logic block has been initiated.

              Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, MufinMcFlufin, Myles_Zadok.

              History

              Calculator OS Version Description
              TI-82 1.0 Added
              Property Value
              Hex Value $D5
              Categories
              Localizations
              • FR: Return

              Return

              Overview

              Returns to the calling program.

              Availability: Token only available from within the Basic editor.

              Syntax

              Return

              Location

              prgm, CTL, E:Return

              Description

              When the Return command is used in a program it exits the program (terminating the program execution) and returns the user to the home screen. If it is encountered within loops, the loops will be stopped.

              There is some distinction when using Return with subprograms: the Return command will stop the program execution of the subprogram, and program execution will go back to the calling program, continuing right after the subprogram call. If this functionality is not desired, then you should use the Stop command instead. Generally, though, you should use Return instead of Stop.

              :ClrHome
:Input "Guess:",A
:Stop
Replace Stop with Return
:ClrHome
:Input "Guess:",A
:Return

              Optimization

              You don't have to put a Return command at the end of a program or subprogram if you can organize the program so that it just naturally quits. When the calculator reaches the end of a program, it will automatically stop executing as if it had encountered a Return command (the Return is implied).

              :ClrHome
:Input "Guess:",A
:Return
Remove the Return
:ClrHome
:Input "Guess:",A

              Error Conditions

              • ERR:INVALID occurs if this statement is used outside a program.

              See Also

              Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

              History

              Calculator OS Version Description
              TI-82 1.0 Added
              Property Value
              Hex Value $D6
              Categories
              Localizations
              • FR: Lbl

              Lbl

              Overview

              Creates a label of one or two characters.

              Availability: Token only available from within the Basic editor.

              Syntax

              Lbl label

              Arguments

              NameTypeOptional
              label

              Location

              prgm, CTL, 9:Lbl

              Description

              The Lbl command is used together with the Goto command to jump (or branch) to another place in a program. When the calculator executes a Goto command, it stores the label name in memory, and then searches from the beginning of the program for the Lbl command with the supplied name. If it finds it, it continues running the program from that point; otherwise, if the label does not exist, it throws a ERR: LABEL error.

              Label names can be either one or two characters long, and the only characters you're allowed to use are letters (including θ) and numbers 0 to 9; this means 37+37*37=1406 possible combinations. Of course, you should use all of the single character names first, before using the two character names. While you can technically have the same label name multiple times in a program, it is rather pointless since the calculator always goes to the first occurrence of the label.

              You can position a Lbl command one or more lines before a Goto command to create a kind of loop structure. However, you have to provide the break-out code, since it isn't built-in. An If conditional is easiest, but if there is no code that ends the branching, then program execution will continue indefinitely, until you manually exit it (by pressing the ON key).

              :Lbl A
:...
:If <exit condition>
:Goto A  // this line is skipped

              Although the Lbl/Goto loop structure may seem like a good alternative to loops, it should be avoided whenever possible, which is especially important when you are first planning a program. This is because it has several serious drawbacks associated with it:

              • It is quite slow, and gets slower the further the Lbl is in your program.
              • It makes reading code (your own, or someone else's) much more confusing.
              • In most cases, If, For(, While, or Repeat can be used instead, saving space and improving speed.
              • Using a Goto to exit any block of code requiring an End command causes a memory leak — around 40 bytes of memory will be rendered useless each time you do it until the program finishes running, which will also slow down your program down.

              They aren't all bad, however, and are actually useful when a loop isn't practical and when something only happens once or twice. Just remember that you should never use Goto to repeat a block of code several times. Use For(, Repeat, or While instead.

              Labels are also used with the Menu( command. The same considerations apply as with Goto, except that (unless you write a custom menu routine) there's no simple alternative to using labels with Menu(.

              Error Conditions

              • ERR:INVALID is thrown if this statement is used outside a program.
              • ERR:LABEL is thrown if the corresponding label doesn't exist.

              Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

              History

              Calculator OS Version Description
              TI-82 1.0 Added
              Property Value
              Hex Value $D7
              Categories
              Localizations
              • FR: Goto

              Goto

              Overview

              Transfers control to label.

              Availability: Token only available from within the Basic editor.

              Syntax

              Gotolabel

              Arguments

              NameTypeOptional
              label

              Location

              prgm, CTL, 0:Goto

              Description

              The Goto command is used together with the Lbl command to jump (or branch) to another place in a program. When the calculator executes a Goto command, it stores the label name in memory, and then searches from the beginning of the program for the Lbl command with the supplied name. If it finds it, it continues running the program from that point; otherwise, if the label does not exist, it throws an ERR: LABEL error.

              Label names can be either one or two characters long, and the only characters you're allowed to use are letters (including θ) and numbers 0 to 9; this means 37+37*37=1406 possible combinations. Of course, you should use all of the single character names first, before using the two character names. While you can technically have the same label name multiple times in a program, it is rather pointless since the calculator always goes to the first occurrence of the label.

              You can position a Lbl command one or more lines before a Goto command to create a kind of loop structure. However, you have to provide the break-out code, since it isn't built-in. An If conditional is easiest, but if there is no code that ends the branching, then program execution will continue indefinitely, until you manually exit it (by pressing the ON key).

              :Lbl A
:...
:If <exit condition>
:Goto A  // this line is skipped

              Although the Goto command may seem like a good alternative to loops, it should be avoided whenever possible, which is especially important when you are first planning a program. This is because it has several serious drawbacks associated with it:

              • It is quite slow, and gets slower the further the Lbl is in your program.
              • It makes reading code (your own, or someone else's) much more confusing.
              • In most cases, If, For(, While, or Repeat can be used instead, saving space and improving speed.
              • Using a Goto to exit any block of code requiring an End command causes a memory leak, which will not be usable until the program finishes running or executes a Return command, and which will slow down your program down. See below for ways to fix this.

              The Goto command isn't all bad, however, and is actually useful when a loop isn't practical and when something only happens once or twice (see below for examples). Just remember that you should never use Goto to repeat a block of code several times. Use For(, Repeat, or While instead.

              Fixing Memory Leaks

              One of the simplest memory leaks that occurs is using branching to exit out of a loop when a certain condition of an If conditional is true. If the loop is an infinite loop (i.e., Repeat 0 or While 1), you should take the condition from the If conditional and place it as the condition of the loop. This allows you to remove the branching, since it is now unnecessary.

              :Repeat 0
:getKey→B
:If B:Goto A
:End:Lbl A
Make Loop Condition
:Repeat B
:getKey→B
:End

              Of course, the only reason that this memory leak fix is possible is because of the If conditional (since the If conditional doesn't need a closing End command). When dealing with a complex If conditional, you will have to rework the conditionals so the branching has its own If conditional. Depending on how many commands there are in the conditionals, you might be able to just use an If conditional or you might need to use an If-Then conditional.

              :If B:Then
:Disp "Hello
:Goto A
:End
Separate Into Conditionals
:If B:Disp "Hello
:If B:Goto A

              This memory leak fix will work most of the time, but it isn't applicable when one of the values of the variables in the condition is changed by one of the commands inside the condition. The way to get around this is by using another variable for the If conditional that the branching uses. You initialize the variable to zero, assign the variable whatever value you want in the conditional, and then check to see if the variable is equal to that value in the branching conditional.

              :If A=1:Then
:3→A:4→B
:Goto A
:End
Use Another Variable
:Delvar CIf A=1:Then
:3→A:4→B:π→C
:End
:If C=π
:Goto A

              Advanced Uses

              If your program requires cleanup after it finishes, but it can exit from several different places, use Goto and place a Lbl at that point. This saves memory over repeating the cleanup code every time you exit. The usual considerations about Goto don't apply here: since you're exiting the program, all memory leaks will be gone anyway, and speed isn't much of an issue for something that only gets done once.

              The code looks something like this:

              :If K=45:Goto Q  //user pressed CLEAR
:...
:If L:Goto Q  // game over
:...
:Lbl Q
:DelVar L1ClrHome

              A common situation in programs is when a decision has to be made about where the program execution should go next. The obvious approach would be to use the value of a variable as the label name (i.e., something like Goto A, with A being a variable), but that doesn't work because the calculator doesn't interpret the label as a variable. So, the next best approach is to use If conditionals with the different values of the variable:

              :If not(A:Goto 0
:If A=1:Goto 1
:If A=2:Goto 2

              Another possible use for Goto is in program protection to break a program with an error without letting the user see where it happened. If the label that you want to Goto doesn't exist, you'll get a ERR: LABEL error, which doesn't provide a 2:Goto option. So, all you have to do is Goto a label that you know doesn't exist.
              An alternative method would be to lock the program from being able to be edited. (which you currently cannot do on-calc without a shell) This gives you the possibility to throw whatever error you want! For example, if the user entered something invalid, you can add a blank line with a closing parenthesis, and a syntax error will be thrown, without the 2:Goto option! If you do go this route, be sure to only lock it when you are done editing. It is also good practice to include a text file with the source, as well.

              Error Conditions

              • ERR:INVALID occurs if this statement is used outside a program.
              • ERR:LABEL is thrown if the corresponding label doesn't exist.

              See Also

              Source: parts of this page were written by the following TI|BD contributors: alexrudd, burr, DarkerLine, GoVegan, iPhoenixOnTIBD, Myles_Zadok.

              History

              Calculator OS Version Description
              TI-82 1.0 Added
              Property Value
              Hex Value $D8
              Categories
              Localizations
              • FR: Pause

              Pause

              Overview

              Suspends program execution until you press 【enter】.

              Availability: Token only available from within the Basic editor.

              Syntax

              Pause

              Location

              prgm, CTL, 8:Pause

              Overview

              Displays value; suspends program execution until you press 【enter】.

              Availability: Token only available from within the Basic editor.

              Syntax

              Pause [value]

              Arguments

              NameTypeOptional
              valueYes

              Location

              prgm, CTL, 8:Pause

              Overview

              Displays value on the current home screen and execution of the program continues after the time period specified. For time only, use Pause “”,time where the value is a blank string. Time is in seconds.
              Pause value,time.

              Availability: Token only available from within the Basic editor.

              Syntax

              Pause [value, time]

              Arguments

              NameTypeOptional
              valueYes
              timeYes

              Location

              prgm, 8:Pause

              Description

              The Pause command is used for suspending the execution of a program at a certain point. This is useful when you have text or instructions on the home screen that you want the user to read before the program continues on to the next thing. While the program is paused, the pause indicator turns on in the top-right corner of the screen (it is the dotted line that moves around).

              After the user is done reading the text or instructions, they must press ENTER to resume program execution. One place the Pause command is commonly used is right before clearing the screen with ClrHome, because otherwise the text on the screen will show up for a split second before it is erased. The Pause command gives the user ample time to look at and read the text.

              :Pause

              An alternative to the Pause command that is commonly used is a Repeat loop with a getKey command as the condition. This is sometimes more appropriate in a program if you don't want to bring the program to a complete standstill, and you want the user to be able to resume program execution with any key instead of just ENTER (see usability for more information).

              :Repeat getKey
:End

              Advanced Uses

              The Pause command has an optional argument that can either be text, a number, a variable, or an expression. This argument will be displayed on the next available blank line on the home screen while the program is paused, and it can be scrolled if it is larger than the screen. Although the Pause command can be used with the graph screen, the argument will still be displayed on the home screen.

              Caution: Unlike any other text command, or indeed any other command at all, this optional argument will be stored to Ans after the pause! This could be used to your advantage, but most of the time, it's a nuisance, and if you use Ans for optimization, watch out for this side effect.

              Displaying text with the Pause command follows the same pattern as the Disp command, so text is displayed on the left and everything else is displayed on the right. It also means that if there is already text on the seventh row, it will automatically move everything up one row so it can display its text. In addition, the Pause command is affected by the Output( command and its text.

              PROGRAM:PAUSE
:ClrHome
:"World!
:Disp " Hello "+Ans
:Output(2,2,"Goodbye
:Pause Ans

              When the calculator is paused, it is possible for another linked calculator to use the GetCalc( command to transfer a variable.

              + Show TI-84+CE specific information

              - Hide TI-84+CE specific information

              The TI-84+CE also introduced an optional second argument to the Pause command. With this argument, you can specify the amount of time you wish to wait for in seconds:

              :Pause "HELLO",2

              Using the empty string "" with the optional second argument will cause the Pause command to wait for the specified amount of time without displaying anything on the screen:

              :Pause "",3.5

              The more recent Wait command can do this as well. Here’s the first example, but using Wait:

              :Disp “HELLO
:Wait 2

              Optimization

              When you have a Disp command before a Pause command, you can take the text or variable from the Disp command and place it after the Pause command as its optional argument. This allows you to remove the Disp command. If the Disp command has multiple arguments, you just take the last one off and put it as the optional argument.

              :Disp A
:Pause
can be
:Pause A

              When using the optional argument of Pause, it is stored to Ans, and this can in rare cases be used for optimization. The most common one would probably be using Pause to show work for a calculation, as in the following program:

              :Disp "A+B=
:Pause A+B
:Disp "(A+B)²=
:Pause Ans²
:Disp "(A+B)²-C²=
:Pause Ans-C²

              Error Conditions

              • ERR:INVALID occurs if this statement is used outside a program.

              Source: parts of this page were written by the following TI|BD contributors: alexrudd, burr, CloudVariable, DarkerLine, GoVegan, iPhoenixOnTIBD, jonbush, kg583, Myles_Zadok, Trenly.

              History

              Calculator OS Version Description
              TI-82 1.0 Added
              Property Value
              Hex Value $D9
              Categories
              Localizations
              • FR: Stop

              Stop

              Overview

              Ends program execution; returns to home screen.

              Availability: Token only available from within the Basic editor.

              Syntax

              Stop

              Location

              prgm, CTL, F:Stop

              Description

              When the Stop command is used in a program it exits the program (terminating the program execution) and returns you to the home screen. If it is encountered within loops, the loops will be stopped.

              There is some distinction when using Stop with subprograms: the Stop command will stop the program execution of the subprogram, as well as the calling program, and return you to the home screen; the program will stop completely. If this functionality is not desired, then you should use the Return command instead.

              Optimization

              You don't have to put a Stop command at the end of a program or subprogram if you can organize the program so that it just naturally quits. When the calculator reaches the end of a program, it will automatically stop executing as if it had encountered a Stop command (the Stop is implied).

              :ClrHome
:Input "Guess:",A
:Stop
Remove the Stop
:ClrHome
:Input "Guess:",A

              Error Conditions

              • ERR:INVALID occurs if this statement is used outside a program.

              See Also

              Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

              History

              Calculator OS Version Description
              TI-82 1.0 Added
              Property Value
              Hex Value $DA
              Categories
              Localizations
              • FR: IS>(

              IS>(

              Overview

              Increments variable by 1; skips commandA if variable>value.

              Comment::commandA,:commands

              Availability: Token only available from within the Basic editor.

              Syntax

              :IS>(variable,value) :commandA:commands

              Arguments

              NameTypeOptional
              variable
              value
              commandA
              commands

              Location

              prgm, CTL, A:IS>(

              Description

              The increment and skip if greater than command — IS>( — is a specialized conditional command. It is equivalent to an If conditional, except the next command will be skipped when the condition is true and it has a variable update built-in. However, it is not used very often (if anything, it is often misused as a looping command) because of its obscure name and somewhat limited application.

              The IS>( command takes two arguments:

              • A variable, which is limited only to one of the real variables (A-Z or θ).
              • A value, which can be any expression which evaluates to a real number.

              When IS>( is executed it adds one to the variable (increments it by one), and compares it to the value. The next command will be skipped if the variable is greater than the value, while the next command will be executed if the variable is less than or equal to the value.

              The command IS>(A,B is equivalent to the following code:

              :A+1→A
:If A≤B

              Here are the two main cases where the IS>( command is used:

              :7→A
:IS>(A,6
:Disp "Skipped
              • Initializes A to 7 and then compares to the value
              • 7>6 is true so the display message won't be displayed
              :1→B
:IS>(B,2
:Disp "Not Skipped
              • Initializes B to 1 and then compares to the value
              • 1>2 is false so the display message will be displayed

              Note: In addition to both of these cases, there is also the case where the variable and the value are equal to each other. This case is shown below under the 'Advanced Uses' section because it has some added background that goes with it.

              Advanced Uses

              When you want the skipping feature of the IS>( command to always occur, you just have to use the same variable for both the variable and value arguments of the command:

              :IS>(B,B

              An undefined error will occur if the variable and/or value doesn't exist before the IS>( command is used, which happens when the DelVar command is used. Consequently, you should not use DelVar with IS>(.

              Similar code can be used as a substitute for B+1→B if you don't want to change Ans:

              :IS>(B,B:

              Note that due to the colon after the line, there will be no statement skipped, so you don't have to worry about that.

              Optimization

              Because the IS>( command has the variable update built-in, it is smaller than manually incrementing a variable by one along with using an If conditional.

              :A+1→A
can be
:IS>(A,0

              The one caution about this is that if the variable is greater than the value (in this case, '0'), the next command will be skipped. If you don't want the skipping functionality, then you need to make sure that the value is never less than the variable. This is not always possible to do. Also, IS>( is slightly slower than its more normal counterpart.

              Related to the example code given, IS>( should always have a command following after it (i.e., it's not the last command in a program) because it will return an error otherwise. If you have no particular code choice, just put an empty line or something meaningless.

              Command Timings

              Using IS>( to increment a variable is approximately 25% slower than using code like X+1→X. However, it is faster to use IS>( than to construct an If statement to do the same thing.

              Note, however, that a quirk in the For( command (see its Optimizations section) will slow down the IS>( command significantly if a closing parenthesis is not used for the For( statement.

              Error Conditions

              • ERR:INVALID occurs if this statement is used outside a program.
              • ERR:UNDEFINED is thrown if the variable to be incremented is not defined.
              • ERR:SYNTAX is thrown if there is no next line to skip, or if there is only one next line and it is empty.

              Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583.

              History

              Calculator OS Version Description
              TI-82 1.0 Added
              Property Value
              Hex Value $DB
              Categories
              Localizations
              • FR: DS<(

              DS<(

              Overview

              Decrements variable by 1; skips commandA if variable< value.

              Availability: Token only available from within the Basic editor.

              Syntax

              DS<(variable,value):commandA:commands

              Arguments

              NameTypeOptional
              variable
              value
              commandA
              commands

              Location

              prgm, CTL, B:DS<(

              Description

              The decrement and skip if less than command — DS<( — is a specialized conditional command. It is equivalent to an If conditional, except the next command will be skipped when the condition is true and it has a variable update built-in. However, it is not used very often (if anything, it is often misused as a looping command) because of its obscure name and somewhat limited application.

              The DS<( command takes two arguments:

              • A variable, which is limited only to one of the real variables (A-Z or θ).
              • A value, which can be any expression which evaluates to a real number.

              When DS<( is executed it subtracts one from the variable (decrements it by one), and compares it to the value. The next command will be skipped if the variable is less than the value, while the next command will be executed if the variable is greater than or equal to the value.

              The command DS<(A,B is equivalent to the following code:

              :A-1→A
:If A≥B

              Here are the two main cases where the DS<( command is used:

              :5→A
:DS<(A,6
:Disp "Skipped
              • Initializes A to 5 and then compares to the value
              • 5<6 is true so the display message won't be displayed
              :3→B
:DS<(B,2
:Disp "Not Skipped
              • Initializes B to 3 and then compares to the value
              • 3<2 is false so the display message will be displayed

              Note: In addition to both of these cases, there is also the case where the variable and the value are equal to each other. This case is shown below under the 'Advanced Uses' section because it has some added background that goes with it.

              Advanced Uses

              When you want the skipping feature of the DS<( command to always occur, you just have to use the same variable for both the variable and value arguments of the command:

              :DS<(B,B

              An undefined error will occur if the variable and/or value doesn't exist before the DS<( command is used, which happens when the DelVar command is used. Consequently, you should not use DelVar with DS<(.

              A similar code can be used as a substitute for B-1→B if you don't want to change Ans:

              :DS<(B,B:

              Note that due to the colon after the line, there will be no statement skipped, so you don't have to worry about that.

              Optimization

              If a program needs to decrement a positive variable, DS<( is one byte smaller than than decrementing a variable normally.

              :A-1→A
can be
:DS<(A,0

              The one caution about this is that if the variable is less than the value (in this case, '0'), the next command will be skipped. If you don't want the skipping functionality, then it is necessary to make sure that the value is never greater than the variable. Also, DS<( is slower than its more often used counterpart.

              Related to the example code given, DS<( should always have a command following after it (i.e. it's not the last command in a program) because it will return an error otherwise. If you have no particular code choice, an empty line will suffice.

              code that will run
:DS<(A,0
:
more code that will run

              Command Timings

              Using DS<( to decrement a variable is approximately 25% slower than using code like X-1→X. However, it is faster to use DS<( than to construct an If statement to do the same thing.

              Note, however, that a quirk in the For( command (see its Optimization section) will slow down the DS<( command significantly if a closing parenthesis is not used for the For( statement.

              Error Conditions

              • ERR:INVALID occurs if this statement is used outside a program.
              • ERR:SYNTAX is thrown if there is no next line to skip.
              • ERR:UNDEFINED is thrown if the variable to be decremented is not defined.

              Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583, Marcsine.

              History

              Calculator OS Version Description
              TI-82 1.0 Added
              Property Value
              Hex Value $DC
              Categories
              Localizations
              • FR: Input

              Input

              Overview

              Displays graph.

              Availability: Token only available from within the Basic editor.

              Syntax

              Input

              Location

              prgm, I/O, 2:Input

              Overview

              Prompts for value to store to variable.

              Availability: Token only available from within the Basic editor.

              Syntax

              Input [variable]

              Arguments

              NameTypeOptional
              variableYes

              Location

              prgm, I/O, 2:Input

              Overview

              Prompts for value to store to variable.

              Availability: Token only available from within the Basic editor.

              Syntax

              Input ["text",variable]

              Arguments

              NameTypeOptional
              textstringYes
              variableYes

              Location

              prgm, I/O, 2:Input

              Overview

              Displays Strn and stores entered value to variable.

              Availability: Token only available from within the Basic editor.

              Syntax

              Input [Strn,variable]

              Arguments

              NameTypeOptional
              nYes
              variableYes

              Location

              prgm, I/O, 2:Input

              Description

              The Input command is the other way of getting user input on the home screen (getting user input on the graph screen is only possible with the getKey command). The Input command asks the user to enter a value for a variable (only one variable can be inputted at a time), waiting until the user enters a value and then presses ENTER. It does not display what variable the user is being asked for, but instead just displays a question mark (?).

              Because just displaying a question mark on the screen does not really tell the user what to enter for input or what the input will be used for, the Input command has an optional text message that can be either text or a string variable that will be displayed alongside the input.

              Only the first sixteen characters of the text message will be shown on the screen (because of the screen dimensions), so the text message should be kept as short as possible (a good goal is twelve characters or less). This is so the value the user inputs can fit on the same line as the text. In the case that the value is too long, it will wrap around to the next line.

              PROGRAM:INPUT
:"Fruit
:Input "Best "+Ans,Str1
:Input "Worst "+Ans,Str2
:Disp "That's "+Ans+"astic!

              Input can be used to display every variable just before it requests user input, but some of the variables have to be entered in a certain way. If the variable is a string or a Y= function, the user must put quotes ("") around the value or expression. The user must also put curly braces ({}) around lists with the list elements separated by commas, and square brackets ([]) around matrices with the matrix elements separated by commas and each row individually wrapped with square brackets.

              Advanced Uses

              When you just use the Input command by itself (without any arguments), the graph screen will be shown and the user can move the cursor around. Program execution will then pause until the user presses ENTER, at which time the coordinates of the cursor will be stored to the respective variables (R and θ for PolarGC format, otherwise X and Y).

              If a text message is longer than twelve characters or you want to give the user plenty of space to enter a value, you can put a Disp command before the Input command. You break the text message up and display it in parts. The Input command will be displayed one line lower, though, because the Disp command automatically creates a new line.

              :Disp "What is your"
:Input "Name",Str0

              Normally you can't get a quote character into a string (because quotes are used to identify the beginning and end of the string), but the Input command actually allows the user to enter a quote character (") as part of a string. This works without problems, and the quote can even be accessed by the user afterwards.

              Because a user-defined list variable doesn't need the ʟ prefixed character before it when referring to the list, you may be only asking the user to input a simple real variable but a list would also be allowed. There is nothing you can really do about this problem, except including the ʟ prefixed character when wanting a list inputted and trying to limit your use of Input and Prompt.

              :Input A
should be
:Input ʟA

              Optimizations

              When you are just using the text message to tell the user what the variable being stored to is, you should use the Prompt command instead. And, if there is a list of Input commands following the same pattern, you can reduce them to just one Prompt command.

              :Input "A",A
:Input "B",B
Replace with Prompt
:Prompt A,B

              Error Conditions

              • ERR:INVALID occurs if this statement is used outside a program.

              Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583.

              History

              Calculator OS Version Description
              TI-82 1.0 Added
              Property Value
              Hex Value $DD
              Categories
              Localizations
              • FR: Prompt

              Prompt

              Overview

              Prompts for value for variableA, then variableB, and so on.

              Availability: Token only available from within the Basic editor.

              Syntax

              Prompt variableA[,variableB,...,variable n]

              Arguments

              NameTypeOptional
              variableA
              variableBYes
              ...Yes
              variable nYes

              Location

              prgm, I/O, 2:Prompt

              Description

              The Prompt command is the simplest way of getting user input on the home screen (getting user input on the graph screen is only possible with the getKey command). Prompt displays variables one per line, with an equal sign and question mark (=?) displayed to the right of each variable. After the user enters a value or expression for the variables and presses ENTER, the values will be stored to the variables and program execution will resume.

              Prompt can be used with every variable, but some of the variables have to be entered in a certain way. If the variable is a string or equation, the user must put quotes ("") around the value; the user must also put curly braces ({}) around lists and square brackets ([]) around matrices. Of course, ending quotes, braces, and brackets can be left off as usual.

              When you use Prompt to input a named list, the ʟ in front of the name is dropped (so Prompt ʟNAME will display NAME=?). This can be confusing with single-letter names: Prompt ʟX and Prompt X both display X=?. Further enhancing the confusion, if the user enters a list for Prompt X, the list will be stored to ʟX instead.

              During the Prompt, the user can press [2nd][MODE] to quit the program immediately.

              Advanced Uses

              Because simply displaying what variable the value will be stored to does not really tell the user what the variable will be used for, you can put a Disp command before Prompt to give the user some more insight into what an appropriate value for the variable would be. The Prompt command will be displayed one line lower, though, because the Disp command automatically creates a new line after itself. (Of course, you could also just use the Input command.)

              :Disp "Enter the Score
:Prompt A

              Optimizations

              When you have a list of Prompt commands (and each one has its own variable), you can just use the first Prompt command and combine the rest of the other Prompt commands with it. You remove the Prompt commands and combine the arguments, separating each argument with a comma. The arguments can be composed of whatever combination of variables is desired.

              The advantages of combining Prompt commands are that it makes scrolling through code faster, and it is more compact (i.e. smaller) and easier to write than using the individual Prompt commands. The primary disadvantage is that it is easier to accidentally erase a Prompt command with multiple arguments.

              :Prompt A
:Prompt Str1
Combine the Prompts
:Prompt A,Str1

              Error Conditions

              • ERR:INVALID occurs if this statement is used outside a program.

              Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583, merthsoft.

              History

              Calculator OS Version Description
              TI-82 1.0 Added
              Property Value
              Hex Value $DE
              Categories
              Localizations
              • FR: Disp

              Disp

              Overview

              Displays the home screen.

              Availability: Token only available from within the Basic editor.

              Syntax

              Disp

              Location

              prgm, I/O, 3:Disp

              Overview

              Displays each value.

              Availability: Token only available from within the Basic editor.

              Syntax

              Disp [valueA,valueB,valueC,...,value n]

              Arguments

              NameTypeOptional
              valueAYes
              valueBYes
              valueCYes
              ...Yes
              value nYes

              Location

              prgm, I/O, 3:Disp

              Description

              The first, and easiest, way to display text is using the Disp command. You can display whatever combination of text and values that you want. Text is displayed on the left side of the screen, while numbers, variables and expressions are displayed on the right side. Text can be moved over to the right by padding it with spaces, but there is no equivalent for numbers, variables, and expressions.

              When displaying a matrix or a list, and the matrix or list is too large to display in its entirety, an ellipsis (…) is displayed at the boundaries of the screen. The matrix or list, unfortunately, cannot be scrolled so the rest of it can be seen (use the Pause command instead).

              With the small screen size, you have to keep formatting in mind when displaying text. Because the text does not wrap to the next line if it is longer than sixteen characters, the text gets cut off and an ellipsis is displayed at the end of the line. When the text you want to display is longer than sixteen characters, you should break the text up and display each part with its own Disp command.

              :Disp "Just Saying Hello
Break the text up
:Disp "Just Saying
:Disp "Hello

              The Disp command displays text line by line, giving each argument its own blank line. If the screen is clear, the arguments are displayed beginning at the first line. But if there is text on the first line, the arguments are displayed beginning at the first available blank line. When all the lines have text on them including the last, the screen will automatically scroll up until every line is blank.

              This means that, while a Disp command can technically display an unlimited amount of lines of text, you should not display more than seven consecutive lines of text at any one time (because of the screen height). If there are too many arguments, the arguments that were displayed will be pushed up out of sight, to allow the other arguments to be displayed. This is usually not desired, but it can be used to create some cool scrolling effects by messing with the text that you display.

              The result is that you can never display text on the last line of the screen using the Disp command; you need to use the Output( command. (Using Output( does not have any affect on Disp and its text.) Also, if you have more than seven lines of text to display, you will need to place the Pause command after every seven lines to prevent the screen from scrolling. These two scenarios come up fairly often, so it is good to know how to deal with them.

              PROGRAM:DISP
:ClrHome
:Disp A,B,C,D,E,F,G
:Pause
:Disp A,B,C,D,E,F,G
:Output(8,16,H

              Like other text display commands, you can display each function and command as text. However, this is not without problems as each function and command is counted as one character. The two characters that you can't display are quotation marks (") and the store command (→). However, you can mimic these respectively by using two apostrophes (''), and two subtract signs and a greater than sign (—>).

              Advanced Uses

              You can use the Disp command by itself, which simply displays the home screen.

              :Disp

              When you use an empty string with no text (i.e., two quotes side by side — ""), a blank line is displayed.

              :Disp ""

              Optimization

              When you have a list of Disp commands (and each one has its own argument), you can just use the first Disp command and combine the rest of the other Disp commands with it. You remove the Disp commands and combine the arguments, separating each argument with a comma. The arguments can be composed of whatever combination of text, numbers, variables, or expressions is desired.

              The advantages of combining Disp commands are that it makes scrolling through code faster, and it is smaller when just displaying numbers, variables, or expressions. The disadvantages are that it can hinder readability (make the code harder to read) when you have lots of varied arguments, and it is easier to accidentally erase a Disp command with multiple arguments.

              :Disp A
:Disp B
Combine the Disp commands
:Disp A,B

              If you have a string of numbers that you are displaying, you do not need to put quotes around the numbers. This causes the numbers to be displayed on the right side of the screen, and they cease being a string. You may want to keep the numbers in a string, though, if they have any leading zeros. Because the numbers are no longer in a string, the leading zeros are truncated (taken off).

              :Disp "2345
Remove the Quotes
:Disp 2345

              Error Conditions

              • ERR:INVALID occurs if this statement is used outside a program.

              Source: parts of this page were written by the following TI|BD contributors: burr, CloudVariable, DarkerLine, GoVegan, Myles_Zadok, Trenly.

              History

              Calculator OS Version Description
              TI-82 1.0 Added
              Property Value
              Hex Value $DF
              Categories
              Localizations
              • FR: AffGraph

              DispGraph

              Overview

              Displays the graph.

              Availability: Token only available from within the Basic editor.

              Syntax

              DispGraph

              Location

              prgm, I/O, 4:DispGraph

              Description

              The DispGraph command displays the graph screen, along with everything drawn or graphed on it.

              In many cases, this doesn't need to be done explicitly: commands from the 2nd DRAW menu, as well as many other graph screen commands, will display the graph screen automatically when they are used. Mainly, it's used for displaying the graphs of equations or plots in a program — you would define the variable in question, then use DispGraph to graph it. For example:

              :"sin(X)"→Y1
:DispGraph

              Advanced Uses

              DispGraph can also be used to update the graph screen, even if it's already being displayed. For example, changing the value of a plot or equation variable doesn't update the graph immediately. Consider this program:

              :0→I
:"Isin(X)"→Y1
:DispGraph
:For(I,1,10)
:End

              At first, it graphs the equation Y=Isin(X) with I=0. After this, I is cycled from 1 to 10. However, though the parameter I changes, the graph screen isn't updated, and only the initial graph of Y=0sin(X) and final graph of Y=10sin(X) are displayed. If, on the other hand, we change the program:

              :0→I
:"Isin(X)"→Y1
:DispGraph
:For(I,1,10)
:DispGraph
:End

              Now the DispGraph inside the loop ensures that the graph screen is updated every time, and the program will correctly display all eleven graphs.

              Error Conditions

              • ERR:INVALID occurs if this statement is used outside a program.

              Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583.

              History

              Calculator OS Version Description
              TI-82 1.0 Added
              Property Value
              Hex Value $E0
              Categories
              Localizations
              • FR: Output(

              Output(

              Overview

              Displays text beginning at specified row and columnof the home screen.

              Availability: Token only available from within the Basic editor.

              Syntax

              Output(row,column,"text")

              Arguments

              NameTypeOptional
              row
              column
              textstring

              Location

              prgm, I/O, 6:Output(

              Overview

              Displays value beginning at specified row and columnof the home screen.

              Availability: Token only available from within the Basic editor.

              Syntax

              Output(row,column,value)

              Arguments

              NameTypeOptional
              row
              column
              value

              Location

              prgm, I/O, 6:Output(

              Description

              The Output( command is the fastest way to display text on the home screen. It takes three arguments: the row (1-8) at which you want to display something, the column (1-16), and whatever it is you want to display. It allows for more freedom than the Disp command.

              Although off-screen values for the row and column values will cause an error, it's okay if part of the text displayed goes off the screen. When text goes past the last (16th on monochrome calculators, 26th on color calculators) column, it will wrap to the first column of the next row. If the text goes past the last column of the last row, the remainder will be truncated. Output( will never cause the screen to scroll.

              When the horizontal screen split mode is activated, only the first four rows of the home screen are available for the Output( command, which may cause undesirable behavior, and trying to output to the last four rows will cause an error. It is advisable to use the Full command at the beginning of a program that relies on Output(.

              Like other text display commands, you can display each function and command as text. However, this is not without problems as each function and command is counted as one character. The two characters that you can't display are quotation marks (") and the store command (→). However, you can mimic these respectively by using two apostrophes (' ' ), and two subtract signs and a greater than sign (—>).

              Advanced Uses

              If the last text display command of a program is an Output( command, then "Done" will not be displayed as the program finishes. Some programmers use this to get rid of the Done message by using an empty Output( command at the end (there is no text after the quote):

              :Output(1,1,"

              This trick does not work on recent "MathPrint" OSes.

              You can also use Output( to get rid of the run indicator. Unfortunately, it only silences it for a moment and needs to be repeated in a loop to make it appear to be gone. In a game, it should be incorporated into the main loop. The run indicator is momentarily stopped every time that you output something to the upper right corner, it just needs to be repeated for it to appear to be gone. If you're on the graph screen, you can accomplish the same thing using the Text( command.

              :Output(1,16," "

              Since the text displayed by an Output( command wraps, a single command can be used to overwrite the entire screen by displaying 816=128 (1026=260 for color calculators) characters of text starting from row 1, column 1. Since every space on the screen is overwritten, this does not require a ClrHome to clear previously displayed characters. Keep in mind that exactly 16 (26 on color calculators) characters will be on each line.

              Optimization

              Output( does not allow for more than one expression to be displayed by a single command. However, if several strings are going to be displayed next to each other by several commands they might be combined into one (keep in mind how wrapping works):

              :Output(3,3,"Some Text Here
:Output(4,3,"More Text Here
can be
:Output(3,3,"Some Text Here    More Text Here

              In addition, if you are displaying text on the entire home screen, you can place the all the text in a string and then simply display the string. This is especially useful when combined with movement because you can shift the screen quite easily.

              :Output(1,1,Str1

              Command Timings

              The Output( command is the fastest possible way of displaying text (short of storing text to a picture and then recalling it). In particular, when going for speed, it should be preferred instead of Disp.

              Error Conditions

              • ERR:DOMAIN is thrown when the starting row or column are not integers in the valid range (this is affected by split screen mode).
              • ERR:INVALID occurs if this statement is used outside a program.
              • An error is not thrown when the argument is an empty list (unlike with Disp or pretty much anything else, really)

              Source: parts of this page were written by the following TI|BD contributors: burr, CloudVariable, DarkerLine, GoVegan, kg583, Myles_Zadok, persalteas, Sleight, Trenly.

              History

              Calculator OS Version Description
              TI-82 1.0 Added
              Property Value
              Hex Value $E1
              Categories
              Localizations
              • FR: EffEcran

              ClrHome

              Overview

              Clears the home screen.

              Availability: Token only available from within the Basic editor.

              Syntax

              ClrHome

              Location

              prgm, I/O, 8:ClrHome

              Description

              There are numerous times in a program that you need a clear screen, so that you can display whatever text you want without it being interrupted. One place, in particular, is at the beginning of a program, since the previous program call(s) and any other text is typically still displayed on the screen. The simple ClrHome command is the command you use to clear the home screen.

              When you use the ClrHome, it resets the cursor position to the top left corner of the home screen. This is what the Disp and Pause commands use as the reference for what line to display their text on, but it does not have any effect on Output(.

              Advanced Uses

              You want to make sure to clear the home screen when exiting programs (at the end of a program). This ensures that the next program that the user runs will not have to deal with whatever text your program left behind. It also helps the user, because they will not have to manually clear the home screen by pressing the CLEAR key; you have already done it for them.

              Error Conditions

              • ERR:INVALID occurs if this statement is used outside a program.

              See Also

              Source: parts of this page were written by the following TI|BD contributors: alexrudd, burr, CloudVariable, DarkerLine, GoVegan, kg583, Trenly.

              History

              Calculator OS Version Description
              TI-82 1.0 Added
              Property Value
              Hex Value $E2
              Categories
              Localizations
              • FR: Remplir(

              Fill(

              Overview

              Stores value to each element in matrixname.

              Availability: Token available everywhere.

              Syntax

              Fill(value,matrixname)

              Arguments

              NameTypeOptional
              value
              matrixnamematrix

              Location

              2nd, matrix, MATH, 4:Fill(

              Overview

              Stores value to each element in listname.

              Availability: Token available everywhere.

              Syntax

              Fill(value,listname)

              Arguments

              NameTypeOptional
              value
              listnamelist

              Location

              2nd, list, OPS, 4:Fill(

              Description

              The Fill( command takes an existing list or matrix variable and sets all its elements to a single number. It doesn't return anything and only works on already defined variables.

              {5}→dim(L1)
Fill(2,L1)
L1
    {2 2 2 2 2}

{3,4}→dim([A])
Fill(1,[A])
[A]
    [[1 1 1 1]
     [1 1 1 1]
     [1 1 1 1]]

              Fill( is very fast: on a twenty-element real list, it takes only about 3.5 ms, much less than any vectorized list operation.

              When Fill( is called on a list, the datatype of the list becomes the datatype of the number. That is, Fill(1,L₁) makes L₁ a real list, and Fill(i,L₁) makes L₁ a complex list.

              Optimization

              When creating a new list or matrix you want to fill with zeroes, it's better to delete it then create it with dim(, which will set all entries to 0, than to set its dimensions with dim( (which may not clear what was there before) then use Fill(.

              Errors

              On a TI-84+CSE, using Fill(List,List) will cause a RAM clear. For example: Fill({1,2,3},{1,2,3} will cause a RAM Clear. This does not apply on any other models, as they only give you argument and data type errors.

              Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, iPhoenixOnTIBD, kg583, lirtosiast, Silver Phantom.

              History

              Calculator OS Version Description
              TI-82 1.0 Added
              Property Value
              Hex Value $E3
              Categories
              Localizations
              • FR: Tricroi(

              SortA(

              Overview

              Sorts elements of listname in ascending order.

              Availability: Token available everywhere.

              Syntax

              SortA(listname)

              Arguments

              NameTypeOptional
              listnamelist

              Location

              2nd, list, OPS, 1:SortA(

              Overview

              Sorts elements of keylistname in ascending order, then sorts each dependlist as a dependent list.

              Availability: Token available everywhere.

              Syntax

              SortA(keylistname,dependlist1[,dependlist2,...,dependlist n])

              Arguments

              NameTypeOptional
              keylistnamelist
              dependlist1list
              dependlist2listYes
              dependlist nlistYes

              Location

              2nd, list, OPS, 1:SortA(

              Description

              The SortA( command sorts a list in ascending order. It does not return it, but instead edits the original list variable (so it takes only list variables as arguments).

              SortA( can also be passed multiple lists. In this case, it will sort the first list, and reorder the others so that elements which had the same indices initially will continue having the same indices. For example, suppose the X and Y coordinates of some points were stored in ʟX and ʟY, so that the Nth point had coordinates ʟX(N) and ʟY(N). Then SortA(ʟX,ʟY) would sort the points by their x-coordinates, still preserving the same points.

              However, SortA( is not stable: if several elements in the first list are equal, then the corresponding elements in the subsequent lists may still end up being in a different order than they were initially.

              Algorithm

              The algorithm used by SortA( and SortD( appears to be a modified selection sort. It is still O(n2) on all inputs, but for some reason takes twice as long on a list with all equal elements. It is not stable.

              Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan.

              History

              Calculator OS Version Description
              TI-82 1.0 Added
              Property Value
              Hex Value $E4
              Categories
              Localizations
              • FR: Tridécroi(

              SortD(

              Overview

              Sorts elements of listname in descending order.

              Availability: Token available everywhere.

              Syntax

              SortD(listname)

              Arguments

              NameTypeOptional
              listnamelist

              Location

              2nd, list, OPS, 2:SortD(

              Overview

              Sorts elements of keylistname in descending order, then sorts each dependlist as a dependent list.

              Availability: Token available everywhere.

              Syntax

              SortD(keylistname,dependlist1[,dependlist2,..., dependlist n])

              Arguments

              NameTypeOptional
              keylistnamelist
              dependlist1list
              dependlist2listYes
              dependlist nlistYes

              Location

              2nd, list, OPS, 2:SortD(

              Description

              The SortD( command sorts a list in descending order. It does not return it, but instead edits the original list variable (so it takes only list variables as arguments).

              SortD( can also be passed multiple lists. In this case, it will sort the first list, and reorder the others so that elements which had the same indices initially will continue having the same indices. For example, suppose the X and Y coordinates of some points were stored in ʟX and ʟY, so that the Nth point had coordinates ʟX(N) and ʟY(N). Then SortD(ʟX,ʟY) would sort the points by their x-coordinates, still preserving the same points.

              However, SortD( is not stable: if several elements in the first list are equal, then the corresponding elements in the subsequent lists may still end up being in a different order than they were initially.

              Algorithm

              The algorithm used by SortD( and SortA( appears to be a modified selection sort. It is still O(n2) on all inputs, but for some reason takes twice as long on a list with all equal elements. It is not stable.

              Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan.

              History

              Calculator OS Version Description
              TI-82 1.0 Added
              Property Value
              Hex Value $E5
              Categories
              Localizations
              • FR: AffTable

              DispTable

              Overview

              Displays the table.

              Availability: Token only available from within the Basic editor.

              Syntax

              DispTable

              Location

              prgm, I/O, 5:DispTable

              Description

              The DispTable comand displays the table screen you normally see by pressing 2nd TABLE, from a running program. The user will see the table screen with a "paused" run indicator, and will be able to use arrows to scroll through it. Pressing ENTER will exit the screen and continue the program.

              Advanced Uses

              The user can't select any cells in the table to be evaluated if they're not, already. So it's best to select the IndpntAuto and DependAuto options from the 2nd TBLSET menu before using this command. IndpntAsk can also work, however, as long as you store to TblInput first.

              Error Conditions

              • ERR:INVALID occurs if this statement is used outside a program.

              Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, kg583.

              History

              Calculator OS Version Description
              TI-82 1.0 Added
              Property Value
              Hex Value $E6
              Categories
              Localizations
              • FR: Menu(

              Menu(

              Overview

              Generates a menu of up to seven items during program execution.

              Availability: Token only available from within the Basic editor.

              Syntax

              Menu("title","text1",label1[,...,"text7",label7])

              Arguments

              NameTypeOptional
              title
              text1string
              label1
              ...Yes
              text7stringYes
              label7Yes

              Location

              prgm, CTL, C:Menu(

              Description

              Menus are used for organization, to provide a list of choices for the user to select from, as well as a good way for users to interact with and navigate programs. Although using the Menu( command requires branching (which is generally frowned upon in most circumstances), the menu looks like a generic built-in menu, so it is familiar and easy to use for the user.

              When the Menu( command is encountered during a program, the menu screen is displayed with the specified menu title in white-on-black text on the top line and each menu item listed below on its own line, the pause indicator turns on, and execution pauses until the user selects a menu item. There is a cursor that the user can move up and down the menu to select a menu item.

              The menu title can be 16 characters or less on monochrome calculators (because of the screen width), and 26 characters or less on color calculators, and must be enclosed in a pair of quotation marks. The menu title looks best if you center it on the screen (using spaces to fill in the rest of the line), so that the entire top line will be highlighted. The menu can have up to seven menu items on monochrome and up to nine on color calculators (because of the screen height and the menu title on top).

              After the menu title, you put a comma and then the menu items. There are two parts to a menu item: the text that will be displayed on the screen and the label that program execution will continue at if the user presses ENTER on the menu item or presses its corresponding number. The text can be fourteen characters or less on monochrome and 24 or less on color (because the menu item number is displayed on the left) and must be enclosed in a pair of quotation marks, and you have to separate the text and label with a comma.

              PROGRAM:MENU
:Lbl NY
:Menu(" Select A Place ","NY",NY,"LA",NY,"MN",MN
:Lbl MN
:Disp "Good Choice!

              Advanced Uses

              When a program needs more than seven (or nine on color calculators) menu items, you will have to create another menu and then link to that menu from the first menu with one of the menu items. Similarly, you can also have two menu items go to the same label (you do not need two labels if they are right next to each other).

              If you get tired of using the Menu( command every time you want to make a menu, the alternative is to make your own custom menu. A custom menu provides a richer experience for the user, and isn't much more work than using the Menu( command. In addition, as you get more experienced as a programmer, you'll come to enjoy using custom menus.

              You can use a string variable for the menu title and menu item text instead of the text in quotes, which may sometimes be smaller if the text is used at other places in the program. Similarly, its possible to place all the menu titles in one string variable, and then just access the respective menu title as a substring Unfortunately, variables will not work for the menu item labels. You can also leave the menu title blank to give the illusion that there is no menu title by using two quotes side by side (i.e. "").

              For many programs, including text-based programs (where menus are heavily used), there is a main menu that is used for navigating to the different parts of the program. While each program's main menu is unique, two of the most standard menu items on a main menu are Start and Quit — Start goes to the beginning of the program, while Quit goes to the end. It is also fairly common to place a label right before the main menu, so you can return to it again later in the program.

              Problems

              1. There is only one line for the title.
              2. There are only seven (or nine on color calculators) slots for the menu items and no scrolling (you CAN add a "next" at the bottom, but that just looks bad, especially if you have a "back" and/or "exit" down there already)
              3. The screen refreshes or blinks when you press down at the bottom to go back to the top.
              4. During the loading of the menu, you can see what is written on the home screen.

              Optimization

              Because the Menu( command displays the menu screen instead of clearing the home screen, you do not need to put the ClrHome command before it.

              :ClrHome
:Menu("Choose","Right",1,"Wrong",2
Remove ClrHome
:Menu("Choose","Right",1,"Wrong",2

              Error Conditions

              • ERR:INVALID occurs if this statement is used outside a program.
              • ERR:LABEL is thrown when an option is chosen whose label doesn't exist.

              See Also

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              Featured Article

              Source: parts of this page were written by the following TI|BD contributors: burr, CloudVariable, DarkerLine, GoVegan, Myles_Zadok, olin3434, Timothy Foster, Trenly.

              History

              Calculator OS Version Description
              TI-82 1.0 Added
              Property Value
              Hex Value $E7
              Categories
              Localizations
              • FR: Envoi(

              Send(

              Overview

              Sends one or more TI-Innovator™ Hub commands to a connected hub.
              Notes:
              See also eval( and Get( command related to the Send( command.
              TI-Innovator™ Hub commands are supported in the HUB submenu in the CE OS v.5.2 program editor.

              Availability: Token only available from within the Basic editor.

              Syntax

              Send(string)

              Arguments

              NameTypeOptional
              stringstring

              Location

              prgm, I/O, B:Send(

              Overview

              Sends one or more TI-Innovator™ Hub commands to a connected hub.
              Notes:
              See also eval( and Get( command related to the Send( command.
              TI-Innovator™ Hub commands are supported in the HUB submenu in the CE OS v.5.2 program editor.

              Availability: Token only available from within the Basic editor.

              Syntax

              Send(string)

              Arguments

              NameTypeOptional
              stringstring

              Location

              prgm, HUB

              Description

              The Send( command is used for sending data to a CBL (Calculator Based Laboratory) device (or another compatible device) via a link cable. With some exceptions, Send('s argument must be a variable: a real number, list, matrix, string, equation, picture, or GDB. An expression or a number will not work — Send(5) or Send([A][B]) is invalid.

              The exceptions are list or matrix elements (that is, you can do Send(A) or Send(L1(2)) without an error) and non-variable lists typed out with { } brackets and commas.

              Norland Robot

              You can use Send( with a Get( for a Norland calculator robot. The format called CLR format. C stands for command number, L stands for left axle, and R stands for right axle. If the command number is 1, it makes the robot moves in a direction for the time specified later in the command. If it is 2, the robot moves until the bumper hits a wall. If it is 3, it moves for a specified amount of time and stops when the robot when the bumper hits a wall. For example, send({122,100}) will make the robot move forward for 100 centiseconds, send({222}) makes it go forward until the bumper hits the wall, and send({322,100}) makes the robot move forward for 100 centiseconds and stops it when the bumper is pressed. The last two axle control numbers are like this:
              0=backwards
              1=stop
              2=forwards

              Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, jonbush, princetonlion.

              History

              Calculator OS Version Description
              TI-82 1.0 Added
              Property Value
              Hex Value $E8
              Categories
              Localizations
              • FR: Capt(

              Get(

              Overview

              Retrieves a value from a connected TI-Innovator™ Hub and stores the data to a variable on the receiving CE calculator.
              Note: See also Send( and eval(

              Availability: Token only available from within the Basic editor.

              Syntax

              Get(variable)

              Arguments

              NameTypeOptional
              variable

              Location

              prgm, I/O, A:Get(

              Overview

              Retrieves a value from a connected TI-Innovator™ Hub and stores the data to a variable on the receiving CE calculator.
              Note: See also Send( and eval(

              Availability: Token only available from within the Basic editor.

              Syntax

              Get(variable

              Arguments

              NameTypeOptional
              variable

              Location

              prgm, HUB, 5:Get

              Special Category

              Ti-Innovator™ Hub

              Description

              The Get( command is meant for use with the CBL (Calculator Based Laboratory) device, or other compatible devices. When the calculator is connected by a link cable to such a device, Get(variable) will read data from the device and store it to variable. Usually, this data is a list, and so you want to Get(L₁) or some other list variable.

              Advanced Uses

              In fact, the Get( command can also be used for linking two calculators, in which case it functions precisely like GetCalc(. This is probably for compatibility with the TI-82, which used Get( rather than GetCalc( for linking two calculators. However, since this isn't a documented feature (in fact, your TI-83+ manual will insist that Get( cannot be used in this way), it isn't guaranteed to work with future calculator versions.

              Optimization

              Nevertheless, using Get( instead of GetCalc( will make your program smaller, and probably preserve functionality.

              Norland Robot

              The Get( command is usually used after a Send command to confirm its transmission like this: Get(var). The variable in the parentheses is where the time of the robot's movement is stored. You can display the time moved with a Disp command.

              Source: parts of this page were written by the following TI|BD contributors: burr, CloudVariable, DarkerLine, GoVegan, jonbush, kg583, princetonlion, Timtech, Trenly.

              History

              Calculator OS Version Description
              TI-82 1.0 Added
              Property Value
              Hex Value $E9
              Categories
              Localizations
              • FR: GraphAff

              PlotsOn

              Overview

              Selects all stat plots or one or more specified stat plots (1, 2, or 3).

              Availability: Token available everywhere.

              Syntax

              PlotsOn [1,2,3]

              Location

              2nd, stat plot, STAT PLOTS, 5:PlotsOn

              Description

              By itself, the command will turn on all three stat plots.

              If it is given arguments, there can be any number of them (actually, no more than 255, but this won't stop most people), but they must all be numbers 1 to 3. Then, the command will only turn on the specified plots. Unlike some commands, it is okay to give PlotsOn an expression as an argument (for example, PlotsOn X), as long as it has a value of 1, 2, or 3.

              Error Conditions

              • ERR:DOMAIN is thrown if a plot that is not 1, 2, or 3 is specified.

              Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

              History

              Calculator OS Version Description
              TI-82 1.0 Added
              Property Value
              Hex Value $EA
              Categories
              Localizations
              • FR: GraphNAff

              PlotsOff

              Overview

              Deselects all stat plots or one or more specified stat plots (1, 2, or 3).

              Availability: Token available everywhere.

              Syntax

              PlotsOff [1,2,3]

              Location

              2nd, stat plot, STAT PLOTS, 4:PlotsOff

              Description

              By itself, the command will turn off all three stat plots.

              If it is given arguments, there can be any number of them (actually, no more than 255, but this won't stop most people), but they must all be numbers 1 to 3. Then, the command will only turn off the specified plots. Unlike some commands, it is okay to give PlotsOff an expression as an argument (for example, PlotsOff X), as long as it has a value of 1, 2, or 3.

              Error Conditions

              • ERR:DOMAIN is thrown if a plot that is not 1, 2, or 3 is specified.

              Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

              History

              Calculator OS Version Description
              TI-82 1.0 Added
              Property Value
              Hex Value $EB
              Categories
                Localizations
                • FR: ʟ

                ʟ

                Overview

                Identifies the next one to five characters as a user-created list name.

                Availability: Token available everywhere.

                Syntax

                ʟlistname

                Arguments

                NameTypeOptional
                listnamelist

                Location

                2nd, list, OPS, B:

                Description

                The ʟ character is used at the start of the name of any custom list you create, for example:

                {1,2,3}→ʟHELLO
{4,5,6}→ʟWORLD

                In most cases you need to include this when accessing or manipulating a custom list (although there's a few exceptions, see the Optimization section below). You do not need this character when accessing the the default lists L₁…L₆).

                The maximum length of the list name (not including the ʟ) is five letters. ʟABCDE works, but ʟABCDEF does not. List names must start with a letter A-Z but can also include numbers so ʟLIST1 and ʟLIST2 are valid list names, but ʟ123 is not.

                There are two ways to insert this character:

                1. Press 2nd, LIST, press right arrow to access the OPS menu, scroll to the bottom, and press ENTER to insert the ʟ character. You can then type the rest of the name of your list.
                2. If your custom list already exists, you can press 2nd, LIST, select the name of your list, and press ENTER. The whole name including the ʟ character will be inserted.

                Optimization

                You don't actually need to include the ʟ command when storing (→) to a list.

                {1,2,3}→HELLO
{4,5,6}→WORLD
{7,8,9}→X

                Although the name X as used above also matches the name of a regular real variable, since the data being stored is a list, it will be saved to ʟX.

                When storing to a specific list item, you MUST still include the ʟ character:

                1→ʟHELLO(1)
2→ʟWORLD(2)
3→ʟX(3)

                Some of the list commands also allow for leaving off the ʟ character, such as SetUpEditor. However, be careful when doing so with Input and Prompt because you might only be asking the user to input a list, but if a real value is entered, it would be saved to a real variable instead.

                Error Conditions

                • ERR:SYNTAX is thrown if you try to reference/create a list with more than 5 characters in its name.
                • ERR:UNDEFINED is thrown if you try to use ʟ on an undefined list.

                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583, Timtech.

                History

                Calculator OS Version Description
                TI-83 0.01013 Added
                Property Value
                Hex Value $EC
                Categories
                Localizations
                • FR: Graph1(

                Plot1(

                Overview

                Defines Plot# (1, 2, or 3) of type Scatter or xyLine for Xlist and Ylist using markand color.
                Color#: 10 - 24 or color name pasted from [vars] COLOR.
                Note: Xlistand Ylistrepresent the Xlist and Ylist names.

                Availability: Token only available from within the Basic editor.

                Syntax

                Plot#(type,Xlist,Ylist[,mark,color#])

                Arguments

                NameTypeOptional
                #
                type
                Xlistlist
                Ylistlist
                markYes
                color#colorNumYes

                Location

                2nd, stat plot, STAT PLOTS, 1:Plot12:Plot23:Plot3

                Overview

                Defines Plot# (1, 2, or 3) of type Histogram or Boxplot for Xlist with frequency freqlistand color #.
                Color#: 10 - 24 or color name pasted from [vars] COLOR.
                Note: Xlistrepresents the Xlist name.

                Availability: Token only available from within the Basic editor.

                Syntax

                Plot#(type,Xlist[,freqlist,color#])

                Arguments

                NameTypeOptional
                #
                type
                Xlistlist
                freqlistlistYes
                color#colorNumYes

                Location

                2nd, stat plot, STAT PLOTS, 1:Plot12:Plot23:Plot3

                Overview

                Defines Plot# (1, 2, or 3) of type ModBoxplot for Xlist with frequency freqlist using markand color #.
                Color#: 10 - 24 or color name pasted from [vars] COLOR.
                Note: Xlistrepresents the Xlist name.

                Availability: Token only available from within the Basic editor.

                Syntax

                Plot#(type,Xlist[,freqlist,mark,color#])

                Arguments

                NameTypeOptional
                #
                type
                Xlistlist
                freqlistlistYes
                markYes
                color#colorNumYes

                Location

                2nd, stat plot, STAT PLOTS, 1:Plot12:Plot23:Plot3

                Overview

                Defines Plot# (1, 2, or 3) of type NormProbPlot for datalist on data axis using markand color # data axis can be X or Y.
                Color#: 10 - 24 or color name pasted from [vars] COLOR.
                Note: datalistrepresents the datalist name.

                Availability: Token only available from within the Basic editor.

                Syntax

                Plot#(type,datalist[,data axis,mark,color#])

                Arguments

                NameTypeOptional
                #
                type
                datalistlist
                data axisYes
                markYes
                color#colorNumYes

                Location

                2nd, stat plot, STAT PLOTS, 1:Plot12:Plot23:Plot3

                Description

                The commands Plot1(, Plot2(, and Plot3(, which are identical except for which stat plot (1, 2, or 3) they affect, define their corresponding stat plot. When the stat plot is defined, it is also turned on so no PlotsOn command is necessary.

                The first argument of the commands is always the type of plot, and is one of Scatter, xyLine, Histogram, Boxplot, ModBoxplot, and NormProbPlot - these types are found in the TYPE submenu of the stat plot menu. The other arguments vary. For all but Histogram and Boxplot, there is a mark argument - this is a dot, a cross, or a box, symbols that can be found in the MARK submenu of the stat plot menu. On color calculators, there is an optional final argument to specify the color of the plot.

                Scatter plot

                Plot#(Scatter, x-list, y-list, mark) defines a scatter plot. The points defined by x-list and y-list are plotted using mark on the graph screen.

                x-list and y-list must be the same length.

                xyLine plot

                Plot#(xyLine, x-list, y-list, mark) defines an xyLine plot. Similarly to a scatter plot, the points defined by x-list and y-list are plotted using mark on the graph screen, but with an xyLine plot they are also connected by a line, in the order that they occur in the lists.

                x-list and y-list must be the same length.

                Histogram plot

                Plot#(Histogram, x-list, freq list) defines a Histogram plot. The x-axis is divided into intervals that are Xscl wide. A bar is drawn in in each interval whose height corresponds to the number of points in the interval. Points that are not between Xmin and Xmax are not tallied.

                Xscl must not be too small - it can divide the screen into no more than 47 different bars.

                Box plot

                Plot#(Boxplot, x-list, freq list) defines a box plot. A rectangular box is drawn whose left edge is Q1 (the first quartile) of the data, and whose right edge is Q3 (the third quartile). A vertical segment is drawn within the box at the median, and 'whiskers' are drawn from the box to the minimum and maximum data points.

                The box plot ignores the Ymax and Ymin dimensions of the screen, and any plots that aren't box plots or modified box plots. Each box plot takes approximately 1/3 of the screen in height, and if more than one are plotted, they will take up different areas of the screen.

                Modified box plot

                Plot#(ModBoxplot, x-list, freq list, mark) defines a modified box plot. This is almost entirely like the normal box plot, except that it also draws outliers. Whiskers are only drawn to the furthers point within 1.5 times the interquartile range (Q3-Q1) of the box. Beyond this point, data points are drawn individually, using mark.

                The box plot ignores the Ymax and Ymin dimensions of the screen, and any plots that aren't box plots or modified box plots. Each box plot takes approximately 1/3 of the screen in height, and if more than one are plotted, they will take up different areas of the screen.

                Normal probability plot

                Plot#(NormProbPlot, data list, data axis, mark) defines a normal probability plot. The mean and standard deviation of the data are calculated. Then for each point, the number of standard deviations it is from the mean is calculated, and the point is plotted against this number using mark. data axis can be either X or Y: it determines whether the value of a point determines it's x-coordinate or y-coordinate.

                The point behind this rather convoluted process is to test the extent to which the data is normally distributed. If it follows the normal distribution closely, then the result will be close to a straight line - otherwise it will be curved.

                Advanced Uses

                After doing a regression, a scatter plot of ʟRESID against the x-list is a useful measure of the effectiveness of the regression. If the plot appears random, this is a good sign; if there is a pattern to the plot, this means it's likely that a better regression model exists.

                Optimization

                The ʟ symbol at the beginning of list names can be omitted everywhere in this command.

                In addition, every element except the plot type and the data list or data lists are optional, and take on the following default values:

                • freq list is 1 by default, meaning that all frequencies are 1.
                • mark is the box by default.
                • data axis is X by default.

                Error Conditions

                • ERR:DIM MISMATCH is thrown if the x and y lists, or the data and frequency lists, have different dimensions.
                • ERR:STAT is thrown if Xscl is too small in the case of a Histogram.

                All errors are thrown when plotting the stat plot, as opposed to when the command is executed, and do not provide a 2:Goto option.

                Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Myles_Zadok.

                History

                Calculator OS Version Description
                TI-82 1.0 Added
                Property Value
                Hex Value $ED
                Categories
                Localizations
                • FR: Graph2(

                Plot2(

                Overview

                Availability: Token available everywhere.

                Syntax

                Plot2(

                Description

                The commands Plot1(, Plot2(, and Plot3(, which are identical except for which stat plot (1, 2, or 3) they affect, define their corresponding stat plot. When the stat plot is defined, it is also turned on so no PlotsOn command is necessary.

                The first argument of the commands is always the type of plot, and is one of Scatter, xyLine, Histogram, Boxplot, ModBoxplot, and NormProbPlot - these types are found in the TYPE submenu of the stat plot menu. The other arguments vary. For all but Histogram and Boxplot, there is a mark argument - this is a dot, a cross, or a box, symbols that can be found in the MARK submenu of the stat plot menu. On color calculators, there is an optional final argument to specify the color of the plot.

                Scatter plot

                Plot#(Scatter, x-list, y-list, mark) defines a scatter plot. The points defined by x-list and y-list are plotted using mark on the graph screen.

                x-list and y-list must be the same length.

                xyLine plot

                Plot#(xyLine, x-list, y-list, mark) defines an xyLine plot. Similarly to a scatter plot, the points defined by x-list and y-list are plotted using mark on the graph screen, but with an xyLine plot they are also connected by a line, in the order that they occur in the lists.

                x-list and y-list must be the same length.

                Histogram plot

                Plot#(Histogram, x-list, freq list) defines a Histogram plot. The x-axis is divided into intervals that are Xscl wide. A bar is drawn in in each interval whose height corresponds to the number of points in the interval. Points that are not between Xmin and Xmax are not tallied.

                Xscl must not be too small - it can divide the screen into no more than 47 different bars.

                Box plot

                Plot#(Boxplot, x-list, freq list) defines a box plot. A rectangular box is drawn whose left edge is Q1 (the first quartile) of the data, and whose right edge is Q3 (the third quartile). A vertical segment is drawn within the box at the median, and 'whiskers' are drawn from the box to the minimum and maximum data points.

                The box plot ignores the Ymax and Ymin dimensions of the screen, and any plots that aren't box plots or modified box plots. Each box plot takes approximately 1/3 of the screen in height, and if more than one are plotted, they will take up different areas of the screen.

                Modified box plot

                Plot#(ModBoxplot, x-list, freq list, mark) defines a modified box plot. This is almost entirely like the normal box plot, except that it also draws outliers. Whiskers are only drawn to the furthers point within 1.5 times the interquartile range (Q3-Q1) of the box. Beyond this point, data points are drawn individually, using mark.

                The box plot ignores the Ymax and Ymin dimensions of the screen, and any plots that aren't box plots or modified box plots. Each box plot takes approximately 1/3 of the screen in height, and if more than one are plotted, they will take up different areas of the screen.

                Normal probability plot

                Plot#(NormProbPlot, data list, data axis, mark) defines a normal probability plot. The mean and standard deviation of the data are calculated. Then for each point, the number of standard deviations it is from the mean is calculated, and the point is plotted against this number using mark. data axis can be either X or Y: it determines whether the value of a point determines it's x-coordinate or y-coordinate.

                The point behind this rather convoluted process is to test the extent to which the data is normally distributed. If it follows the normal distribution closely, then the result will be close to a straight line - otherwise it will be curved.

                Advanced Uses

                After doing a regression, a scatter plot of ʟRESID against the x-list is a useful measure of the effectiveness of the regression. If the plot appears random, this is a good sign; if there is a pattern to the plot, this means it's likely that a better regression model exists.

                Optimization

                The ʟ symbol at the beginning of list names can be omitted everywhere in this command.

                In addition, every element except the plot type and the data list or data lists are optional, and take on the following default values:

                • freq list is 1 by default, meaning that all frequencies are 1.
                • mark is the box by default.
                • data axis is X by default.

                Error Conditions

                • ERR:DIM MISMATCH is thrown if the x and y lists, or the data and frequency lists, have different dimensions.
                • ERR:STAT is thrown if Xscl is too small in the case of a Histogram.

                All errors are thrown when plotting the stat plot, as opposed to when the command is executed, and do not provide a 2:Goto option.

                Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Myles_Zadok.

                History

                Calculator OS Version Description
                TI-82 1.0 Added
                Property Value
                Hex Value $EE
                Categories
                Localizations
                • FR: Graph3(

                Plot3(

                Overview

                Availability: Token available everywhere.

                Syntax

                Plot3(

                Description

                The commands Plot1(, Plot2(, and Plot3(, which are identical except for which stat plot (1, 2, or 3) they affect, define their corresponding stat plot. When the stat plot is defined, it is also turned on so no PlotsOn command is necessary.

                The first argument of the commands is always the type of plot, and is one of Scatter, xyLine, Histogram, Boxplot, ModBoxplot, and NormProbPlot - these types are found in the TYPE submenu of the stat plot menu. The other arguments vary. For all but Histogram and Boxplot, there is a mark argument - this is a dot, a cross, or a box, symbols that can be found in the MARK submenu of the stat plot menu. On color calculators, there is an optional final argument to specify the color of the plot.

                Scatter plot

                Plot#(Scatter, x-list, y-list, mark) defines a scatter plot. The points defined by x-list and y-list are plotted using mark on the graph screen.

                x-list and y-list must be the same length.

                xyLine plot

                Plot#(xyLine, x-list, y-list, mark) defines an xyLine plot. Similarly to a scatter plot, the points defined by x-list and y-list are plotted using mark on the graph screen, but with an xyLine plot they are also connected by a line, in the order that they occur in the lists.

                x-list and y-list must be the same length.

                Histogram plot

                Plot#(Histogram, x-list, freq list) defines a Histogram plot. The x-axis is divided into intervals that are Xscl wide. A bar is drawn in in each interval whose height corresponds to the number of points in the interval. Points that are not between Xmin and Xmax are not tallied.

                Xscl must not be too small - it can divide the screen into no more than 47 different bars.

                Box plot

                Plot#(Boxplot, x-list, freq list) defines a box plot. A rectangular box is drawn whose left edge is Q1 (the first quartile) of the data, and whose right edge is Q3 (the third quartile). A vertical segment is drawn within the box at the median, and 'whiskers' are drawn from the box to the minimum and maximum data points.

                The box plot ignores the Ymax and Ymin dimensions of the screen, and any plots that aren't box plots or modified box plots. Each box plot takes approximately 1/3 of the screen in height, and if more than one are plotted, they will take up different areas of the screen.

                Modified box plot

                Plot#(ModBoxplot, x-list, freq list, mark) defines a modified box plot. This is almost entirely like the normal box plot, except that it also draws outliers. Whiskers are only drawn to the furthers point within 1.5 times the interquartile range (Q3-Q1) of the box. Beyond this point, data points are drawn individually, using mark.

                The box plot ignores the Ymax and Ymin dimensions of the screen, and any plots that aren't box plots or modified box plots. Each box plot takes approximately 1/3 of the screen in height, and if more than one are plotted, they will take up different areas of the screen.

                Normal probability plot

                Plot#(NormProbPlot, data list, data axis, mark) defines a normal probability plot. The mean and standard deviation of the data are calculated. Then for each point, the number of standard deviations it is from the mean is calculated, and the point is plotted against this number using mark. data axis can be either X or Y: it determines whether the value of a point determines it's x-coordinate or y-coordinate.

                The point behind this rather convoluted process is to test the extent to which the data is normally distributed. If it follows the normal distribution closely, then the result will be close to a straight line - otherwise it will be curved.

                Advanced Uses

                After doing a regression, a scatter plot of ʟRESID against the x-list is a useful measure of the effectiveness of the regression. If the plot appears random, this is a good sign; if there is a pattern to the plot, this means it's likely that a better regression model exists.

                Optimization

                The ʟ symbol at the beginning of list names can be omitted everywhere in this command.

                In addition, every element except the plot type and the data list or data lists are optional, and take on the following default values:

                • freq list is 1 by default, meaning that all frequencies are 1.
                • mark is the box by default.
                • data axis is X by default.

                Error Conditions

                • ERR:DIM MISMATCH is thrown if the x and y lists, or the data and frequency lists, have different dimensions.
                • ERR:STAT is thrown if Xscl is too small in the case of a Histogram.

                All errors are thrown when plotting the stat plot, as opposed to when the command is executed, and do not provide a 2:Goto option.

                Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Myles_Zadok.

                History

                Calculator OS Version Description
                TI-82 1.0 Added
                Property Value
                Hex Value $EF00
                Categories
                Localizations
                • FR: défDate(

                setDate(

                Overview

                Sets the date using a year, month, day format. The year must be 4 digits; month and day can be 1 or 2 digit.

                Comment:EFXX tokens are TI-84+ and later only

                Availability: Token available everywhere.

                Syntax

                setDate(year,month,day)

                Arguments

                NameTypeOptional
                year
                month
                day

                Location

                2nd, catalog, setDate(

                Description

                The setDate( command sets the date of the clock on the TI-84+/SE calculators. It takes three arguments: the year, the month, and the day. All three of these must be integers; in particular, year must be four digits, and month and day can be one or two digits. They represent the associated value that goes with a respective date. For example, this would set the date to January 1, 2008:

                :setDate(2008,1,1

                Once you have set the date, you can display it in three different formats on the mode screen using the setDtFmt( command: Month/Day/Year, Day/Month/Year, or Year/Month/Day. Of course, the date will only show up if the clock is on; if you need to turn the clock on, use the ClockOn command or select 'TURN CLOCK ON' , displayed in place of the clock on the mode screen.

                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Jonathan King, RandomProductions, Timtech.

                History

                Calculator OS Version Description
                TI-84+ 0.01 Added
                Property Value
                Hex Value $EF01
                Categories
                Localizations
                • FR: défHeure(

                setTime(

                Overview

                Sets the time using an hour, minute, second format. The hour must be in 24 hour format, in which 13 = 1 p.m.

                Availability: Token available everywhere.

                Syntax

                setTime(hour,minute, second)

                Arguments

                NameTypeOptional
                hour
                minute
                second

                Location

                2nd, catalog, setTime(

                Description

                The setTime( command sets the time of the clock on the TI-84+/SE calculators. It takes three arguments: the hour, the minute, and the second. The hour must be in 24 hour format — where 13 is equal to 1 P.M. — and the minute and second need to be a valid number within the appropriate range (1-60). For example, this would set the time to 12:30:30:

                :setTime(12,30,30

                Once you have set the time, you can display it in two different formats on the mode screen using the setTmFmt( command: 12 (12 hour) or 24 (24 hour). Of course, the time will only show up if the clock is on; if you need to turn the clock on, use the ClockOn command, or scroll down to the 'TURN CLOCK ON' message that is displayed in place of the clock on the mode screen and press ENTER twice.

                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, RandomProductions.

                History

                Calculator OS Version Description
                TI-84+ 0.01 Added
                Property Value
                Hex Value $EF02
                Categories
                Localizations
                • FR: AffMintr(

                checkTmr(

                Overview

                Returns the number of seconds since you used startTmr to start the timer. The starttime is the value displayed by startTmr.

                Availability: Token available everywhere.

                Syntax

                checkTmr(starttime)

                Arguments

                NameTypeOptional
                starttime

                Location

                2nd, catalog, checkTmr(

                Description

                The checkTmr( command is used together with the startTmr command to determine how much time has elapsed since the timer was started on the TI-84+/SE calculators. In particular, it returns the number of seconds since the built-in timer was started. An application of these commands is timing different commands or pieces of code, as well as countdowns in games, or a time-based score (such as in Minesweeper).

                To use the timer, you first store startTmr to a variable (usually, a real variable) whenever you want the count to start. Now, whenever you want to check the elapsed time, you can use checkTmr( with the variable from above, giving you the number of seconds that have passed. Using checkTmr( doesn't stop the timer, you can do it as many times as you want to.

                In the case of Minesweeper, for example, you would store startTmr to, for example, T, after setting up and displaying the board, display the result of checkTmr(T) in the game's key-reading loop, and store checkTmr(T) to the player's score if he wins.

                Advanced Uses

                To time a command or routine using startTmr and checkTmr(, use the following template:

                :ClockOn
:startTmr→T
:Repeat checkTmr(Ans
:End
:For(n,1,(number)                    //sequence variable n
   (command(s) to be tested)
:End
:checkTmr(T+1)/(number)

                Making (number) higher increases accuracy, but takes longer. Also, make sure not to modify the variables n or T inside the For( loop.

                While this method eliminates human error from counting, it's prone to its own faults. For example, startTmr and checkTmr( always return the time rounded down to a whole second. To take this into account, replace the last line:

                :(checkTmr(T+{1,0})/(number)

                When testing code, be aware that many different things affect the time: the strength of the batteries, the amount of free RAM, and including the closing parenthesis on the For( loop. The last one, in particular, has an impact when using a single-line If statement or one of the IS>( and DS<( commands on the first line inside a For( loop.

                Source: parts of this page were written by the following TI|BD contributors: Austin 332000, burr, DarkerLine, Electromagnet8, GoVegan, Kenta Lynn, kg583, lirtosiast, Xphoenix.

                History

                Calculator OS Version Description
                TI-84+ 0.01 Added
                Property Value
                Hex Value $EF03
                Categories
                Localizations
                • FR: défFmtDt(

                setDtFmt(

                Overview

                Sets the date format.
                1 = M/D/Y2 = D/M/Y3 = Y/M/D

                Availability: Token available everywhere.

                Syntax

                setDtFmt(integer)

                Arguments

                NameTypeOptional
                integer

                Location

                2nd, catalog, setDtFmt(

                Description

                The setDtFmt( command sets the date format of the clock on the TI-84+/SE calculators when displaying the date on the mode screen. There are three different formats available, and you simply use the respective value (can be either a literal number or a variable) to display the desired one: 1 (M/D/Y), 2 (D/M/Y), or 3 (Y/M/D). For example, this would set the date format to Month/Day/Year:

                :setDtFmt(1

                In order for the date format to work, you need to set the date using either the setDate( command, or by going into the set clock menu (accessible by pressing ENTER on the 'SET CLOCK' message that is displayed at the bottom of the mode screen). Of course, the date will only show up if the clock is on; if you need to turn the clock on, use the ClockOn command, or scroll down to the 'TURN CLOCK ON' message that is displayed in place of the clock on the mode screen and press ENTER twice.

                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, RandomProductions.

                History

                Calculator OS Version Description
                TI-84+ 0.01 Added
                Property Value
                Hex Value $EF04
                Categories
                Localizations
                • FR: défFmtHr(

                setTmFmt(

                Overview

                Sets the time format.
                12 = 12 hour format24 = 24 hour format

                Availability: Token available everywhere.

                Syntax

                setTmFmt(integer)

                Arguments

                NameTypeOptional
                integer

                Location

                2nd, catalog, setTmFmt(

                Description

                The setTmFmt( command sets the time format of the clock on the TI-84+/SE calculators when displaying the time on the mode screen. There are two different formats available, and you simply use the respective value (can be either a literal number or a variable) to display the desired one: 12 (12 hour) or 24 (24 hour). For example, this would set the time format to 24 hour:

                :setTmFmt(24

                In order for the time format to work, you need to set the time using either the setTime( command, or by going into the set clock menu (accessible by pressing ENTER on the 'SET CLOCK' message that is displayed at the bottom of the mode screen). Of course, the time will only show up if the clock is on; if you need to turn the clock on, use the ClockOn command, or scroll down to the 'TURN CLOCK ON' message that is displayed in place of the clock on the mode screen and press ENTER twice.

                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, RandomProductions.

                History

                Calculator OS Version Description
                TI-84+ 0.01 Added
                Property Value
                Hex Value $EF05
                Categories
                Localizations
                • FR: convHeur(

                timeCnv(

                Overview

                Converts seconds to units of time that can be more easily understood for evaluation. The list is in {days,hours,minutes,seconds} format.

                Availability: Token available everywhere.

                Syntax

                timeCnv(seconds)

                Arguments

                NameTypeOptional
                seconds

                Location

                2nd, catalog, timeCnv

                Description

                The timeCnv( command converts seconds into the equivalent days, hours, minutes, and seconds. You just specify a number of seconds (should be a whole number, although a decimal number would work too; the calculator will simply use the integer part and discard the decimal) and the calculator will automatically break the seconds up into the standard parts of time, storing them in list format — {days,hours,minutes,seconds}. You can store this list to a variable for later use, or manipulate it the same way you do with other lists.

                The number of seconds you specify can be as small or large as you want, although the number must be at least zero (in which case, the time list will be all zeroes). At the same time, you will run into the standard number precision problems that plague TI-Basic when specifying an extremely large or small number. Because of this, you should try to use numbers with less than 10 digits. Here is a simple example, where the time is exactly 1 day, 1 hour, 1 minute, and 1 second:

                :timeCnv(90061→L1
:Disp Ans

                The time conversion is 60 seconds for a minute, 3600 (6060) seconds for an hour, and 86400 (6060*24) seconds for a day. Adding these three together plus the one second gives you the value that you see in the example. This is pretty basic math, so it should be easy to understand.

                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Thom M, Xphoenix.

                History

                Calculator OS Version Description
                TI-84+ 0.01 Added
                Property Value
                Hex Value $EF06
                Categories
                Localizations
                • FR: joursem(

                dayOfWk(

                Overview

                Returns an integer from 1 to 7, with each integer representing a day of the week. Use dayOfWk( to determine on which day of the week a particular date would occur. The year must be 4 digits; month and day can be 1 or 2 digits.

                Availability: Token available everywhere.

                Syntax

                dayOfWk(year,month,day)

                Arguments

                NameTypeOptional
                year
                month
                day

                Location

                2nd, catalog, dayOfWk(, 1:Sunday, 2:Monday, 3:Tuesday...

                Description

                dayOfWk(year,month,day) returns an integer from 1 to 7, each representing a separate day of the week. 1 represents Sunday, 2 represents Monday, and so on, with 7 representing Saturday. The date format is different than the normal American format (month/day/year), so be careful to put the arguments in the right order. You can remember this by thinking of the descending lengths of time in each of the arguments.

                :dayOfWk(2007,12,30)

                The above code returns 1, because the 30th of December, 2007, is a Sunday.

                Error Conditions

                • ERR:DOMAIN is thrown if any of the arguments are non-integers, or the date does not exist, such as the 42nd of February. However, the year does not matter (a date that takes place in the year 10000 is valid). However, there are exceptions, even if some dates do exist, this error may still occur. If you attempt to calculate the previous day of a week such as the previous day, the error may still occur.

                See Also

                • Day of Week — routine to calculate the day of the week

                Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, iPhoenixOnTIBD, Myles_Zadok, nap386, Weregoose, Xphoenix.

                History

                Calculator OS Version Description
                TI-84+ 0.01 Added
                Property Value
                Hex Value $EF07
                Categories
                Localizations
                • FR: AffChDt(

                getDtStr(

                Overview

                Returns a string of the current date in the format specified by integer, where:
                1 = M/D/Y2 = D/M/Y3 = Y/M/D

                Availability: Token available everywhere.

                Syntax

                getDtStr(integer)

                Arguments

                NameTypeOptional
                integer

                Location

                2nd, catalog, getDtStr(

                Description

                The getDtStr( command returns the current date of the clock on the TI-84+/SE/CE calculators as a string based on the date format that is specified. There are three different date formats available: 1 (M/D/Y), 2 (D/M/Y), or 3 (Y/M/D). You can store this value to a string variable for later use, or manipulate it the same way you do with other strings. Of course, this command only works if the date format has actually been set, so you should use the setDtFmt( command before using it.

                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583, RandomProductions.

                History

                Calculator OS Version Description
                TI-84+ 0.01 Added
                Property Value
                Hex Value $EF08
                Categories
                Localizations
                • FR: affChHr(

                getTmStr(

                Overview

                Returns a string of the current clock time in the format specified by integer, where:
                12 = 12 hour format24 = 24 hour format

                Availability: Token available everywhere.

                Syntax

                getTmStr(integer)

                Arguments

                NameTypeOptional
                integer

                Location

                2nd, catalog, getTmStr(

                Description

                The getTmStr( command returns the current time of the clock on the TI-84+/SE calculators as a string based on the time format that is specified. There are two different time formats available: 12 (12 hour) or 24 (24 hour). You can store this value to a string variable for later use, or manipulate it the same way you do with other strings. Of course, this command only works if the time format has actually been set, so you should use the setTmFmt( command before using it.

                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, RandomProductions.

                History

                Calculator OS Version Description
                TI-84+ 0.01 Added
                Property Value
                Hex Value $EF09
                Categories
                Localizations
                • FR: affDate

                getDate

                Overview

                Returns a list giving the date according to the current value of the clock. The list is in {year,month,day} format.

                Availability: Token available everywhere.

                Syntax

                getDate

                Location

                2nd, catalog, getDate

                Description

                The getDate command returns the current date that the clock has on the TI-84+/SE/CE calculators in list format — {year, month, day}. You can store this list to a variable for later use, or manipulate it the same way you do with other lists. Of course, this command only works if the date has actually been set, so you should use the setDate( command before using it.

                An interesting note about this command is that you cannot index getDate directly to get individual elements; if you try, each element of the clock is instead multiplied by the number. You may, however, call the command and thus store it in Ans, then retrieve individual elements.

                SCREEN02.BMP

                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Jonathan King, kg583, RandomProductions.

                History

                Calculator OS Version Description
                TI-84+ 0.01 Added
                Property Value
                Hex Value $EF0A
                Categories
                Localizations
                • FR: affHeure

                getTime

                Overview

                Returns a list giving the time according to the current value of the clock. The list is in {hour,minute,second} format. The time is returned in the 24 hour format.

                Availability: Token available everywhere.

                Syntax

                getTime

                Location

                2nd, catalog, getTime

                Description

                The getTime command returns the current time that the clock has on the TI-84+/SE/CE calculators in list format — {hour, minute, second}. You can store this list to a variable for later use, or manipulate it the same way you do with other lists. Of course, this command only works if the time has actually been set, so you should use the setTime( command before using it.

                An interesting note about this command is that you cannot index individual elements directly; if you try, each element of the clock is multiplied by the index. You can, however, call the demand and thus store the result in Ans, and then retrieve the individual elements.

                SCREEN01.JPG

                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Jonathan King, kg583, RandomProductions, Socks.

                History

                Calculator OS Version Description
                TI-84+ 0.01 Added
                Property Value
                Hex Value $EF0B
                Categories
                Localizations
                • FR: actMintr

                startTmr

                Overview

                Starts the clock timer. Store or note the displayed value, and use it as the argument for checkTmr( ) to check the elapsed time.

                Availability: Token available everywhere.

                Syntax

                startTmr

                Location

                2nd, catalog, startTmr

                Description

                The startTmr command is used with the built-in timer that is available on the TI-84+/SE calculators. It is used together with the checkTmr( command to determine how much time has elapsed since the timer was started. An application of these commands is timing different commands or pieces of code, as well as countdowns in games, or a time-based score (such as in Minesweeper).

                To use the timer, you first store startTmr to a variable (usually, a real variable) whenever you want the count to start. Now, whenever you want to check the elapsed time, you can use checkTmr( with the variable from above, giving you the number of seconds that have passed. Using checkTmr( doesn't stop the timer, you can do it as many times as you want to.

                In the case of Minesweeper, for example, you would store startTmr to, for example, T, after setting up and displaying the board, display the result of checkTmr(T) in the game's key-reading loop, and store checkTmr(T) to the player's score if he wins.

                Despite the name of the command, startTmr doesn't start the clock if it's stopped; use ClockOn instead to start the clock.

                Advanced Uses

                To time a command or routine using startTmr and checkTmr(, use the following template:

                :ClockOn
:startTmr→T
:Repeat checkTmr(Ans
:End
:For(n,1,(number)                    //sequence variable n
   (command(s) to be tested)
:End
:checkTmr(T+1)/(number)

                Making (number) higher increases accuracy, but takes longer. Also, make sure not to modify the variables n or T inside the For( loop.

                While this method eliminates human error from counting, it's prone to its own faults. For example, startTmr and checkTmr( always return the time rounded down to a whole second. To take this into account, replace the last line:

                :(checkTmr(T+{1,0})/(number)

                When testing code, be aware that many different things affect the time: the strength of the batteries, the amount of free RAM, and including the closing parenthesis on the For( loop. The last one, in particular, has an impact when using a single-line If statement or one of the [IS>(](IS(.html) and [DS<(](DS(.html) commands on the first line inside a For( loop.

                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Jonathan King, lirtosiast, Xphoenix.

                History

                Calculator OS Version Description
                TI-84+ 0.01 Added
                Property Value
                Hex Value $EF0C
                Categories
                Localizations
                • FR: affFmtDt

                getDtFmt

                Overview

                Returns an integer representing the date format that is currently set on the device.
                1 = M/D/Y2 = D/M/Y3 = Y/M/D

                Availability: Token available everywhere.

                Syntax

                getDtFmt

                Location

                2nd, catalog, getDtFmt

                Description

                The getDtFmt( command returns the current date format of the clock on the TI-84+/SE/CE calculators as an integer. There are three different date formats available: 1 (M/D/Y), 2 (D/M/Y), and 3 (Y/M/D). You can store this value to a variable for later use. Of course, this command only works if the date format has actually been set, so you should use the setDtFmt( command before using it.

                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Jonathan King, kg583, RandomProductions.

                History

                Calculator OS Version Description
                TI-84+ 0.01 Added
                Property Value
                Hex Value $EF0D
                Categories
                Localizations
                • FR: affFmtHr

                getTmFmt

                Overview

                Returns an integer representing the clock time format that is currently set on the device.
                12 = 12 hour format24 = 24 hour format

                Availability: Token available everywhere.

                Syntax

                getTmFmt

                Location

                2nd, catalog, getTmFmt

                Description

                The getTmFmt( command returns the current time format of the clock on the TI-84+/SE/CE calculators as an integer. There are two different time formats available: 12 (12 hour) and 24 (24 hours). You can store this value to a variable for later use. Of course, this command only works if the time format has actually been set, so you should use the setTmFmt( command before using it.

                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583, RandomProductions.

                History

                Calculator OS Version Description
                TI-84+ 0.01 Added
                Property Value
                Hex Value $EF0E
                Categories
                Localizations
                • FR: actHorl

                isClockOn

                Overview

                Identifies if clock is ON or OFF. Returns 1 if the clock is ON. Returns 0 if the clock is OFF.

                Availability: Token available everywhere.

                Syntax

                isClockOn

                Location

                2nd, catalog, isClockOn

                Description

                The isClockOn command returns whether the clock on the TI-84+/SE calculators is on or off. The command will return 1 if the clock is enabled and 0 if it is not. You can store it to a variable for later use, or use it in conditionals and loops as part of the condition. For example, here is how you would check to see if the clock is on:

                :If isClockOn
:Then
  (code if clock is on)
:Else
  (code if clock is off)
:End

                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Jonathan King, kg583, Xphoenix.

                History

                Calculator OS Version Description
                TI-84+ 0.01 Added
                Property Value
                Hex Value $EF0F
                Categories
                Localizations
                • FR: HorlNAff

                ClockOff

                Overview

                Turns off the clock display in the mode screen.

                Availability: Token available everywhere.

                Syntax

                ClockOff

                Location

                2nd, catalog, ClockOff

                Description

                The ClockOff command turns off the clock display at the bottom of the mode screen on the TI-84+/SE calculators. You can turn the clock back on by using the ClockOn command, or by selecting 'TURN CLOCK ON' ,displayed in place of the clock on the mode screen.

                The ClockOff command does not actually turn the clock off. The time can still be accessed through use of the getTime and getDate commands, and all their cousins.

                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Jonathan King, Myles_Zadok.

                History

                Calculator OS Version Description
                TI-84+ 0.01 Added
                Property Value
                Hex Value $EF10
                Categories
                Localizations
                • FR: HorlAff

                ClockOn

                Overview

                Turns on the clock display in the mode screen.

                Availability: Token available everywhere.

                Syntax

                ClockOn

                Location

                2nd, catalog, ClockOn

                Description

                The ClockOn command turns on the clock display at the bottom of the mode screen on the TI-84+/SE calculators. Alternatively, you can scroll down to the 'TURN CLOCK ON' message that is displayed in place of the clock on the mode screen and press ENTER twice. You can turn the clock off by using the ClockOff command.

                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Myles_Zadok.

                History

                Calculator OS Version Description
                TI-84+ 0.01 Added
                Property Value
                Hex Value $EF11
                Categories
                Localizations
                • FR: OuvrirBiblio(

                OpenLib(

                Overview

                Extends TI-Basic. (Not available.)

                Availability: Token only available from within the Basic editor.

                Syntax

                OpenLib(

                Location

                prgm, CTL, J:OpenLib(

                Description

                Together with ExecLib, OpenLib( is used on the TI-84 Plus and TI-84 Plus SE for running routines from a Flash App library. This only works, of course, with libraries that have been specifically written for this purpose. The only such library so far is usb8x, for advanced interfacing with the USB port.

                The following program, which displays the version of usb8x, is an example of how to use OpenLib( and ExecLib:

                :OpenLib(USBDRV8X
:{6
:ExecLib
:Ans(2)+.01Ans(3

                Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, kg583, seb83.

                History

                Calculator OS Version Description
                TI-84+ 0.01 Added
                Property Value
                Hex Value $EF12
                Categories
                Localizations
                • FR: ExécBiblio

                ExecLib

                Overview

                Extends TI-Basic (not available)

                Availability: Token only available from within the Basic editor.

                Syntax

                ExecLib

                Location

                prgm

                Description

                Together with OpenLib(, ExecLib is used on the TI-84 Plus and TI-84 Plus SE for running routines from a Flash App library. This only works, of course, with libraries that have been specifically written for this purpose. The only such library so far is usb8x, for advanced interfacing with the USB port.

                Since ExecLib doesn't have any arguments, it would normally be able to run only one library routine. To get around this, usb8x uses a list passed in Ans as arguments to the command. This is most likely how any future libraries will do it as well.

                The following program, which displays the version of usb8x, is an example of how to use OpenLib( and ExecLib:

                :OpenLib(USBDRV8X
:{6
:ExecLib
:Ans(2)+.01Ans(3

                Download usb8x here. You may also be interested in MSD8x which is a GUI for usb8x.

                Source: parts of this page were written by the following TI|BD contributors: Battlesquid, DarkerLine, GoVegan, Mapar007, Myles_Zadok, seb83.

                History

                Calculator OS Version Description
                TI-84+ 0.01 Added
                Property Value
                Hex Value $EF13
                Categories
                  Localizations
                  • FR: invT(

                  invT(

                  Overview

                  Computes the inverse cumulative student-t probability function specified by degree of freedom, df for a given area under the curve.

                  Availability: Token available everywhere.

                  Syntax

                  invT(area,df)

                  Arguments

                  NameTypeOptional
                  area
                  df

                  Location

                  2nd, distr, DISTR, 4:invT(

                  Description

                  invT( is the inverse of the cumulative Student t distribution function: given a probability p and a specified degrees of freedom v, it will return the number x such that tcdf(E-99,x,v) is equal to p

                  :invT(.95,24
    1.710882023

                  Advanced

                  invT( is meant for use with so-called "one-tailed' tests; for two-tailed tests, the proper expression to use (corresponding to the inverse of tcdf(-x,x,v)) is invT(.5(1+p),v)

                  Formulas

                  Unlike the tpdf( and tcdf( commands, the invT( command does not have a closed-form formula. However, it can be expressed in terms of the inverse incomplete beta function.

                  For one degree of freedom, invT( is expressible in terms of simpler functions:

                  (1) \(\begin{align} \texttt{invT}(p,1)=\tan\left(\pi\left(p-\frac1{2}\right)\right) \end{align}\)

                  Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, jonbush, kg583, Thom M, thornahawk.

                  History

                  Calculator OS Version Description
                  TI-84+ 2.30 Added
                  Property Value
                  Hex Value $EF14
                  Categories
                    Localizations
                    • FR: χ²GOF-Test(

                    χ²GOF-Test(

                    Overview

                    Performs a test to confirm that sample data is from a population that conforms to a specified distribution.
                    Color#: 10 - 24 or color name pasted from [vars] COLOR.

                    Availability: Token only available from within the Basic editor.

                    Syntax

                    χ²GOF-Test(observedlist,expectedlist,df [,drawflag,color#])

                    Arguments

                    NameTypeOptional
                    χ²
                    -
                    observedlistlist
                    expectedlistlist
                    df
                    drawflagYes
                    color#colorNumYes

                    Location

                    stat, TESTS, D:, GOF, Test(

                    Description

                    The χ²GOF-Test( command performs a χ² goodness-of-fit test. Given an expected ideal distribution of a variable across several categories, and a sample from this variable, it tests the hypothesis that the variable actually fits the ideal distribution. As a special case, you could take the ideal distribution to be evenly divided across all categories. Then, the goodness-of-fit test will test the hypothesis that the variable is independent of the category.

                    The command takes three arguments:

                    • An observed list with an element for each category: the element records the number of times this category appeared in the sample.
                    • An expected list with an element for each category: the element records the frequency with which the category was expected to appear.
                    • The degrees of freedom — usually taken to be one less than the number of categories.

                    The output is two-fold:

                    • The test statistic, χ². If the null hypothesis (that the variable fits the distribution) is true, this should be close to 1.
                    • The probability, p, of the observed distribution assuming the null hypothesis. If this value is low (usually, if it's lower than .05, or lower than .01) this is sufficient evidence to reject the null hypothesis, and conclude that the variable fits a different distribution.

                    Sample Problem

                    Working as a sales clerk, you're wondering if the number of customers depends on the day of week. You've taken a count of the number of customers every day for a week: 17 on Monday, 21 on Tuesday, 18 on Wednesday, 10 on Thursday, 24 on Friday, 28 on Saturday, and 24 on Sunday. Store this observed count: {17,21,18,10,24,28,24} to L1.

                    There were a total of sum(L1)=142 customers. So the expected number of customers on each day was 142/7. Store all the expected counts: {142/7,142/7,142/7,142/7,142/7,142/7,142/7} to L2 (as a shortcut, you can store 142/7{1,1,1,1,1,1,1}).

                    Since there are 7 days, there are 6 (one less) degrees of freedom. So the resulting command is χ²GOF-Test(L1,L2,6).

                    The output will give a χ² of 10.32394366, and a p value of 0.1116563376. This is higher than 5%, so the test is not significant on a 95 percent level. It's perfectly possible, in other words, that the number of customers is independent of the day of week.

                    (Note that in this case, if you suspected the number of customers to be higher on weekends, you could use a more sensitive test for only two categories: 2-SampTTest)

                    Advanced Uses

                    The χ²GOF-Test( command is only on TI-84 Plus and newer calculator models. However, it's possible to use the χ²cdf( command to simulate it on the other calculators: see the χ² Goodness-of-fit Test routine.

                    Formulas

                    The formula for calculating the test statistic is as follows (Oi is the observed count of the ith category, and Ei is the expected count):

                    (1) \(\begin{align} \chi_{n-1}^2 = \sum_{i=1}^n \frac{(O_i-E_i)^2}{E_i} \end{align}\)

                    The p-value, then, is the probability that the χ² statistic would be this high, using the χ²cdf( command with the appropriate value for degrees of freedom.

                    Error Conditions

                    • ERR:DIM MISMATCH is thrown if the two lists are of different length.
                    • ERR:DOMAIN is thrown if they only have one element, or if df is not a positive integer.

                    See Also

                    Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Myles_Zadok.

                    History

                    Calculator OS Version Description
                    TI-84+ 2.30 Added
                    Property Value
                    Hex Value $EF15
                    Categories
                      Localizations
                      • FR: LinRegTInt

                      LinRegTInt

                      Overview

                      Performs a linear regression and computes the t confidence interval for the slope coefficient b.

                      Availability: Token only available from within the Basic editor.

                      Syntax

                      LinRegTInt [Xlistname,Ylistname,freqlist,confidence level, regequ]

                      Arguments

                      NameTypeOptional
                      XlistnamelistYes
                      YlistnamelistYes
                      freqlistlistYes
                      confidence levelYes
                      regequYes

                      Location

                      stat, TESTS, G:LinRegTInt

                      Description

                      Like LinReg(ax+b) and similar commands, LinRegTInt finds the best fit line through a set of points. However, LinRegTInt adds another method of checking the quality of the fit, by calculating a t confidence interval for the slope b. If the confidence interval calculated contains zero, the data supplied is insufficient to conclude a linear relation between the variables.

                      To use LinRegTInt, you must first store the points to two lists: one of the x-coordinates and one of the y-coordinates, ordered so that the nth element of one list matches up with the nth element of the other list. L₁ and L₂ are the default lists to use, and the List Editor (STAT > Edit…) is a useful window for entering the points. You do not have to do the regression on L₁ and L₂, but if you don't you'll have to enter the names of the lists after the command.

                      You can attach frequencies to points, for when a point occurs more than once, by supplying an additional argument - the frequency list. This list does not have to contain integer frequencies. If you add a frequency list, you must supply the names of the x-list and y-list as well, even when they are L₁ and L₂.

                      You can supply a confidence level probability as the fourth argument. It should be a real number between zero and one. If not supplied, the default value is .95. (95% confidence level) If you need to specify a different confidence level, you must enter the names of the lists as well, even if they're L₁ and L₂.

                      Finally, you can enter an equation variable (such as Y₁) after the command, so that the line of best fit is stored to this equation automatically. This doesn't require you to supply the names of the lists, but if you do, the equation variable must come last.

                      For example, both

                      :{4,5,6,7,8→L₁
:{1,2,3,3.5,4.5→L₂
:LinRegTInt

                      and

                      :{4,5,6,7,8→X
:{1,2,3,3.5,4.5→Y
:{1,1,1,1,1→FREQ
:LinRegTTest ʟX,ʟY,ʟFREQ,.95,Y₁

                      will give the following output:

                      LinRegTInt
    y=a+bx
    (.69088,1.0091)
    b=.85
    df=3
    s=.158113883
    a=-2.3
    r²=.9897260274
    r=.9948497512

                      (the last two lines will only appear if diagnostics have been turned on - see DiagnosticOn)

                      • The first line shows the confidence interval containing the slope of the fitted line; as mentioned above, if the interval contains 0, it cannot be concluded that the two variables have a linear relationship. Also, the smaller the difference between the two numbers, the more precision that can be attributed to the calculated slope.
                      • df is the degrees of freedom, equal to the number of points minus two.
                      • a and b are the parameters of the equation y=a+bx, the regression line we've calculated
                      • s is the standard error about the line, a measure of the typical size of a residual (the numbers stored in ʟRESID). It is the square root of the sum of squares of the residuals divided by the degrees of freedom. Smaller values indicate that the points tend to be close to the fitted line, while large values indicate scattering.
                      • r² and r are respectively the coefficients of determination and correlation: a value near 1 or -1 for the former, and near 1 for the latter, indicates a good fit.

                      Source: parts of this page were written by the following TI|BD contributors: Mapar007, thornahawk, Timothy Foster.

                      History

                      Calculator OS Version Description
                      TI-84+ 2.30 Added
                      Property Value
                      Hex Value $EF16
                      Categories
                        Localizations
                        • FR: Manual-Fit

                        Manual-Fit

                        Overview

                        Fits a linear equation to a scatter plot with specified color and line style.
                        Color#: 10 - 24 or color name pasted from [vars] COLOR.
                        line style #: 1-4.

                        Availability: Token available everywhere.

                        Syntax

                        Manual-Fit[equname,color#,line style#]

                        Arguments

                        NameTypeOptional
                        equnameYes
                        color#colorNumYes
                        line style#Yes

                        Location

                        stat, CALC, D:Manual-Fit

                        Description

                        This command will allow the user to create a line of best fit according to their judgment. Activate the command by just pasting it on the screen. Then, click on a point for the line to begin followed by an end point. The calculator will then draw your line and display its equation at the top left corner of the screen. You can modify it by selecting the equation part and pressing enter. Input your desired value for the calculator to change it. The equation is stored into Y₁. If you specify what equation you want to store it to, then it will store to that function.

                        :Manual-Fit
(this activates the command and stores to Y₁
:Manual-Fit Y₃
(this stores to Y₃ instead)

                        One note about this is that it only graphs linear models. It is written in the form y=mx+b, and you can modify m or b.
                        Exit out by 2nd QUIT.

                        Advanced Uses

                        This command is able to function in a program, but you cannot modify the values. This is a unique form of gathering user input that stores into the specified Y= function. Of course, this draws a line across the graph screen. You can then convert the function into a different form, like this:

                        :Manual-Fit
:Equ▶String(Y₁,Str1

                        This will turn the equation the user drew into a string which can then be used for output or calculations.

                        Source: parts of this page were written by the following TI|BD contributors: burr, thornahawk, Timothy Foster.

                        History

                        Calculator OS Version Description
                        TI-84+ 0.46 Added
                        Property Value
                        Hex Value $EF17
                        Categories
                          Localizations
                          • FR: ZQuadrant1

                          ZQuadrant1

                          Overview

                          Displays the portion of the graph that is in quadrant 1.

                          Availability: Token available everywhere.

                          Syntax

                          ZQuadrant1

                          Location

                          zoom, ZOOM, A:ZQuadrant1

                          Description

                          ZQuadrant1 was introduced in OS 2.53MP. As it's name might imply, it puts Quadrant I in the viewing window (the upper-left quadrant). Here are the window settings it affects:

                          • Xmin is set to 0 and Xmax is set to 9.4 making each pixel .1 units.
                          • Ymin is set to 0 and Ymax is set to 9.4 (each pixel is 47/310 units)
                          • Xscl and Yscl are set to 1
                          • ΔX is set to .1
                          • ΔY is set to 47/310
                          • Xres is set to 1

                          This command does not seem to work in programs.

                          Source: parts of this page were written by the following TI|BD contributors: burr, Xeda Elnara.

                          History

                          Calculator OS Version Description
                          TI-84+ 0.01 Added
                          Property Value
                          Hex Value $EF18
                          Categories
                            Localizations
                            • FR: ZFrac1⁄2

                            ZFrac1⁄2

                            Overview

                            Sets the window variables so that you can trace in increments of , if possible. Sets TraceStepto and ΔX and ΔYto .

                            Availability: Token available everywhere.

                            Syntax

                            ZFrac1/2

                            Location

                            zoom, ZOOM, B:ZFrac1/2

                            Description

                            ZFrac_X_ refers to a collection of Zoom commands in for the OS 2.53MP and up. The calculator boasts six such commands, each replacing X with a fraction of some sort. The commands all essentially operate in the same manner, so they are all covered here on this page.

                            This command centers the origin of the graph and makes each pixel X units tall and wide where "X" refers to the suffix of the command. For example, ZFrac1/3 makes each pixel a length of and height of 1/3, which means that each square unit would be a 3x3 square of pixels. It also sets Xscale and Yscale to 1.

                            It is useful when the users wants each pixel to be a uniform length and height, though other commands such as ZSquare, ZDecimal, and ZInteger also create a friendly window, and being more compatible, they would be more useful in programming across calculators.

                            The following is a list of the available ZFrac_X_ commands:

                            • ZFrac1/2
                            • ZFrac1/3
                            • ZFrac1/4
                            • ZFrac1/5
                            • ZFrac1/8
                            • ZFrac1/10

                            Source: parts of this page were written by the following TI|BD contributors: Timothy Foster, Xeda Elnara.

                            History

                            Calculator OS Version Description
                            TI-84+ 2.53 Added
                            Property Value
                            Hex Value $EF19
                            Categories
                              Localizations
                              • FR: ZFrac1⁄3

                              ZFrac1⁄3

                              Overview

                              Sets the window variables so that you can trace in increments of , if possible. Sets TraceStepto and ΔX and ΔYto .

                              Availability: Token available everywhere.

                              Syntax

                              ZFrac1/3

                              Location

                              zoom, ZOOM, C:ZFrac1/3

                              Description

                              ZFrac_X_ refers to a collection of Zoom commands in for the OS 2.53MP and up. The calculator boasts six such commands, each replacing X with a fraction of some sort. The commands all essentially operate in the same manner, so they are all covered here on this page.

                              This command centers the origin of the graph and makes each pixel X units tall and wide where "X" refers to the suffix of the command. For example, ZFrac1/3 makes each pixel a length of and height of 1/3, which means that each square unit would be a 3x3 square of pixels. It also sets Xscale and Yscale to 1.

                              It is useful when the users wants each pixel to be a uniform length and height, though other commands such as ZSquare, ZDecimal, and ZInteger also create a friendly window, and being more compatible, they would be more useful in programming across calculators.

                              The following is a list of the available ZFrac_X_ commands:

                              • ZFrac1/2
                              • ZFrac1/3
                              • ZFrac1/4
                              • ZFrac1/5
                              • ZFrac1/8
                              • ZFrac1/10

                              Source: parts of this page were written by the following TI|BD contributors: Timothy Foster, Xeda Elnara.

                              History

                              Calculator OS Version Description
                              TI-84+ 2.53 Added
                              Property Value
                              Hex Value $EF1A
                              Categories
                                Localizations
                                • FR: ZFrac1⁄4

                                ZFrac1⁄4

                                Overview

                                Sets the window variables so that you can trace in increments of , if possible. Sets TraceStepto and ΔX and ΔYto .

                                Availability: Token available everywhere.

                                Syntax

                                ZFrac1/4

                                Location

                                zoom, ZOOM, D:ZFrac1/4

                                Description

                                ZFrac_X_ refers to a collection of Zoom commands in for the OS 2.53MP and up. The calculator boasts six such commands, each replacing X with a fraction of some sort. The commands all essentially operate in the same manner, so they are all covered here on this page.

                                This command centers the origin of the graph and makes each pixel X units tall and wide where "X" refers to the suffix of the command. For example, ZFrac1/3 makes each pixel a length of and height of 1/3, which means that each square unit would be a 3x3 square of pixels. It also sets Xscale and Yscale to 1.

                                It is useful when the users wants each pixel to be a uniform length and height, though other commands such as ZSquare, ZDecimal, and ZInteger also create a friendly window, and being more compatible, they would be more useful in programming across calculators.

                                The following is a list of the available ZFrac_X_ commands:

                                • ZFrac1/2
                                • ZFrac1/3
                                • ZFrac1/4
                                • ZFrac1/5
                                • ZFrac1/8
                                • ZFrac1/10

                                Source: parts of this page were written by the following TI|BD contributors: Timothy Foster, Xeda Elnara.

                                History

                                Calculator OS Version Description
                                TI-84+ 2.53 Added
                                Property Value
                                Hex Value $EF1B
                                Categories
                                  Localizations
                                  • FR: ZFrac1⁄5

                                  ZFrac1⁄5

                                  Overview

                                  Sets the window variables so that you can trace in increments of , if possible. Sets TraceStepto and ΔX and ΔYto .

                                  Availability: Token available everywhere.

                                  Syntax

                                  ZFrac1/5

                                  Location

                                  zoom, ZOOM, E:ZFrac1/5

                                  Description

                                  ZFrac_X_ refers to a collection of Zoom commands in for the OS 2.53MP and up. The calculator boasts six such commands, each replacing X with a fraction of some sort. The commands all essentially operate in the same manner, so they are all covered here on this page.

                                  This command centers the origin of the graph and makes each pixel X units tall and wide where "X" refers to the suffix of the command. For example, ZFrac1/3 makes each pixel a length of and height of 1/3, which means that each square unit would be a 3x3 square of pixels. It also sets Xscale and Yscale to 1.

                                  It is useful when the users wants each pixel to be a uniform length and height, though other commands such as ZSquare, ZDecimal, and ZInteger also create a friendly window, and being more compatible, they would be more useful in programming across calculators.

                                  The following is a list of the available ZFrac_X_ commands:

                                  • ZFrac1/2
                                  • ZFrac1/3
                                  • ZFrac1/4
                                  • ZFrac1/5
                                  • ZFrac1/8
                                  • ZFrac1/10

                                  Source: parts of this page were written by the following TI|BD contributors: Timothy Foster, Xeda Elnara.

                                  History

                                  Calculator OS Version Description
                                  TI-84+ 2.53 Added
                                  Property Value
                                  Hex Value $EF1C
                                  Categories
                                    Localizations
                                    • FR: ZFrac1⁄8

                                    ZFrac1⁄8

                                    Overview

                                    Sets the window variables so that you can trace in increments of , if possible. Sets TraceStepto and ΔX and ΔYto .

                                    Availability: Token available everywhere.

                                    Syntax

                                    ZFrac1/8

                                    Location

                                    zoom, ZOOM, F:ZFrac1/8

                                    Description

                                    ZFrac_X_ refers to a collection of Zoom commands in for the OS 2.53MP and up. The calculator boasts six such commands, each replacing X with a fraction of some sort. The commands all essentially operate in the same manner, so they are all covered here on this page.

                                    This command centers the origin of the graph and makes each pixel X units tall and wide where "X" refers to the suffix of the command. For example, ZFrac1/3 makes each pixel a length of and height of 1/3, which means that each square unit would be a 3x3 square of pixels. It also sets Xscale and Yscale to 1.

                                    It is useful when the users wants each pixel to be a uniform length and height, though other commands such as ZSquare, ZDecimal, and ZInteger also create a friendly window, and being more compatible, they would be more useful in programming across calculators.

                                    The following is a list of the available ZFrac_X_ commands:

                                    • ZFrac1/2
                                    • ZFrac1/3
                                    • ZFrac1/4
                                    • ZFrac1/5
                                    • ZFrac1/8
                                    • ZFrac1/10

                                    Source: parts of this page were written by the following TI|BD contributors: Timothy Foster, Xeda Elnara.

                                    History

                                    Calculator OS Version Description
                                    TI-84+ 2.53 Added
                                    Property Value
                                    Hex Value $EF1D
                                    Categories
                                      Localizations
                                      • FR: ZFrac1⁄10

                                      ZFrac1⁄10

                                      Overview

                                      Sets the window variables so that you can trace in increments of , if possible. Sets TraceStepto and ΔX and ΔYto .

                                      Availability: Token available everywhere.

                                      Syntax

                                      ZFrac1/10

                                      Location

                                      zoom, ZOOM, G:ZFrac1/10

                                      Description

                                      ZFrac_X_ refers to a collection of Zoom commands in for the OS 2.53MP and up. The calculator boasts six such commands, each replacing X with a fraction of some sort. The commands all essentially operate in the same manner, so they are all covered here on this page.

                                      This command centers the origin of the graph and makes each pixel X units tall and wide where "X" refers to the suffix of the command. For example, ZFrac1/3 makes each pixel a length of and height of 1/3, which means that each square unit would be a 3x3 square of pixels. It also sets Xscale and Yscale to 1.

                                      It is useful when the users wants each pixel to be a uniform length and height, though other commands such as ZSquare, ZDecimal, and ZInteger also create a friendly window, and being more compatible, they would be more useful in programming across calculators.

                                      The following is a list of the available ZFrac_X_ commands:

                                      • ZFrac1/2
                                      • ZFrac1/3
                                      • ZFrac1/4
                                      • ZFrac1/5
                                      • ZFrac1/8
                                      • ZFrac1/10

                                      Source: parts of this page were written by the following TI|BD contributors: Timothy Foster, Xeda Elnara.

                                      History

                                      Calculator OS Version Description
                                      TI-84+ 2.53 Added
                                      Property Value
                                      Hex Value $EF1E
                                      Categories
                                      Localizations
                                      • FR: ⬚

                                      ⬚

                                      Overview

                                      Syntax

                                      ⬚

                                      Description

                                      Examples

                                      Explanation 1

                                      code 1

                                      Explanation 2

                                      code 2

                                      Error Conditions

                                      Advanced Notes

                                      History

                                      Calculator OS Version Description
                                      TI-84+ 2.53 Added
                                      Property Value
                                      Hex Value $EF2E
                                      Categories
                                      Localizations
                                      • FR: ⁄

                                      ⁄

                                      Overview

                                      Syntax

                                      ⁄

                                      Description

                                      Examples

                                      Explanation 1

                                      code 1

                                      Explanation 2

                                      code 2

                                      Error Conditions

                                      Advanced Notes

                                      History

                                      Calculator OS Version Description
                                      TI-84+ 2.53 Added
                                      Property Value
                                      Hex Value $EF2F
                                      Categories
                                      Localizations
                                      • FR: ᵤ

                                      ᵤ

                                      Overview

                                      Syntax

                                      ᵤ

                                      Description

                                      Examples

                                      Explanation 1

                                      code 1

                                      Explanation 2

                                      code 2

                                      Error Conditions

                                      Advanced Notes

                                      History

                                      Calculator OS Version Description
                                      TI-84+ 2.53 Added
                                      Property Value
                                      Hex Value $EF30
                                      Categories
                                        Localizations
                                        • FR: ►n⁄d◄►Un⁄d

                                        ►n⁄d◄►Un⁄d

                                        Overview

                                        Converts the results from a fraction to mixed number or from a mixed number to a fraction, if applicable.

                                        Availability: Token available everywhere.

                                        Syntax

                                        ►n/d ◄►Un/d

                                        Arguments

                                        NameTypeOptional
                                        ◄►

                                        Location

                                        alpha, F1, 3:, n/d, Un/d

                                        Description

                                        n/d_Un/d is the command for switching between an improper fraction and a mixed number.
                                        It is accessible by pressing ALPHA then Y= then 3.

                                        Source: parts of this page were written by the following TI|BD contributors: ccrh2009.

                                        History

                                        Calculator OS Version Description
                                        TI-84+ 2.53 Added
                                        Property Value
                                        Hex Value $EF31
                                        Categories
                                          Localizations
                                          • FR: ►F◄►D

                                          ►F◄►D

                                          Overview

                                          Converts an answer from a fraction to a decimal or from a decimal to a fraction. Fraction and or decimal may be an approximation.

                                          Availability: Token available everywhere.

                                          Syntax

                                          ►F ◄►D

                                          Arguments

                                          NameTypeOptional
                                          ◄►

                                          Location

                                          alpha, F1, 4:

                                          Description

                                          The ►F◄►D command is used to convert a number from fraction form to decimal form, or vice versa. Regardless of what form the given number is, this command is meant to automatically determine the form so that it returns the other. It is in essence a combination of the ►Frac and ►Dec commands, applying ►Frac if the input is in decimal form and ►Dec if it is a fraction.

                                          7.5►F◄ ►D
        15/2
Ans►F◄ ►D
        7.5

                                          Source: parts of this page were written by the following TI|BD contributors: Battlesquid, burr, ccrh2009, kg583, Timothy Foster.

                                          History

                                          Calculator OS Version Description
                                          TI-84+ 2.53 Added
                                          Property Value
                                          Hex Value $EF32
                                          Categories
                                            Localizations
                                            • FR: remainder(

                                            remainder(

                                            Overview

                                            Reports the remainder as a whole number from a division of two whole numbers where the divisor is not zero.

                                            Availability: Token available everywhere.

                                            Syntax

                                            remainder(dividend, divisor)

                                            Arguments

                                            NameTypeOptional
                                            dividend
                                            divisor

                                            Location

                                            math, NUM, 0:remainder(

                                            Overview

                                            Reports the remainder as a whole number from a division of two lists where the divisor is not zero.

                                            Availability: Token available everywhere.

                                            Syntax

                                            remainder(list, divisor)

                                            Arguments

                                            NameTypeOptional
                                            listlist
                                            divisor

                                            Location

                                            math, NUM, 0:remainder(

                                            Overview

                                            Reports the remainder as a whole number from a division of two whole numbers where the divisor is a list.

                                            Availability: Token available everywhere.

                                            Syntax

                                            remainder(dividend, list)

                                            Arguments

                                            NameTypeOptional
                                            dividend
                                            listlist

                                            Location

                                            math, NUM, 0:remainder(

                                            Overview

                                            Reports the remainder as a whole number from a division of two lists.

                                            Availability: Token available everywhere.

                                            Syntax

                                            remainder(list, list)

                                            Arguments

                                            NameTypeOptional
                                            listlist
                                            listlist

                                            Location

                                            math, NUM, 0:remainder(

                                            Description

                                            The remainder( function divides the first number given by the second number, and returns the remainder similar to the modulus. This command is only available if you have the TI-84+/SE and the new 2.53 MP operating system on your calculator. This command can be used both on the Home screen and when programming.

                                            See the code segment below for an example:

                                            remainder(30,7)
               2

                                            This returns a value of 2 because 30 divided by 7 has a remainder of 2.

                                            The first input must be an integer in the range 0 to 1012 and the second must be an integer in the range 1 to 1012 (since division by zero is not allowed).

                                            Compatibility

                                            As said earlier, this command only works on a TI-84+ Silver Edition with the 2.53 MP OS, so this will not work on earlier OSes. To avoid non-portability, use the following code.

                                            BfPart(A/B

instead of

remainder(A,B

                                            fPart( is a command that works in more OSes and more models. They also are the same size (5 bytes), as long as B is one byte.

                                            There is one difference: remainder( is guaranteed to return the correct answer for inputs in its accepted domain, and if you enter numbers that are too large, it will throw an error. The method with fPart(, on the other hand, will work for numbers of any size that does not actually cause an overflow - but when the numbers get too large, it will give the wrong answer. Compare:

                                            remainder(18!,19
           Error
19fPart(18!/19
               0

                                            Here, the remainder( command fails because the input is out of range.. The fPart( method returns an answer, but it is wrong: 18! is not divisible by 19, because 18! is the product of the integers 1 through 18, and none of them are divisible by the prime number 19. When using fPart( as a substitute for remainder(, make sure that the inputs are within the proper range.

                                            Error Conditions

                                            • ERR:DIVIDE BY 0 occurs if the divisor is zero.
                                            • ERR:DOMAIN occurs if the divisor or dividend is out of range: only integers between 0 and 1E12 are allowed.
                                            • ERR:SYNTAX occurs if the divisor or dividend is a symbol, or character or non-real number
                                            • ERR:DATA TYPE occurs if the divisor or dividend is not a number, (i.e. text)

                                            Source: parts of this page were written by the following TI|BD contributors: 12Me21, DarkerLine, Deflect, kg583, Kydapoot, Michael2_3B, Silver Phantom, sonic65101, Timothy Foster, tyler999.

                                            History

                                            Calculator OS Version Description
                                            TI-84+ 2.53 Added
                                            Property Value
                                            Hex Value $EF33
                                            Categories
                                              Localizations
                                              • FR: Σ(

                                              Σ(

                                              Overview

                                              Classic command as shown.
                                              In MathPrint™ the summation entry template displays and returns the sum of elements of list from start to end,wherestart<=end.

                                              Availability: Token available everywhere.

                                              Syntax

                                              Σ(expression[,start,end])

                                              Arguments

                                              NameTypeOptional
                                              expressionexpression
                                              startYes
                                              endYes

                                              Location

                                              math

                                              Description

                                              Examples

                                              Explanation 1

                                              code 1

                                              Explanation 2

                                              code 2

                                              Error Conditions

                                              Advanced Notes

                                              History

                                              Calculator OS Version Description
                                              TI-84+ 2.53 Added
                                              Property Value
                                              Hex Value $EF34
                                              Categories
                                                Localizations
                                                • FR: logBASE(

                                                logBASE(

                                                Overview

                                                Returns the logarithm of a specifed value determined from a specified base: logBASE(value, base).

                                                Availability: Token available everywhere.

                                                Syntax

                                                logBASE(value, base)

                                                Arguments

                                                NameTypeOptional
                                                value
                                                base

                                                Location

                                                math

                                                Description

                                                The logBASE( command is a visual upgrade to the log( command to compute logarithms in any base b. That is, the command finds the exponent that base b must be raised to obtain the given value.

                                                This command can be used on both the home screen and while programming. If you are using CLASSIC mode, the command appears as:

                                                logBASE(8,2)
            3

                                                But in MATHPRINT mode, this is improved to:

                                                log2(8)
                                                            3

                                                Formulas

                                                The log in base b can also be found using the ln( or log( commands. This can be done indirectly using the change-of-base formula:

                                                (1) \(\begin{align} \log_bx = {\ln x \over \ln b} = {\log x \over \log b} \end{align}\)

                                                Or directly, using the optional second argument of log(:

                                                logBASE(X,B

can be

log(X,B

                                                The logBASE( command costs one extra byte compared to log(, providing only a visual improvement over its counterpart in MATHPRINT mode. The log( command is also compatible with older OS's, although its second argument is not. Both logBASE( and the second argument of log( are disabled in exam mode.

                                                Error Conditions

                                                Source: parts of this page were written by the following TI|BD contributors: Deflect, kg583, Myles_Zadok, Timothy Foster.

                                                History

                                                Calculator OS Version Description
                                                TI-84+ 2.53 Added
                                                Property Value
                                                Hex Value $EF35
                                                Categories
                                                  Localizations
                                                  • FR: randIntNoRep(

                                                  randIntNoRep(

                                                  Overview

                                                  Returns a random ordered list of integers from a lower integer to an upper integer which may include the lower integer and upper integer. If the optional argument numelements is specified, the first numelements are listed. The first numelements term in the list of random integers are displayed.

                                                  Availability: Token available everywhere.

                                                  Syntax

                                                  randIntNoRep(lowerint,upperint [,numelements])

                                                  Arguments

                                                  NameTypeOptional
                                                  lowerint
                                                  upperint
                                                  numelementsYes

                                                  Location

                                                  math, PRB, 8:randIntNoRep(

                                                  Description

                                                  randIntNoRep( is used when you need to create a list of numbers in random order in which no integer is repeated. This command is useful for things such as simulating decks of cards. Commonly, before this command was introduced, the following code would shuffle a deck:

                                                  rand(52→L₂
seq(X,X,0,51→L₁
SortA(L₂,L₁

                                                  This result can now be achieved with the following code:

                                                  randIntNoRep(0,51→L₁

                                                  Advanced Uses

                                                  seed→rand affects the output of randIntNoRep(

                                                  What this does is quite simple. When you seed rand, then the next time you use randIntNoRep(, you will get a result that will be fairly random, but the same on all calculators. This allows several things to be possible, including password protection and encryption. For example, if you were to use the following code, you could encrypt and decrypt messages only if you use the same encryption value. In this example, Str1 contains the message:

                                                  Decode:

                                                  "ABCDEFGHIJKLMNOPQRSTUVWXYZ .!,0123456789→Str2
Input "CODE:",A
A→rand
randIntNoRep(1,length(Str2→L1
length(Str1→B
".
For(A,1,B
Ans+sub(Str2,sum(cumSum(L1=inString(Str2,sub(Str1,A,1)))),1
End
sub(Ans,2,B

                                                  Encode:

                                                  "ABCDEFGHIJKLMNOPQRSTUVWXYZ .!,0123456789→Str2
Input "CODE:",A
A→rand
length(Str2→C
randIntNoRep(1,Ans→L1
length(Str1→B
".
For(A,1,B
Ans+sub(Str2,L1(C+1-inString(Str2,sub(Str1,A,1))),1
End
sub(Ans,2,B

                                                  The output strings are in Ans

                                                  Source: parts of this page were written by the following TI|BD contributors: burr, MrTanookiMario, Timothy Foster, Xeda Elnara.

                                                  History

                                                  Calculator OS Version Description
                                                  TI-84+ 2.53 Added
                                                  Property Value
                                                  Hex Value $EF36
                                                  Categories
                                                  Localizations
                                                  • FR: CLASSIC

                                                  CLASSIC

                                                  Overview

                                                  Comment:Alias / Old

                                                  Syntax

                                                  CLASSIC

                                                  Description

                                                  Examples

                                                  Explanation 1

                                                  code 1

                                                  Explanation 2

                                                  code 2

                                                  Error Conditions

                                                  Advanced Notes

                                                  History

                                                  Calculator OS Version Description
                                                  Property Value
                                                  Hex Value $EF37
                                                  Categories
                                                    Localizations
                                                    • FR: MATHPRINT

                                                    MATHPRINT

                                                    Overview

                                                    Displays most entries and answers the way they are displayed in textbooks, such as .

                                                    Availability: Token available everywhere.

                                                    Syntax

                                                    MATHPRINT

                                                    Location

                                                    mode

                                                    Description

                                                    MATHPRINT will put the calculator into Mathprint mode as opposed to Classic mode. In MathPrint mode, enhanced homescreen input formatting is available. The Classic mode will make the calculator display everything as a calculator of lower OS would, including input. For instance, rather than superscripting exponents as Mathprint mode would, Classic mode uses the simple caret syntax (^).

                                                    Mathprint mode:
                                                    24
                                                         16

                                                    Classic mode:
                                                    2^4
                                                         16

                                                    When in Mathprint mode, text and numbers are displayed much slower than classic on the home screen and the function menus load slower. This can be inconvenient in games that use the home screen, but can also make solving equations that involve fractions and exponents easier as the numbers are in their correct positions and are the appropriate size.

                                                    Source: parts of this page were written by the following TI|BD contributors: burr, jonbush, Kydapoot.

                                                    History

                                                    Calculator OS Version Description
                                                    TI-84+ 2.53 Added
                                                    Property Value
                                                    Hex Value $EF38
                                                    Categories
                                                      Localizations
                                                      • FR: CLASSIC

                                                      CLASSIC

                                                      Overview

                                                      Displays inputs and outputs on a single line, such as 1/2+3/4.

                                                      Availability: Token available everywhere.

                                                      Syntax

                                                      CLASSIC

                                                      Location

                                                      mode, CLASSIC

                                                      Description

                                                      CLASSIC will put the calculator into Classic mode as opposed to MathPrint mode. The Classic mode will make the calculator display everything as pre-MathPrint OS would, including input. For instance, rather than superscripting exponents as MathPrint mode would, Classic mode uses the simple caret syntax (^).

                                                      MathPrint mode:
                                                      24
                                                           16

                                                      Classic mode:
                                                      2^4
                                                           16

                                                      Advanced Uses

                                                      When in Classic mode, text and numbers are displayed much faster on the home screen and the function menus load faster. This can be useful in games that use the home screen, or just with calculations in general.

                                                      Source: parts of this page were written by the following TI|BD contributors: ccrh2009, jonbush, Kydapoot, lirtosiast, Myles_Zadok, Timothy Foster.

                                                      History

                                                      Calculator OS Version Description
                                                      TI-84+ 2.53 Added
                                                      Property Value
                                                      Hex Value $EF39
                                                      Categories
                                                        Localizations
                                                        • FR: n⁄d

                                                        n⁄d

                                                        Overview

                                                        Displays results as a simple fraction.

                                                        Availability: Token available everywhere.

                                                        Syntax

                                                        n/d

                                                        Location

                                                        alpha, F1, 1:n/d

                                                        Description

                                                        n/d is the template for entering a simple fraction.
                                                        n/d is accessible by pressing ALPHA then Y= then enter.

                                                        Source: parts of this page were written by the following TI|BD contributors: ccrh2009.

                                                        History

                                                        Calculator OS Version Description
                                                        TI-84+ 2.53 Added
                                                        Property Value
                                                        Hex Value $EF3A
                                                        Categories
                                                          Localizations
                                                          • FR: Un⁄d

                                                          Un⁄d

                                                          Overview

                                                          Displays results as a mixed number, if applicable.

                                                          Availability: Token available everywhere.

                                                          Syntax

                                                          Un/d

                                                          Location

                                                          math, NUMC: Un/d

                                                          Description

                                                          Un/d is a template that allows you to input a fraction with a whole number in front of it.
                                                          Un/d is accessible from most screens by pressing ALPHA and Y= then 2.
                                                          What this command does is that it adds the whole number to the fraction. It does not calculate a product but instead it calculates an addition.

                                                          Source: parts of this page were written by the following TI|BD contributors: burr, ccrh2009, DracoMhuuh.

                                                          History

                                                          Calculator OS Version Description
                                                          TI-84+ 2.53 Added
                                                          Property Value
                                                          Hex Value $EF3B
                                                          Categories
                                                            Localizations
                                                            • FR: AUTO

                                                            AUTO

                                                            Overview

                                                            Displays answers in a similar format as the input.

                                                            Availability: Token available everywhere.

                                                            Syntax

                                                            AUTO

                                                            Location

                                                            mode, Answers: AUTO

                                                            Description

                                                            Examples

                                                            Explanation 1

                                                            code 1

                                                            Explanation 2

                                                            code 2

                                                            Error Conditions

                                                            Advanced Notes

                                                            History

                                                            Calculator OS Version Description
                                                            TI-84+ 2.53 Added
                                                            Property Value
                                                            Hex Value $EF3C
                                                            Categories
                                                              Localizations
                                                              • FR: DEC

                                                              DEC

                                                              Overview

                                                              Displays answers as integers or decimal numbers.

                                                              Availability: Token available everywhere.

                                                              Syntax

                                                              DEC

                                                              Location

                                                              mode, Answers: DEC

                                                              Description

                                                              Examples

                                                              Explanation 1

                                                              code 1

                                                              Explanation 2

                                                              code 2

                                                              Error Conditions

                                                              Advanced Notes

                                                              History

                                                              Calculator OS Version Description
                                                              TI-84+ 2.53 Added
                                                              Property Value
                                                              Hex Value $EF3D
                                                              Categories
                                                              Localizations
                                                              • FR: FRAC-APPROX

                                                              FRAC-APPROX

                                                              Overview

                                                              Syntax

                                                              FRAC-APPROX

                                                              Description

                                                              Examples

                                                              Explanation 1

                                                              code 1

                                                              Explanation 2

                                                              code 2

                                                              Error Conditions

                                                              Advanced Notes

                                                              History

                                                              Calculator OS Version Description
                                                              TI-84+ 2.53 FRAC added
                                                              TI-84+CSE 4.0 Renamed FRAC to FRAC-APPROX
                                                              Property Value
                                                              Hex Value $EF3F
                                                              Categories
                                                                Localizations
                                                                • FR: STATWIZARD ON

                                                                STATWIZARD ON

                                                                Overview

                                                                Enables wizard syntax help for statistical commands, distributions, and seq(.

                                                                Availability: Token available everywhere.

                                                                Syntax

                                                                STATWIZARD ON

                                                                Location

                                                                2nd, catalog, STATWIZARD ON(

                                                                Description

                                                                Examples

                                                                Explanation 1

                                                                code 1

                                                                Explanation 2

                                                                code 2

                                                                Error Conditions

                                                                Advanced Notes

                                                                History

                                                                Calculator OS Version Description
                                                                TI-84+ 2.55 Added
                                                                Property Value
                                                                Hex Value $EF40
                                                                Categories
                                                                  Localizations
                                                                  • FR: STATWIZARD OFF

                                                                  STATWIZARD OFF

                                                                  Overview

                                                                  Disables wizard syntax help for statistical commands, distributions, and seq(.

                                                                  Availability: Token available everywhere.

                                                                  Syntax

                                                                  STATWIZARD OFF

                                                                  Location

                                                                  2nd, catalog, STATWIZARD OFF

                                                                  Description

                                                                  Examples

                                                                  Explanation 1

                                                                  code 1

                                                                  Explanation 2

                                                                  code 2

                                                                  Error Conditions

                                                                  Advanced Notes

                                                                  History

                                                                  Calculator OS Version Description
                                                                  TI-84+ 2.55 Added
                                                                  Property Value
                                                                  Hex Value $EF41
                                                                  Categories
                                                                  Localizations
                                                                  • FR: BLEU

                                                                  BLUE

                                                                  Overview

                                                                  Availability: Token available everywhere.

                                                                  Syntax

                                                                  BLUE

                                                                  Description

                                                                  Examples

                                                                  Explanation 1

                                                                  code 1

                                                                  Explanation 2

                                                                  code 2

                                                                  Error Conditions

                                                                  Advanced Notes

                                                                  History

                                                                  Calculator OS Version Description
                                                                  TI-84+CSE 4.0 Added
                                                                  Property Value
                                                                  Hex Value $EF42
                                                                  Categories
                                                                  Localizations
                                                                  • FR: ROUGE

                                                                  RED

                                                                  Overview

                                                                  Availability: Token available everywhere.

                                                                  Syntax

                                                                  RED

                                                                  Description

                                                                  Examples

                                                                  Explanation 1

                                                                  code 1

                                                                  Explanation 2

                                                                  code 2

                                                                  Error Conditions

                                                                  Advanced Notes

                                                                  History

                                                                  Calculator OS Version Description
                                                                  TI-84+CSE 4.0 Added
                                                                  Property Value
                                                                  Hex Value $EF43
                                                                  Categories
                                                                  Localizations
                                                                  • FR: NOIR

                                                                  BLACK

                                                                  Overview

                                                                  Availability: Token available everywhere.

                                                                  Syntax

                                                                  BLACK

                                                                  Description

                                                                  Examples

                                                                  Explanation 1

                                                                  code 1

                                                                  Explanation 2

                                                                  code 2

                                                                  Error Conditions

                                                                  Advanced Notes

                                                                  History

                                                                  Calculator OS Version Description
                                                                  TI-84+CSE 4.0 Added
                                                                  Property Value
                                                                  Hex Value $EF44
                                                                  Categories
                                                                  Localizations
                                                                  • FR: MAGENTA

                                                                  MAGENTA

                                                                  Overview

                                                                  Availability: Token available everywhere.

                                                                  Syntax

                                                                  MAGENTA

                                                                  Description

                                                                  Examples

                                                                  Explanation 1

                                                                  code 1

                                                                  Explanation 2

                                                                  code 2

                                                                  Error Conditions

                                                                  Advanced Notes

                                                                  History

                                                                  Calculator OS Version Description
                                                                  TI-84+CSE 4.0 Added
                                                                  Property Value
                                                                  Hex Value $EF45
                                                                  Categories
                                                                  Localizations
                                                                  • FR: VERT

                                                                  GREEN

                                                                  Overview

                                                                  Availability: Token available everywhere.

                                                                  Syntax

                                                                  GREEN

                                                                  Description

                                                                  Examples

                                                                  Explanation 1

                                                                  code 1

                                                                  Explanation 2

                                                                  code 2

                                                                  Error Conditions

                                                                  Advanced Notes

                                                                  History

                                                                  Calculator OS Version Description
                                                                  TI-84+CSE 4.0 Added
                                                                  Property Value
                                                                  Hex Value $EF46
                                                                  Categories
                                                                  Localizations
                                                                  • FR: ORANGE

                                                                  ORANGE

                                                                  Overview

                                                                  Availability: Token available everywhere.

                                                                  Syntax

                                                                  ORANGE

                                                                  Description

                                                                  Examples

                                                                  Explanation 1

                                                                  code 1

                                                                  Explanation 2

                                                                  code 2

                                                                  Error Conditions

                                                                  Advanced Notes

                                                                  History

                                                                  Calculator OS Version Description
                                                                  TI-84+CSE 4.0 Added
                                                                  Property Value
                                                                  Hex Value $EF47
                                                                  Categories
                                                                  Localizations
                                                                  • FR: MARRON

                                                                  BROWN

                                                                  Overview

                                                                  Availability: Token available everywhere.

                                                                  Syntax

                                                                  BROWN

                                                                  Description

                                                                  Examples

                                                                  Explanation 1

                                                                  code 1

                                                                  Explanation 2

                                                                  code 2

                                                                  Error Conditions

                                                                  Advanced Notes

                                                                  History

                                                                  Calculator OS Version Description
                                                                  TI-84+CSE 4.0 Added
                                                                  Property Value
                                                                  Hex Value $EF48
                                                                  Categories
                                                                  Localizations
                                                                  • FR: BLEU MRN

                                                                  NAVY

                                                                  Overview

                                                                  Availability: Token available everywhere.

                                                                  Syntax

                                                                  NAVY

                                                                  Description

                                                                  Examples

                                                                  Explanation 1

                                                                  code 1

                                                                  Explanation 2

                                                                  code 2

                                                                  Error Conditions

                                                                  Advanced Notes

                                                                  History

                                                                  Calculator OS Version Description
                                                                  TI-84+CSE 4.0 Added
                                                                  Property Value
                                                                  Hex Value $EF49
                                                                  Categories
                                                                  Localizations
                                                                  • FR: BLEU CLR

                                                                  LTBLUE

                                                                  Overview

                                                                  Availability: Token available everywhere.

                                                                  Syntax

                                                                  LTBLUE

                                                                  Description

                                                                  Examples

                                                                  Explanation 1

                                                                  code 1

                                                                  Explanation 2

                                                                  code 2

                                                                  Error Conditions

                                                                  Advanced Notes

                                                                  History

                                                                  Calculator OS Version Description
                                                                  TI-84+CSE 4.0 Added
                                                                  Property Value
                                                                  Hex Value $EF4A
                                                                  Categories
                                                                  Localizations
                                                                  • FR: JAUNE

                                                                  YELLOW

                                                                  Overview

                                                                  Availability: Token available everywhere.

                                                                  Syntax

                                                                  YELLOW

                                                                  Description

                                                                  Examples

                                                                  Explanation 1

                                                                  code 1

                                                                  Explanation 2

                                                                  code 2

                                                                  Error Conditions

                                                                  Advanced Notes

                                                                  History

                                                                  Calculator OS Version Description
                                                                  TI-84+CSE 4.0 Added
                                                                  Property Value
                                                                  Hex Value $EF4B
                                                                  Categories
                                                                  Localizations
                                                                  • FR: BLANC

                                                                  WHITE

                                                                  Overview

                                                                  Availability: Token available everywhere.

                                                                  Syntax

                                                                  WHITE

                                                                  Description

                                                                  Examples

                                                                  Explanation 1

                                                                  code 1

                                                                  Explanation 2

                                                                  code 2

                                                                  Error Conditions

                                                                  Advanced Notes

                                                                  History

                                                                  Calculator OS Version Description
                                                                  TI-84+CSE 4.0 Added
                                                                  Property Value
                                                                  Hex Value $EF4C
                                                                  Categories
                                                                  Localizations
                                                                  • FR: GRIS CLR

                                                                  LTGRAY

                                                                  Overview

                                                                  Availability: Token available everywhere.

                                                                  Syntax

                                                                  LTGRAY

                                                                  Description

                                                                  Examples

                                                                  Explanation 1

                                                                  code 1

                                                                  Explanation 2

                                                                  code 2

                                                                  Error Conditions

                                                                  Advanced Notes

                                                                  History

                                                                  Calculator OS Version Description
                                                                  TI-84+CSE 4.0 Added
                                                                  Property Value
                                                                  Hex Value $EF4D
                                                                  Categories
                                                                  Localizations
                                                                  • FR: GRIS MOY

                                                                  MEDGRAY

                                                                  Overview

                                                                  Availability: Token available everywhere.

                                                                  Syntax

                                                                  MEDGRAY

                                                                  Description

                                                                  Examples

                                                                  Explanation 1

                                                                  code 1

                                                                  Explanation 2

                                                                  code 2

                                                                  Error Conditions

                                                                  Advanced Notes

                                                                  History

                                                                  Calculator OS Version Description
                                                                  TI-84+CSE 4.0 Added
                                                                  Property Value
                                                                  Hex Value $EF4E
                                                                  Categories
                                                                  Localizations
                                                                  • FR: GRIS

                                                                  GRAY

                                                                  Overview

                                                                  Availability: Token available everywhere.

                                                                  Syntax

                                                                  GRAY

                                                                  Description

                                                                  Examples

                                                                  Explanation 1

                                                                  code 1

                                                                  Explanation 2

                                                                  code 2

                                                                  Error Conditions

                                                                  Advanced Notes

                                                                  History

                                                                  Calculator OS Version Description
                                                                  TI-84+CSE 4.0 Added
                                                                  Property Value
                                                                  Hex Value $EF4F
                                                                  Categories
                                                                  Localizations
                                                                  • FR: GRIS FON

                                                                  DARKGRAY

                                                                  Overview

                                                                  Availability: Token available everywhere.

                                                                  Syntax

                                                                  DARKGRAY

                                                                  Description

                                                                  Examples

                                                                  Explanation 1

                                                                  code 1

                                                                  Explanation 2

                                                                  code 2

                                                                  Error Conditions

                                                                  Advanced Notes

                                                                  History

                                                                  Calculator OS Version Description
                                                                  TI-84+CSE 4.0 Added
                                                                  Property Value
                                                                  Hex Value $EF50
                                                                  Categories
                                                                  Localizations
                                                                  • FR: Image1

                                                                  Image1

                                                                  Overview

                                                                  Availability: Token available everywhere.

                                                                  Syntax

                                                                  Image1

                                                                  Description

                                                                  Examples

                                                                  Explanation 1

                                                                  code 1

                                                                  Explanation 2

                                                                  code 2

                                                                  Error Conditions

                                                                  Advanced Notes

                                                                  History

                                                                  Calculator OS Version Description
                                                                  TI-84+CSE 4.0 Added
                                                                  Property Value
                                                                  Hex Value $EF51
                                                                  Categories
                                                                  Localizations
                                                                  • FR: Image2

                                                                  Image2

                                                                  Overview

                                                                  Availability: Token available everywhere.

                                                                  Syntax

                                                                  Image2

                                                                  Description

                                                                  Examples

                                                                  Explanation 1

                                                                  code 1

                                                                  Explanation 2

                                                                  code 2

                                                                  Error Conditions

                                                                  Advanced Notes

                                                                  History

                                                                  Calculator OS Version Description
                                                                  TI-84+CSE 4.0 Added
                                                                  Property Value
                                                                  Hex Value $EF52
                                                                  Categories
                                                                  Localizations
                                                                  • FR: Image3

                                                                  Image3

                                                                  Overview

                                                                  Availability: Token available everywhere.

                                                                  Syntax

                                                                  Image3

                                                                  Description

                                                                  Examples

                                                                  Explanation 1

                                                                  code 1

                                                                  Explanation 2

                                                                  code 2

                                                                  Error Conditions

                                                                  Advanced Notes

                                                                  History

                                                                  Calculator OS Version Description
                                                                  TI-84+CSE 4.0 Added
                                                                  Property Value
                                                                  Hex Value $EF53
                                                                  Categories
                                                                  Localizations
                                                                  • FR: Image4

                                                                  Image4

                                                                  Overview

                                                                  Availability: Token available everywhere.

                                                                  Syntax

                                                                  Image4

                                                                  Description

                                                                  Examples

                                                                  Explanation 1

                                                                  code 1

                                                                  Explanation 2

                                                                  code 2

                                                                  Error Conditions

                                                                  Advanced Notes

                                                                  History

                                                                  Calculator OS Version Description
                                                                  TI-84+CSE 4.0 Added
                                                                  Property Value
                                                                  Hex Value $EF54
                                                                  Categories
                                                                  Localizations
                                                                  • FR: Image5

                                                                  Image5

                                                                  Overview

                                                                  Availability: Token available everywhere.

                                                                  Syntax

                                                                  Image5

                                                                  Description

                                                                  Examples

                                                                  Explanation 1

                                                                  code 1

                                                                  Explanation 2

                                                                  code 2

                                                                  Error Conditions

                                                                  Advanced Notes

                                                                  History

                                                                  Calculator OS Version Description
                                                                  TI-84+CSE 4.0 Added
                                                                  Property Value
                                                                  Hex Value $EF55
                                                                  Categories
                                                                  Localizations
                                                                  • FR: Image6

                                                                  Image6

                                                                  Overview

                                                                  Availability: Token available everywhere.

                                                                  Syntax

                                                                  Image6

                                                                  Description

                                                                  Examples

                                                                  Explanation 1

                                                                  code 1

                                                                  Explanation 2

                                                                  code 2

                                                                  Error Conditions

                                                                  Advanced Notes

                                                                  History

                                                                  Calculator OS Version Description
                                                                  TI-84+CSE 4.0 Added
                                                                  Property Value
                                                                  Hex Value $EF56
                                                                  Categories
                                                                  Localizations
                                                                  • FR: Image7

                                                                  Image7

                                                                  Overview

                                                                  Availability: Token available everywhere.

                                                                  Syntax

                                                                  Image7

                                                                  Description

                                                                  Examples

                                                                  Explanation 1

                                                                  code 1

                                                                  Explanation 2

                                                                  code 2

                                                                  Error Conditions

                                                                  Advanced Notes

                                                                  History

                                                                  Calculator OS Version Description
                                                                  TI-84+CSE 4.0 Added
                                                                  Property Value
                                                                  Hex Value $EF57
                                                                  Categories
                                                                  Localizations
                                                                  • FR: Image8

                                                                  Image8

                                                                  Overview

                                                                  Availability: Token available everywhere.

                                                                  Syntax

                                                                  Image8

                                                                  Description

                                                                  Examples

                                                                  Explanation 1

                                                                  code 1

                                                                  Explanation 2

                                                                  code 2

                                                                  Error Conditions

                                                                  Advanced Notes

                                                                  History

                                                                  Calculator OS Version Description
                                                                  TI-84+CSE 4.0 Added
                                                                  Property Value
                                                                  Hex Value $EF58
                                                                  Categories
                                                                  Localizations
                                                                  • FR: Image9

                                                                  Image9

                                                                  Overview

                                                                  Availability: Token available everywhere.

                                                                  Syntax

                                                                  Image9

                                                                  Description

                                                                  Examples

                                                                  Explanation 1

                                                                  code 1

                                                                  Explanation 2

                                                                  code 2

                                                                  Error Conditions

                                                                  Advanced Notes

                                                                  History

                                                                  Calculator OS Version Description
                                                                  TI-84+CSE 4.0 Added
                                                                  Property Value
                                                                  Hex Value $EF59
                                                                  Categories
                                                                  Localizations
                                                                  • FR: Image0

                                                                  Image0

                                                                  Overview

                                                                  Availability: Token available everywhere.

                                                                  Syntax

                                                                  Image0

                                                                  Description

                                                                  Examples

                                                                  Explanation 1

                                                                  code 1

                                                                  Explanation 2

                                                                  code 2

                                                                  Error Conditions

                                                                  Advanced Notes

                                                                  History

                                                                  Calculator OS Version Description
                                                                  TI-84+CSE 4.0 Added
                                                                  Property Value
                                                                  Hex Value $EF5A
                                                                  Categories
                                                                    Localizations
                                                                    • FR: LigneAff

                                                                    GridLine

                                                                    Overview

                                                                    Turns on grid lines in the graph area in the specified color.
                                                                    Color#: 10 - 24 or color name pasted from [vars] COLOR.

                                                                    Availability: Token only available from within the Basic editor.

                                                                    Syntax

                                                                    GridLine [color#]

                                                                    Arguments

                                                                    NameTypeOptional
                                                                    color#colorNumYes

                                                                    Location

                                                                    2nd, format, GridLine

                                                                    Description

                                                                    Examples

                                                                    Explanation 1

                                                                    code 1

                                                                    Explanation 2

                                                                    code 2

                                                                    Error Conditions

                                                                    Advanced Notes

                                                                    History

                                                                    Calculator OS Version Description
                                                                    TI-84+CSE 4.0 Added
                                                                    Property Value
                                                                    Hex Value $EF5B
                                                                    Categories
                                                                      Localizations
                                                                      • FR: ArrPlanAff

                                                                      BackgroundOn

                                                                      Overview

                                                                      Displays a menu the Background Image Var n (Image#n) specified in the graph area.

                                                                      Availability: Token only available from within the Basic editor.

                                                                      Syntax

                                                                      BackgroundOn n

                                                                      Location

                                                                      2nd, draw, BACKGROUND, 1:BackgroundOn

                                                                      Description

                                                                      With the introduction of color and a higher resolution screen than the monochrome calculators, the TI-84+CSE and TI-84+CE included the ability to display a background image on the graphscreen. The images variables are similar to the picture variables in that there 10 slots. In addition, functions can be drawn on top of images.

                                                                      BackgroundOn recalls an image variable or color and displays it on the graphscreen.

                                                                      :BackgroundOn Image1
is the same as
:BackgroundOn 1

                                                                      Intrestingly, the following is a valid syntax, which fills the graphscreen with a light blue (18).

                                                                      :15→B
:BackgroundOn B+3

                                                                      In addition, BackgroundOn can be used to fill the graphscreen with a solid color. The color variables range from 10 to 24, blue to dark gray, as documented here. For example, BackgroundOn 12 will fill the graphscreen with black.

                                                                      :BackgroundOn 12

                                                                      Error Conditions

                                                                      • ERR:DOMAIN is thrown if the number is not an integer between 0 and 24.

                                                                      Source: parts of this page were written by the following TI|BD contributors: Battlesquid, Electromagnet8, MrWompWomp, Myles_Zadok, Trenly.

                                                                      History

                                                                      Calculator OS Version Description
                                                                      TI-84+CSE 4.0 Added
                                                                      Property Value
                                                                      Hex Value $EF64
                                                                      Categories
                                                                        Localizations
                                                                        • FR: ArrPlanNAff

                                                                        BackgroundOff

                                                                        Overview

                                                                        Turns off background image in the graph area.

                                                                        Availability: Token only available from within the Basic editor.

                                                                        Syntax

                                                                        BackgroundOff

                                                                        Location

                                                                        2nd, draw, BACKGROUND, 2:BackgroundOff:

                                                                        Description

                                                                        The BackgroundOff command has only one purpose: turn the background off. Run the command on its own line in a program with no other characters or arguments.

                                                                        :BackgroundOn BLUE //Makes background blue
:BackgroundOff //Makes background white again

                                                                        Optimization

                                                                        BackgroundOff does essentially the same thing as turning the background on to the color white, as shown below.

                                                                        :BackgroundOn WHITE
can be
:BackgroundOff

                                                                        Source: parts of this page were written by the following TI|BD contributors: Battlesquid, kg583, Michael2_3B, MrWompWomp, Myles_Zadok, Trenly.

                                                                        History

                                                                        Calculator OS Version Description
                                                                        TI-84+CSE 4.0 Added
                                                                        Property Value
                                                                        Hex Value $EF65
                                                                        Categories
                                                                          Localizations
                                                                          • FR: CouleurGraph(

                                                                          GraphColor(

                                                                          Overview

                                                                          Sets the color for function#.
                                                                          Color#: 10 - 24 or color name pasted from [vars] COLOR.

                                                                          Availability: Token only available from within the Basic editor.

                                                                          Syntax

                                                                          GraphColor(function#,color#)

                                                                          Arguments

                                                                          NameTypeOptional
                                                                          function#
                                                                          color#colorNum

                                                                          Location

                                                                          prgm, CTL, H:GraphColor(

                                                                          Description

                                                                          The GraphColor( command will change the color of any function from Y0 to Y9. So, for example, to change the color of Y3 to NAVY, do:

                                                                          GraphColor(3,NAVY

                                                                          Notice, you must use the number of the function, rather than the entire function name, which would be Y3.

                                                                          As you may know, you can also use the value of the color, which can be any integer between 10 and 24. So, our last command could also be:

                                                                          GraphColor(3,17

                                                                          Source: parts of this page were written by the following TI|BD contributors: kg583, Michael2_3B.

                                                                          History

                                                                          Calculator OS Version Description
                                                                          TI-84+CSE 4.0 Added
                                                                          Property Value
                                                                          Hex Value $EF66
                                                                          Categories
                                                                          Localizations
                                                                          • FR: TracéAjust-Éq

                                                                          QuickPlot&Fit-EQ

                                                                          Overview

                                                                          Comment:84+CSE and later

                                                                          Syntax

                                                                          QuickPlot&Fit-EQ

                                                                          Description

                                                                          Examples

                                                                          Explanation 1

                                                                          code 1

                                                                          Explanation 2

                                                                          code 2

                                                                          Error Conditions

                                                                          Advanced Notes

                                                                          History

                                                                          Calculator OS Version Description
                                                                          TI-84+CSE 4.0 Added
                                                                          Property Value
                                                                          Hex Value $EF67
                                                                          Categories
                                                                            Localizations
                                                                            • FR: CouleurTexte(

                                                                            TextColor(

                                                                            Overview

                                                                            Set text color prior to using the Text(command.
                                                                            Color#: 10 - 24 or color name pasted from [vars] COLOR.

                                                                            Availability: Token only available from within the Basic editor.

                                                                            Syntax

                                                                            TextColor([color#]

                                                                            Arguments

                                                                            NameTypeOptional
                                                                            color#colorNumYes

                                                                            Location

                                                                            2nd, draw, DRAW, A:TextColor(

                                                                            Description

                                                                            The TextColor( token is used to set the color for Text(. Although the default color is Blue, the calculator saves the color until it is changed again using TextColor( or when a memory reset occurs. When a memory reset occurs, the text color is reset back to blue.

                                                                            :TextColor(BLUE
:Text(0,0,"THIS TEXT IS BLUE
:TextColor(GRAY
:Text(12,0,"THIS TEXT IS GRAY
:Text(24,0,"THIS IS GRAY AS WELL
:TextColor(12
:Text(36,0,"THIS TEXT IS BLACK

                                                                            The following table are the colors associated with their numeric values.

                                                                            Color Token

                                                                            Numeric Value

                                                                            BLUE

                                                                            10

                                                                            RED

                                                                            11

                                                                            BLACK

                                                                            12

                                                                            MAGENTA

                                                                            13

                                                                            GREEN

                                                                            14

                                                                            ORANGE

                                                                            15

                                                                            BROWN

                                                                            16

                                                                            NAVY

                                                                            17

                                                                            LTBLUE

                                                                            18

                                                                            YELLOW

                                                                            19

                                                                            WHITE

                                                                            20

                                                                            LTGRAY

                                                                            21

                                                                            MEDGRAY

                                                                            22

                                                                            GRAY

                                                                            23

                                                                            DARKGRAY

                                                                            24

                                                                            Each color token is 2 bytes.
                                                                            The color tokens can be used in calculations. For example, LTBLUE/3 will equal 6.

                                                                            Background Colors

                                                                            When the calculator displays text on the graphscreen, it displays it on top of a predetermined background color. This background color is white for all colors of text, except for yellow, white, and light gray (LTGRAY), which have a background color of medium gray (MEDGRAY). If you want to display text in your game without the annoying text-background, you need to have the graphscreen background be white or medium gray so the text-background doesn't show. The only known alternative is to use Pxl-On to draw the text manually, so how you work around this issue depends almost entirely on how lazy you are. You can see how this works by looking at the image in the Command Summary sidebar.

                                                                            Error Conditions

                                                                            • ERR:DOMAIN is thrown if the argument specified is not an integer within the 10-24 range.

                                                                            Source: parts of this page were written by the following TI|BD contributors: Battlesquid, Electromagnet8, iPhoenixOnTIBD, Myles_Zadok.

                                                                            History

                                                                            Calculator OS Version Description
                                                                            TI-84+CSE 4.0 Added
                                                                            Property Value
                                                                            Hex Value $EF68
                                                                            Categories
                                                                            Localizations
                                                                            • FR: Asm84CPrgm

                                                                            Asm84CPrgm

                                                                            Overview

                                                                            Syntax

                                                                            Asm84CPrgm

                                                                            Description

                                                                            Please see the AsmPrgm page. The functionality and use is the same between both commands. However, the Asm84CPrgm is only available on the TI-84+CSE calculator. Keep in mind that hexadecimal for the monochrome calculators may not work on color calculators.

                                                                            Source: parts of this page were written by the following TI|BD contributors: Electromagnet8, jonbush, Myles_Zadok, Trenly.

                                                                            History

                                                                            Calculator OS Version Description
                                                                            TI-84+CSE 4.0 Added
                                                                            Property Value
                                                                            Hex Value $EF69
                                                                            Categories
                                                                            Localizations
                                                                            • FR: [CompiledAsm84C]

                                                                            [CompiledAsm84C]

                                                                            Overview

                                                                            Syntax

                                                                            [CompiledAsm84C]

                                                                            Description

                                                                            Examples

                                                                            Explanation 1

                                                                            code 1

                                                                            Explanation 2

                                                                            code 2

                                                                            Error Conditions

                                                                            Advanced Notes

                                                                            History

                                                                            Calculator OS Version Description
                                                                            Property Value
                                                                            Hex Value $EF6A
                                                                            Categories
                                                                              Localizations
                                                                              • FR: DétectAsymAct

                                                                              DetectAsymOn

                                                                              Overview

                                                                              Turns on checks for rational function asymptotes when graphing. Impacts graph speed. Performs more calculations and will not connect pixels across an asymptote on a graph.

                                                                              Availability: Token only available from within the Basic editor.

                                                                              Syntax

                                                                              DetectAsymOn

                                                                              Location

                                                                              2nd, format

                                                                              Description

                                                                              When DetectAsymOn is selected, the calculator will detect asymptotes, adjusting the graph accordingly. This method of graphing is the most accurate but is also much slower than graphing with asymptotes turned off.

                                                                              An asymptote is, by definition, "a line that continually approaches a given curve but does not meet it at any finite distance." Basically, an asymptote is the line where a function does not have any values on a certain axis.

                                                                              Source: parts of this page were written by the following TI|BD contributors: kg583, Michael2_3B, Myles_Zadok.

                                                                              History

                                                                              Calculator OS Version Description
                                                                              TI-84+CSE 4.0 Added
                                                                              Property Value
                                                                              Hex Value $EF6B
                                                                              Categories
                                                                                Localizations
                                                                                • FR: DétectAsymDés

                                                                                DetectAsymOff

                                                                                Overview

                                                                                Turns off checks for rational function asymptotes when graphing. Impacts graph speed. Does not perform extra calculations to detect asymptotes pixel to pixel while graphing. Pixels will connect across the screen even across an asymptote.

                                                                                Availability: Token only available from within the Basic editor.

                                                                                Syntax

                                                                                DetectAsymOff

                                                                                Location

                                                                                2nd, format, DetectAsymOff

                                                                                Description

                                                                                When DetectAsymOff is selected, the calculator will not detect asymptotes, adjusting the graph accordingly. This method of graphing is much faster than with asymptotes turned on. However, the graph can be erroneous when dealing with rational functions, as it will often draw extra lines to connect points near undefined values.

                                                                                An asymptote is, by definition, "a line that continually approaches a given curve but does not meet it at any finite distance." Basically, an asymptote is the line where a function does not have any values on a certain axis.

                                                                                Source: parts of this page were written by the following TI|BD contributors: kg583, Michael2_3B, Myles_Zadok.

                                                                                History

                                                                                Calculator OS Version Description
                                                                                TI-84+CSE 4.0 Added
                                                                                Property Value
                                                                                Hex Value $EF6C
                                                                                Categories
                                                                                  Localizations
                                                                                  • FR: CouleurBord

                                                                                  BorderColor

                                                                                  Overview

                                                                                  Turns on a border color surrounding the graph area with the specified color. Color #:1-4.

                                                                                  Availability: Token only available from within the Basic editor.

                                                                                  Syntax

                                                                                  BorderColor[color#]

                                                                                  Arguments

                                                                                  NameTypeOptional
                                                                                  color#colorNumYes

                                                                                  Location

                                                                                  2nd, format, BorderColor

                                                                                  Description

                                                                                  Examples

                                                                                  Explanation 1

                                                                                  code 1

                                                                                  Explanation 2

                                                                                  code 2

                                                                                  Error Conditions

                                                                                  Advanced Notes

                                                                                  History

                                                                                  Calculator OS Version Description
                                                                                  TI-84+CSE 4.0 Added
                                                                                  Property Value
                                                                                  Hex Value $EF73
                                                                                  Categories
                                                                                  Localizations
                                                                                  • FR: ·

                                                                                  ·

                                                                                  Overview

                                                                                  Syntax

                                                                                  ·

                                                                                  Description

                                                                                  Examples

                                                                                  Explanation 1

                                                                                  code 1

                                                                                  Explanation 2

                                                                                  code 2

                                                                                  Error Conditions

                                                                                  Advanced Notes

                                                                                  History

                                                                                  Calculator OS Version Description
                                                                                  TI-84+CSE 4.0 Added
                                                                                  Property Value
                                                                                  Hex Value $EF74
                                                                                  Categories
                                                                                    Localizations
                                                                                    • FR: Fin

                                                                                    Thin

                                                                                    Overview

                                                                                    Resets all Y=editor line-style settings to Thin.

                                                                                    Availability: Token only available from within the Basic editor.

                                                                                    Syntax

                                                                                    Thin

                                                                                    Location

                                                                                    zT, Thin

                                                                                    Description

                                                                                    The Thin command will set all lines in the current function type to be only 1 pixel wide (hence "Thin"). The command can be run on the homescreen or within a program.

                                                                                    :AxesOff
:GridOff
:Thin

                                                                                    Error Conditions

                                                                                    • ERR:SYNTAX is thrown if additional arguments are put on the command.

                                                                                    Source: parts of this page were written by the following TI|BD contributors: Battlesquid, kg583, MrWompWomp.

                                                                                    History

                                                                                    Calculator OS Version Description
                                                                                    TI-84+CSE 4.0 Added
                                                                                    Property Value
                                                                                    Hex Value $EF75
                                                                                    Categories
                                                                                      Localizations
                                                                                      • FR: Point fin

                                                                                      Dot-Thin

                                                                                      Overview

                                                                                      Sets dot plotting mode; resets all Y=editor graph-style settings to Dot-Thin.

                                                                                      Availability: Token only available from within the Basic editor.

                                                                                      Syntax

                                                                                      Dot-Thin

                                                                                      Location

                                                                                      mode, Dot-Thin

                                                                                      Description

                                                                                      The Dot-Thin command sets all lines in the current function type to be drawn using a series of individual pixels at each interval of TraceStep. The command can be called on the homescreen or within a program.

                                                                                      :ClrDraw
:AxesOn
:Dot-Thin

                                                                                      Error Conditions

                                                                                      • ERR:SYNTAX is thrown if the command is executed with any additional arguments

                                                                                      Source: parts of this page were written by the following TI|BD contributors: Battlesquid, kg583, MrWompWomp.

                                                                                      History

                                                                                      Calculator OS Version Description
                                                                                      TI-84+CSE 4.0 Added
                                                                                      Property Value
                                                                                      Hex Value $EF7A
                                                                                      Categories
                                                                                      Localizations
                                                                                      • FR: Asm84CEPrgm

                                                                                      Asm84CEPrgm

                                                                                      Overview

                                                                                      Comment:Asm83CEPrgm on the TI-83 Premium CE

                                                                                      Syntax

                                                                                      Asm84CEPrgm

                                                                                      Description

                                                                                      Please see the AsmPrgm page. The functionality and use are the same between both commands. However, the Asm84CEPrgm is only available on the TI-84+CE calculator. Keep in mind that hexadecimal for the monochrome calculators may not work on color calculators. This token does not work on OS 5.3.1, it has been deprecated by Texas Instruments for no good reason. Even uploading a program with this token in it will not work as it will throw an INVALID error.

                                                                                      There is a workaround to this problem. A sendable program containing the command can be found here.

                                                                                      To run assembly programs on the calculator, recall the command from the program you sent. Type your hex code in the editor. When you're done, quit the program. Type the following on the homescreen:

                                                                                      AsmComp(prgmNAME1,prgmNAME2

                                                                                      Then, find the program you compressed and run it with either the Asm( command or like a normal BASIC progam.

                                                                                      Source: parts of this page were written by the following TI|BD contributors: jonbush, Myles_Zadok, Trenly, VoxelPrismatic.

                                                                                      History

                                                                                      Calculator OS Version Description
                                                                                      TI-84+CE 5.0.0 Added
                                                                                      Property Value
                                                                                      Hex Value $EF7B
                                                                                      Categories
                                                                                      Localizations
                                                                                      • FR: [CompiledAsmCE]

                                                                                      [CompiledAsmCE]

                                                                                      Overview

                                                                                      Syntax

                                                                                      [CompiledAsmCE]

                                                                                      Description

                                                                                      Examples

                                                                                      Explanation 1

                                                                                      code 1

                                                                                      Explanation 2

                                                                                      code 2

                                                                                      Error Conditions

                                                                                      Advanced Notes

                                                                                      History

                                                                                      Calculator OS Version Description
                                                                                      Property Value
                                                                                      Hex Value $EF81
                                                                                      Categories
                                                                                      Localizations
                                                                                      • FR: Quartiles réglage…

                                                                                      Quartiles Setting…

                                                                                      Overview

                                                                                      Comment:CE OS 5.2+

                                                                                      Syntax

                                                                                      Quartiles Setting…

                                                                                      Description

                                                                                      Examples

                                                                                      Explanation 1

                                                                                      code 1

                                                                                      Explanation 2

                                                                                      code 2

                                                                                      Error Conditions

                                                                                      Advanced Notes

                                                                                      History

                                                                                      Calculator OS Version Description
                                                                                      TI-84+CE 5.1.0 Added
                                                                                      Property Value
                                                                                      Hex Value $EF82
                                                                                      Categories
                                                                                      Localizations
                                                                                      • FR: u(𝑛-2)

                                                                                      u(𝑛-2)

                                                                                      Overview

                                                                                      Comment:CE OS 5.2+

                                                                                      Availability: Token available everywhere.

                                                                                      Syntax

                                                                                      u(𝑛-2)

                                                                                      Description

                                                                                      Examples

                                                                                      Explanation 1

                                                                                      code 1

                                                                                      Explanation 2

                                                                                      code 2

                                                                                      Error Conditions

                                                                                      Advanced Notes

                                                                                      History

                                                                                      Calculator OS Version Description
                                                                                      TI-84+CE 5.2.0 Added
                                                                                      Property Value
                                                                                      Hex Value $EF83
                                                                                      Categories
                                                                                      Localizations
                                                                                      • FR: v(𝑛-2)

                                                                                      v(𝑛-2)

                                                                                      Overview

                                                                                      Comment:CE OS 5.2+

                                                                                      Availability: Token available everywhere.

                                                                                      Syntax

                                                                                      v(𝑛-2)

                                                                                      Description

                                                                                      Examples

                                                                                      Explanation 1

                                                                                      code 1

                                                                                      Explanation 2

                                                                                      code 2

                                                                                      Error Conditions

                                                                                      Advanced Notes

                                                                                      History

                                                                                      Calculator OS Version Description
                                                                                      TI-84+CE 5.2.0 Added
                                                                                      Property Value
                                                                                      Hex Value $EF84
                                                                                      Categories
                                                                                      Localizations
                                                                                      • FR: w(𝑛-2)

                                                                                      w(𝑛-2)

                                                                                      Overview

                                                                                      Comment:CE OS 5.2+

                                                                                      Availability: Token available everywhere.

                                                                                      Syntax

                                                                                      w(𝑛-2)

                                                                                      Description

                                                                                      Examples

                                                                                      Explanation 1

                                                                                      code 1

                                                                                      Explanation 2

                                                                                      code 2

                                                                                      Error Conditions

                                                                                      Advanced Notes

                                                                                      History

                                                                                      Calculator OS Version Description
                                                                                      TI-84+CE 5.2.0 Added
                                                                                      Property Value
                                                                                      Hex Value $EF85
                                                                                      Categories
                                                                                      Localizations
                                                                                      • FR: u(𝑛-1)

                                                                                      u(𝑛-1)

                                                                                      Overview

                                                                                      Comment:CE OS 5.2+

                                                                                      Availability: Token available everywhere.

                                                                                      Syntax

                                                                                      u(𝑛-1)

                                                                                      Description

                                                                                      Examples

                                                                                      Explanation 1

                                                                                      code 1

                                                                                      Explanation 2

                                                                                      code 2

                                                                                      Error Conditions

                                                                                      Advanced Notes

                                                                                      History

                                                                                      Calculator OS Version Description
                                                                                      TI-84+CE 5.2.0 Added
                                                                                      Property Value
                                                                                      Hex Value $EF86
                                                                                      Categories
                                                                                      Localizations
                                                                                      • FR: v(𝑛-1)

                                                                                      v(𝑛-1)

                                                                                      Overview

                                                                                      Comment:CE OS 5.2+

                                                                                      Availability: Token available everywhere.

                                                                                      Syntax

                                                                                      v(𝑛-1)

                                                                                      Description

                                                                                      Examples

                                                                                      Explanation 1

                                                                                      code 1

                                                                                      Explanation 2

                                                                                      code 2

                                                                                      Error Conditions

                                                                                      Advanced Notes

                                                                                      History

                                                                                      Calculator OS Version Description
                                                                                      TI-84+CE 5.2.0 Added
                                                                                      Property Value
                                                                                      Hex Value $EF87
                                                                                      Categories
                                                                                      Localizations
                                                                                      • FR: w(𝑛-1)

                                                                                      w(𝑛-1)

                                                                                      Overview

                                                                                      Comment:CE OS 5.2+

                                                                                      Availability: Token available everywhere.

                                                                                      Syntax

                                                                                      w(𝑛-1)

                                                                                      Description

                                                                                      Examples

                                                                                      Explanation 1

                                                                                      code 1

                                                                                      Explanation 2

                                                                                      code 2

                                                                                      Error Conditions

                                                                                      Advanced Notes

                                                                                      History

                                                                                      Calculator OS Version Description
                                                                                      TI-84+CE 5.2.0 Added
                                                                                      Property Value
                                                                                      Hex Value $EF88
                                                                                      Categories
                                                                                      Localizations
                                                                                      • FR: u(𝑛)

                                                                                      u(𝑛)

                                                                                      Overview

                                                                                      Comment:CE OS 5.2+

                                                                                      Availability: Token available everywhere.

                                                                                      Syntax

                                                                                      u(𝑛)

                                                                                      Description

                                                                                      Examples

                                                                                      Explanation 1

                                                                                      code 1

                                                                                      Explanation 2

                                                                                      code 2

                                                                                      Error Conditions

                                                                                      Advanced Notes

                                                                                      History

                                                                                      Calculator OS Version Description
                                                                                      TI-84+CE 5.2.0 Added
                                                                                      Property Value
                                                                                      Hex Value $EF89
                                                                                      Categories
                                                                                      Localizations
                                                                                      • FR: v(𝑛)

                                                                                      v(𝑛)

                                                                                      Overview

                                                                                      Comment:CE OS 5.2+

                                                                                      Availability: Token available everywhere.

                                                                                      Syntax

                                                                                      v(𝑛)

                                                                                      Description

                                                                                      Examples

                                                                                      Explanation 1

                                                                                      code 1

                                                                                      Explanation 2

                                                                                      code 2

                                                                                      Error Conditions

                                                                                      Advanced Notes

                                                                                      History

                                                                                      Calculator OS Version Description
                                                                                      TI-84+CE 5.2.0 Added
                                                                                      Property Value
                                                                                      Hex Value $EF8A
                                                                                      Categories
                                                                                      Localizations
                                                                                      • FR: w(𝑛)

                                                                                      w(𝑛)

                                                                                      Overview

                                                                                      Comment:CE OS 5.2+

                                                                                      Availability: Token available everywhere.

                                                                                      Syntax

                                                                                      w(𝑛)

                                                                                      Description

                                                                                      Examples

                                                                                      Explanation 1

                                                                                      code 1

                                                                                      Explanation 2

                                                                                      code 2

                                                                                      Error Conditions

                                                                                      Advanced Notes

                                                                                      History

                                                                                      Calculator OS Version Description
                                                                                      TI-84+CE 5.2.0 Added
                                                                                      Property Value
                                                                                      Hex Value $EF8B
                                                                                      Categories
                                                                                      Localizations
                                                                                      • FR: u(𝑛+1)

                                                                                      u(𝑛+1)

                                                                                      Overview

                                                                                      Comment:CE OS 5.2+

                                                                                      Availability: Token available everywhere.

                                                                                      Syntax

                                                                                      u(𝑛+1)

                                                                                      Description

                                                                                      Examples

                                                                                      Explanation 1

                                                                                      code 1

                                                                                      Explanation 2

                                                                                      code 2

                                                                                      Error Conditions

                                                                                      Advanced Notes

                                                                                      History

                                                                                      Calculator OS Version Description
                                                                                      TI-84+CE 5.2.0 Added
                                                                                      Property Value
                                                                                      Hex Value $EF8C
                                                                                      Categories
                                                                                      Localizations
                                                                                      • FR: v(𝑛+1)

                                                                                      v(𝑛+1)

                                                                                      Overview

                                                                                      Comment:CE OS 5.2+

                                                                                      Availability: Token available everywhere.

                                                                                      Syntax

                                                                                      v(𝑛+1)

                                                                                      Description

                                                                                      Examples

                                                                                      Explanation 1

                                                                                      code 1

                                                                                      Explanation 2

                                                                                      code 2

                                                                                      Error Conditions

                                                                                      Advanced Notes

                                                                                      History

                                                                                      Calculator OS Version Description
                                                                                      TI-84+CE 5.2.0 Added
                                                                                      Property Value
                                                                                      Hex Value $EF8D
                                                                                      Categories
                                                                                      Localizations
                                                                                      • FR: w(𝑛+1)

                                                                                      w(𝑛+1)

                                                                                      Overview

                                                                                      Comment:CE OS 5.2+

                                                                                      Availability: Token available everywhere.

                                                                                      Syntax

                                                                                      w(𝑛+1)

                                                                                      Description

                                                                                      Examples

                                                                                      Explanation 1

                                                                                      code 1

                                                                                      Explanation 2

                                                                                      code 2

                                                                                      Error Conditions

                                                                                      Advanced Notes

                                                                                      History

                                                                                      Calculator OS Version Description
                                                                                      TI-84+CE 5.2.0 Added
                                                                                      Property Value
                                                                                      Hex Value $EF8F
                                                                                      Categories
                                                                                        Localizations
                                                                                        • FR: SUITE(𝑛)

                                                                                        SEQ(𝑛)

                                                                                        Overview

                                                                                        In sequence mode, SEQ(n) sets the sequence editor type to enter sequence functions, u, v, or w, as a function of the independent variable n. Can also be set from the Y= editor in SEQ mode.

                                                                                        Comment:CE OS 5.2+

                                                                                        Availability: Token only available from within the Basic editor.

                                                                                        Syntax

                                                                                        Seq(n)

                                                                                        Arguments

                                                                                        NameTypeOptional
                                                                                        n

                                                                                        Location

                                                                                        mode, SEQ(n)

                                                                                        Description

                                                                                        Examples

                                                                                        Explanation 1

                                                                                        code 1

                                                                                        Explanation 2

                                                                                        code 2

                                                                                        Error Conditions

                                                                                        Advanced Notes

                                                                                        History

                                                                                        Calculator OS Version Description
                                                                                        TI-84+CE 5.2.0 Added
                                                                                        Property Value
                                                                                        Hex Value $EF90
                                                                                        Categories
                                                                                          Localizations
                                                                                          • FR: SUITE(𝑛+1)

                                                                                          SEQ(𝑛+1)

                                                                                          Overview

                                                                                          In sequence mode, SEQ(n+1) sets the sequence editor type to enter sequence functions, u, v, or w, as a function of the independent variable n+1. Can also be set from the Y= editor in SEQ mode.

                                                                                          Comment:CE OS 5.2+

                                                                                          Availability: Token only available from within the Basic editor.

                                                                                          Syntax

                                                                                          Seq(n+1)

                                                                                          Arguments

                                                                                          NameTypeOptional
                                                                                          n+1

                                                                                          Location

                                                                                          mode, SEQ(n+1)

                                                                                          Description

                                                                                          Examples

                                                                                          Explanation 1

                                                                                          code 1

                                                                                          Explanation 2

                                                                                          code 2

                                                                                          Error Conditions

                                                                                          Advanced Notes

                                                                                          History

                                                                                          Calculator OS Version Description
                                                                                          TI-84+CE 5.2.0 Added
                                                                                          Property Value
                                                                                          Hex Value $EF91
                                                                                          Categories
                                                                                            Localizations
                                                                                            • FR: SUITE(𝑛+2)

                                                                                            SEQ(𝑛+2)

                                                                                            Overview

                                                                                            In sequence mode, SEQ(n+2) sets the sequence editor type to enter sequence functions, u, v, or w, as a function of the independent variable n+2. Can also be set from the Y= editor in SEQ mode.

                                                                                            Comment:CE OS 5.2+

                                                                                            Availability: Token only available from within the Basic editor.

                                                                                            Syntax

                                                                                            Seq(n+2)

                                                                                            Arguments

                                                                                            NameTypeOptional
                                                                                            n+2

                                                                                            Location

                                                                                            mode, SEQ(n+2)

                                                                                            Description

                                                                                            Examples

                                                                                            Explanation 1

                                                                                            code 1

                                                                                            Explanation 2

                                                                                            code 2

                                                                                            Error Conditions

                                                                                            Advanced Notes

                                                                                            History

                                                                                            Calculator OS Version Description
                                                                                            TI-84+CE 5.2.0 Added
                                                                                            Property Value
                                                                                            Hex Value $EF92
                                                                                            Categories
                                                                                              Localizations
                                                                                              • FR: GAUCHE

                                                                                              LEFT

                                                                                              Overview

                                                                                              LEFT is a tail argument for the invNorm( command where the optional argument tail can be LEFT (-∞,-a), CENTER [-a,a] or RIGHT (a, ∞) for Real a.
                                                                                              See also invNorm(.

                                                                                              Comment:CE OS 5.2+

                                                                                              Availability: Token available everywhere.

                                                                                              Syntax

                                                                                              LEFT

                                                                                              Location

                                                                                              2nd, catalog

                                                                                              Description

                                                                                              Examples

                                                                                              Explanation 1

                                                                                              code 1

                                                                                              Explanation 2

                                                                                              code 2

                                                                                              Error Conditions

                                                                                              Advanced Notes

                                                                                              History

                                                                                              Calculator OS Version Description
                                                                                              TI-84+CE 5.2.0 Added
                                                                                              Property Value
                                                                                              Hex Value $EF93
                                                                                              Categories
                                                                                                Localizations
                                                                                                • FR: CENTRE

                                                                                                CENTER

                                                                                                Overview

                                                                                                CENTER is a tail argument for the invNorm( command where the optional argument tail can be LEFT (-∞,-a), CENTER [-a,a] or RIGHT (a, ∞) for Real a.
                                                                                                See also invNorm(.

                                                                                                Comment:CE OS 5.2+

                                                                                                Availability: Token available everywhere.

                                                                                                Syntax

                                                                                                CENTER

                                                                                                Location

                                                                                                2nd, catalog

                                                                                                Description

                                                                                                Examples

                                                                                                Explanation 1

                                                                                                code 1

                                                                                                Explanation 2

                                                                                                code 2

                                                                                                Error Conditions

                                                                                                Advanced Notes

                                                                                                History

                                                                                                Calculator OS Version Description
                                                                                                TI-84+CE 5.2.0 Added
                                                                                                Property Value
                                                                                                Hex Value $EF94
                                                                                                Categories
                                                                                                  Localizations
                                                                                                  • FR: DROITE

                                                                                                  RIGHT

                                                                                                  Overview

                                                                                                  RIGHT is a tail argument for the invNorm( command where the optional argument tail can be LEFT (-∞,-a), CENTER [-a,a] or RIGHT (a, ∞) for Real a.
                                                                                                  See also invNorm(.

                                                                                                  Comment:CE OS 5.2+

                                                                                                  Availability: Token available everywhere.

                                                                                                  Syntax

                                                                                                  RIGHT

                                                                                                  Location

                                                                                                  2nd, catalog

                                                                                                  Description

                                                                                                  Examples

                                                                                                  Explanation 1

                                                                                                  code 1

                                                                                                  Explanation 2

                                                                                                  code 2

                                                                                                  Error Conditions

                                                                                                  Advanced Notes

                                                                                                  History

                                                                                                  Calculator OS Version Description
                                                                                                  TI-84+CE 5.2.0 Added
                                                                                                  Property Value
                                                                                                  Hex Value $EF95
                                                                                                  Categories
                                                                                                    Localizations
                                                                                                    • FR: invBinom(

                                                                                                    invBinom(

                                                                                                    Overview

                                                                                                    The inverse binomial cumulative distribution function results in the minimum number of successes, such that the cumulative probability for that minimum number of successes ≥ the given cumulative probability (area). If more information is needed, also find the binomcdf for the result from invBinom( as shown below for a full analysis.
                                                                                                    Details:
                                                                                                    Assume the toss of a fair coin 30 times. What is the minimum number of heads you must observe such that the cumulative probability for that number of observed heads is at least 0.95?
                                                                                                    The results on the screen first show that the minimum number of successes to obtain at least the given cumulative probability of 0.95 is 19. Next, the cumulative probability for up to 19 is computed using binomcdf( and is approximately 0.9506314271 which meets the criteria of 0.9506314271≥0.95

                                                                                                    Alternate Method:
                                                                                                    Set Y1=binomcdf(30,0.5,X) and use the table of values (starting at 0 and increment by 1) to find when the cumulative probability is at or just above the given cumulative probability. This gives you a view of all values to make decisions. For this example, search in the table to find the cumulative probability just larger than 0.95. Again, the number of successes is 19.

                                                                                                    Comment:CE OS 5.2+

                                                                                                    Availability: Token available everywhere.

                                                                                                    Syntax

                                                                                                    invBinom(area,trial,p)

                                                                                                    Arguments

                                                                                                    NameTypeOptional
                                                                                                    area
                                                                                                    trial
                                                                                                    p

                                                                                                    Location

                                                                                                    2nd, distr, DISTR, C:invBinom(

                                                                                                    Description

                                                                                                    Examples

                                                                                                    Explanation 1

                                                                                                    code 1

                                                                                                    Explanation 2

                                                                                                    code 2

                                                                                                    Error Conditions

                                                                                                    Advanced Notes

                                                                                                    History

                                                                                                    Calculator OS Version Description
                                                                                                    TI-84+CE 5.2.0 Added
                                                                                                    Property Value
                                                                                                    Hex Value $EF96
                                                                                                    Categories
                                                                                                      Localizations
                                                                                                      • FR: Wait

                                                                                                      Wait

                                                                                                      Overview

                                                                                                      Suspends execution of a program for a given time. Maximum time is 100 seconds.

                                                                                                      Comment:CE OS 5.2+

                                                                                                      Availability: Token only available from within the Basic editor.

                                                                                                      Syntax

                                                                                                      Waittime

                                                                                                      Arguments

                                                                                                      NameTypeOptional
                                                                                                      time

                                                                                                      Location

                                                                                                      prgm, A:Wait

                                                                                                      Overview

                                                                                                      Suspends execution of a program for a given time. Maximum time is 100 seconds.

                                                                                                      Comment:CE OS 5.2+

                                                                                                      Availability: Token only available from within the Basic editor.

                                                                                                      Syntax

                                                                                                      Waittime

                                                                                                      Arguments

                                                                                                      NameTypeOptional
                                                                                                      time

                                                                                                      Location

                                                                                                      prgm, 4:Wait

                                                                                                      Special Category

                                                                                                      TI-Innovator™ Hub

                                                                                                      Description

                                                                                                      The Wait command was introduced in TI-OS 5.2 for the TI-84+CE. The Wait command tells the calculator to wait for a specified number of seconds before continuing. The specified amount of seconds can be a decimal, as it is not limited to whole numbers. This command can be useful for displaying information momentarily before proceeding in a program. The Wait command functions similarly to the Pause command, but without the extra arguments.

                                                                                                      :Disp "WAIT FOR IT!
:Wait 4
:Disp "Surprise

                                                                                                      Advanced Uses

                                                                                                      The Wait command is useful for facilitating automatic linking within programs. Since the Get( and GetCalc( commands only work when the sending calculator is in a preemptible state, including a small Wait delay will allow the other calculator to receive data.

                                                                                                      Because the Wait command is relatively new, it may be advisable to avoid using it to ensure compatibility with older operating systems. Similar functionality can be achieved with the second optional argument to the Pause command.

                                                                                                      Optimization

                                                                                                      Traditionally it was recommended to use either a For( loop or the rand( command to create a delay within a program. The For( loop takes more space, and the rand( command uses more memory during execution.

                                                                                                      :rand(100
can be
:Wait 1

                                                                                                      Error Conditions

                                                                                                      • ERROR: INVALID is thrown if the Wait command is executed on the home screen.

                                                                                                      Source: parts of this page were written by the following TI|BD contributors: Battlesquid, jonbush, Michael2_3B.

                                                                                                      History

                                                                                                      Calculator OS Version Description
                                                                                                      TI-84+CE 5.2.0 Added
                                                                                                      Property Value
                                                                                                      Hex Value $EF97
                                                                                                      Categories
                                                                                                        Localizations
                                                                                                        • FR: versChaîne(

                                                                                                        toString(

                                                                                                        Overview

                                                                                                        Converts value to a string where value can be real, complex, an evaluated expression, list, or matrix. String value displays in classic format (0) following the mode setting AUTO/DEC or in decimal format (1).

                                                                                                        Comment:CE OS 5.2+

                                                                                                        Availability: Token only available from within the Basic editor.

                                                                                                        Syntax

                                                                                                        toString((value[,format])

                                                                                                        Arguments

                                                                                                        NameTypeOptional
                                                                                                        valueYes
                                                                                                        formatYes

                                                                                                        Location

                                                                                                        prgm, E:toString(, C:toString(

                                                                                                        Description

                                                                                                        The toString( command, given any value including real numbers, complex numbers, lists, or matrices, returns the string representation of the value of the input.

                                                                                                        toString(1337       //returns "1337"

toString({1,2,3}    //returns "{1,2,3}"

toString([[1,2][3,4]]   //returns "[[1,2][3,4]]"

toString(√-1     //returns imaginary number "i"

                                                                                                        toString( has less limitations than the eval( command. It can handle lists, matrices, and complex numbers. Another difference from eval( is that toString( is affected by display mode changes like Fix.

                                                                                                        toString( replaces the old number-to-string routine previously used prior to OS 5.2.

                                                                                                        Error Conditions

                                                                                                        • ERR:DATA TYPE is thrown when the input is a string.
                                                                                                        • ERR:NONREAL ANSWERS is thrown when the input is a complex number and your calculator is in REAL mode.
                                                                                                        • ERR:SYNTAX is thrown when trying to evaluate a command that doesn't return a value.

                                                                                                        Source: parts of this page were written by the following TI|BD contributors: Battlesquid, jonbush, kg583, Michael2_3B, VoxelPrismatic.

                                                                                                        History

                                                                                                        Calculator OS Version Description
                                                                                                        TI-84+CE 5.2.0 Added
                                                                                                        Property Value
                                                                                                        Hex Value $EF98
                                                                                                        Categories
                                                                                                          Localizations
                                                                                                          • FR: eval(

                                                                                                          eval(

                                                                                                          Overview

                                                                                                          Returns an evaluated expression as a string with 8 significant digits. The expression must be real.

                                                                                                          Comment:CE OS 5.2+

                                                                                                          Availability: Token only available from within the Basic editor.

                                                                                                          Syntax

                                                                                                          eval(expression)

                                                                                                          Arguments

                                                                                                          NameTypeOptional
                                                                                                          expressionexpression

                                                                                                          Location

                                                                                                          prgm, I/O, C:eval(

                                                                                                          Overview

                                                                                                          Returns an evaluated expression as a string with 8 significant digits. The expression must simplify to a real expression.

                                                                                                          Comment:CE OS 5.2+

                                                                                                          Availability: Token only available from within the Basic editor.

                                                                                                          Syntax

                                                                                                          eval(expression)

                                                                                                          Arguments

                                                                                                          NameTypeOptional
                                                                                                          expressionexpression

                                                                                                          Location

                                                                                                          prgm, 6:eval(

                                                                                                          Special Category

                                                                                                          TI-Innovator™ Hub

                                                                                                          Description

                                                                                                          The eval( command, given an expression that evaluates to a real number, returns the string representation of that number.

                                                                                                          eval(1337       //returns "1337"

eval(2.0-3.0    //returns "‾1"

eval(.0001234   //returns "1.234ᴇ‾4"

                                                                                                          eval( has more limitations than the toString( command. It cannot handle lists, matrices, or complex numbers (even when the imaginary part of the complex number is zero). Another difference from toString( is that eval( is unaffected by display mode changes like Fix.

                                                                                                          Advanced Uses

                                                                                                          Use eval( in conjunction with expr( to evaluate a real expression in a string and return the answer in a string.

                                                                                                          3.14->X
eval(expr("2X+3
//returns "9.28"

                                                                                                          Error Conditions

                                                                                                          • ERR:DATA TYPE is thrown when the expression contains a list, matrix, imaginary number, or string.
                                                                                                          • ERR:SYNTAX is thrown when trying to evaluate a command that doesn't return a value.

                                                                                                          Source: parts of this page were written by the following TI|BD contributors: Battlesquid, jonbush, lirtosiast, Michael2_3B.

                                                                                                          History

                                                                                                          Calculator OS Version Description
                                                                                                          TI-84+CE 5.2.0 Added
                                                                                                          Property Value
                                                                                                          Hex Value $EF9E
                                                                                                          Categories
                                                                                                          Localizations
                                                                                                          • FR: Exécuter programme

                                                                                                          Execute Program

                                                                                                          Overview

                                                                                                          Comment:CE OS 5.3+

                                                                                                          Syntax

                                                                                                          Execute Program

                                                                                                          Description

                                                                                                          Examples

                                                                                                          Explanation 1

                                                                                                          code 1

                                                                                                          Explanation 2

                                                                                                          code 2

                                                                                                          Error Conditions

                                                                                                          Advanced Notes

                                                                                                          History

                                                                                                          Calculator OS Version Description
                                                                                                          TI-84+CE 5.3.0 Added
                                                                                                          Property Value
                                                                                                          Hex Value $EF9F
                                                                                                          Categories
                                                                                                          Localizations
                                                                                                          • FR: Annuler effacer

                                                                                                          Undo Clear

                                                                                                          Overview

                                                                                                          Comment:CE OS 5.3+

                                                                                                          Syntax

                                                                                                          Undo Clear

                                                                                                          Description

                                                                                                          Examples

                                                                                                          Explanation 1

                                                                                                          code 1

                                                                                                          Explanation 2

                                                                                                          code 2

                                                                                                          Error Conditions

                                                                                                          Advanced Notes

                                                                                                          History

                                                                                                          Calculator OS Version Description
                                                                                                          TI-84+CE 5.3.0 Added
                                                                                                          Property Value
                                                                                                          Hex Value $EFA0
                                                                                                          Categories
                                                                                                          Localizations
                                                                                                          • FR: Insérer ligne ↑

                                                                                                          Insert Line Above

                                                                                                          Overview

                                                                                                          Comment:CE OS 5.3+

                                                                                                          Syntax

                                                                                                          Insert Line Above

                                                                                                          Description

                                                                                                          Examples

                                                                                                          Explanation 1

                                                                                                          code 1

                                                                                                          Explanation 2

                                                                                                          code 2

                                                                                                          Error Conditions

                                                                                                          Advanced Notes

                                                                                                          History

                                                                                                          Calculator OS Version Description
                                                                                                          TI-84+CE 5.3.0 Added
                                                                                                          Property Value
                                                                                                          Hex Value $EFA1
                                                                                                          Categories
                                                                                                          Localizations
                                                                                                          • FR: Couper ligne

                                                                                                          Cut Line

                                                                                                          Overview

                                                                                                          Comment:CE OS 5.3+

                                                                                                          Syntax

                                                                                                          Cut Line

                                                                                                          Description

                                                                                                          Examples

                                                                                                          Explanation 1

                                                                                                          code 1

                                                                                                          Explanation 2

                                                                                                          code 2

                                                                                                          Error Conditions

                                                                                                          Advanced Notes

                                                                                                          History

                                                                                                          Calculator OS Version Description
                                                                                                          TI-84+CE 5.3.0 Added
                                                                                                          Property Value
                                                                                                          Hex Value $EFA2
                                                                                                          Categories
                                                                                                          Localizations
                                                                                                          • FR: Copier ligne

                                                                                                          Copy Line

                                                                                                          Overview

                                                                                                          Comment:CE OS 5.3+

                                                                                                          Syntax

                                                                                                          Copy Line

                                                                                                          Description

                                                                                                          Examples

                                                                                                          Explanation 1

                                                                                                          code 1

                                                                                                          Explanation 2

                                                                                                          code 2

                                                                                                          Error Conditions

                                                                                                          Advanced Notes

                                                                                                          History

                                                                                                          Calculator OS Version Description
                                                                                                          TI-84+CE 5.3.0 Added
                                                                                                          Property Value
                                                                                                          Hex Value $EFA3
                                                                                                          Categories
                                                                                                          Localizations
                                                                                                          • FR: Coller ligne ↓

                                                                                                          Paste Line Below

                                                                                                          Overview

                                                                                                          Comment:CE OS 5.3+

                                                                                                          Syntax

                                                                                                          Paste Line Below

                                                                                                          Description

                                                                                                          Examples

                                                                                                          Explanation 1

                                                                                                          code 1

                                                                                                          Explanation 2

                                                                                                          code 2

                                                                                                          Error Conditions

                                                                                                          Advanced Notes

                                                                                                          History

                                                                                                          Calculator OS Version Description
                                                                                                          TI-84+CE 5.3.0 Added
                                                                                                          Property Value
                                                                                                          Hex Value $EFA4
                                                                                                          Categories
                                                                                                          Localizations
                                                                                                          • FR: Insérer commentaire ↑

                                                                                                          Insert Comment Above

                                                                                                          Overview

                                                                                                          Comment:CE OS 5.3+

                                                                                                          Syntax

                                                                                                          Insert Comment Above

                                                                                                          Description

                                                                                                          Examples

                                                                                                          Explanation 1

                                                                                                          code 1

                                                                                                          Explanation 2

                                                                                                          code 2

                                                                                                          Error Conditions

                                                                                                          Advanced Notes

                                                                                                          History

                                                                                                          Calculator OS Version Description
                                                                                                          TI-84+CE 5.3.0 Added
                                                                                                          Property Value
                                                                                                          Hex Value $EFA5
                                                                                                          Categories
                                                                                                          Localizations
                                                                                                          • FR: Quitter

                                                                                                          Quit Editor

                                                                                                          Overview

                                                                                                          Comment:CE OS 5.3+

                                                                                                          Syntax

                                                                                                          Quit Editor

                                                                                                          Description

                                                                                                          Examples

                                                                                                          Explanation 1

                                                                                                          code 1

                                                                                                          Explanation 2

                                                                                                          code 2

                                                                                                          Error Conditions

                                                                                                          Advanced Notes

                                                                                                          History

                                                                                                          Calculator OS Version Description
                                                                                                          TI-84+CE 5.3.0 Added
                                                                                                          Property Value
                                                                                                          Hex Value $EFA6
                                                                                                          Categories
                                                                                                            Localizations
                                                                                                            • FR: parmorceaux(

                                                                                                            piecewise(

                                                                                                            Overview

                                                                                                            New piecewise function to support entry of functions as they are seen in textbook. This command can be found in » MATH B:piecewise(

                                                                                                            Comment:CE OS 5.3+

                                                                                                            Availability: Token available everywhere.

                                                                                                            Syntax

                                                                                                            piecewise(

                                                                                                            Location

                                                                                                            math

                                                                                                            Description

                                                                                                            The piecewise( command is a new addition in the release of OS 5.3 for the TI-84 Plus CE. As implied, it allows for the graphing of piecewise functions in the Y= editor. The example code demonstrates how this works from within a program.

                                                                                                            :ClrDraw
:Input "Y1=",Str1
:Input "Y2=",Str2
:Str1→Y1
:Str2→Y2
:FnOff
:"piecewise(Y1,X≥0,Y2,X<0→Y3
:DispGraph

                                                                                                            Advanced Uses

                                                                                                            One use of the piecewise( function is to evaluate an expression for a given value of X. For example:

                                                                                                            :piecewise(X²+2,X≥0

                                                                                                            This code will return the value of the expression if X≥0. So if X=0, then the program will return a value of 2. If X=3, it will return a value of 11. If X=-5, it will return an error.

                                                                                                            Optimization

                                                                                                            This command can simplify and compact the usage of piecewise expressions in programs. If you have less than 6 conditions that will never overlap, and they all affect a single variable, you can use the piecewise( command to make your code smaller, as shown below. Beware of comparability, though.

                                                                                                            :If X<2
:Then
:4.5X→N
:Else
:8X+3→N
:End
can be
:piecewise(4.5X,X<2,8X+3,X≥2→N

                                                                                                            Error Conditions

                                                                                                            • ERR:INVALID is thrown if expressions are not defined.
                                                                                                            • ERR:DATA TYPE is thrown if a quotation mark is not placed before a piecewise command that is to be stored to an equation variable.

                                                                                                            See Also

                                                                                                            Source: parts of this page were written by the following TI|BD contributors: Battlesquid, iPhoenixOnTIBD, kg583, Myles_Zadok.

                                                                                                            History

                                                                                                            Calculator OS Version Description
                                                                                                            TI-84+CE 5.3.0 Added
                                                                                                            Property Value
                                                                                                            Hex Value $F0
                                                                                                            Categories
                                                                                                            Localizations
                                                                                                            • FR: ^

                                                                                                            ^

                                                                                                            Overview

                                                                                                            Availability: Token available everywhere.

                                                                                                            Syntax

                                                                                                            ^

                                                                                                            Description

                                                                                                            Examples

                                                                                                            Explanation 1

                                                                                                            code 1

                                                                                                            Explanation 2

                                                                                                            code 2

                                                                                                            Error Conditions

                                                                                                            Advanced Notes

                                                                                                            History

                                                                                                            Calculator OS Version Description
                                                                                                            TI-82 1.0 Added
                                                                                                            Property Value
                                                                                                            Hex Value $F1
                                                                                                            Categories
                                                                                                            Localizations
                                                                                                            • FR: ˣ√

                                                                                                            ˣ√

                                                                                                            Overview

                                                                                                            Availability: Token available everywhere.

                                                                                                            Syntax

                                                                                                            ˣ√

                                                                                                            Description

                                                                                                            Examples

                                                                                                            Explanation 1

                                                                                                            code 1

                                                                                                            Explanation 2

                                                                                                            code 2

                                                                                                            Error Conditions

                                                                                                            Advanced Notes

                                                                                                            History

                                                                                                            Calculator OS Version Description
                                                                                                            TI-82 1.0 Added
                                                                                                            Property Value
                                                                                                            Hex Value $F2
                                                                                                            Categories
                                                                                                            Localizations
                                                                                                            • FR: Stats 1-Var

                                                                                                            1-Var Stats

                                                                                                            Overview

                                                                                                            Performs one-variable analysis on the data in Xlistname with frequency freqlist.

                                                                                                            Availability: Token available everywhere.

                                                                                                            Syntax

                                                                                                            1-VarStats [Xlistname,freqlist]

                                                                                                            Arguments

                                                                                                            NameTypeOptional
                                                                                                            XlistnamelistYes
                                                                                                            freqlistlistYes

                                                                                                            Location

                                                                                                            stat, CALC, 1:1-Var Stats

                                                                                                            Description

                                                                                                            This command calculates a bunch of common (and a few uncommon) statistics for a list (it uses L1 by default, but you can use any list by supplying it as an argument). You have to store the list to a variable first, though, before calculating statistics for it. For example:

                                                                                                            :{5,12,7,8,4,9→L1
:1-Var Stats

                                                                                                            Like other statistical commands, you can use a frequency list as well, for cases where one element occurs more times than another (you can do this with a normal list, too, but that might be inconvenient when an element occurs very many times). For example:

                                                                                                            :{1,2,3→L1
:{5,3,2→L2
:1-Var Stats L1,L2

                                                                                                            is the frequency-list equivalent of:

                                                                                                            :{1,1,1,1,1,2,2,2,3,3→L1
:1-Var Stats

                                                                                                            When you're running it from the home screen, 1-Var Stats will display the statistics; this won't happen if you do it inside a program. Either way, it will also store what it calculated to the statistics variables found in VARS>Statistics… The variables 1-Var Stats affects are:

                                                                                                            • \(\overline{\textrm{x}}\) is the mean (average) of the elements, as returned by mean(
                                                                                                            • Σx is the sum of the elements, as returned by sum(
                                                                                                            • Σx² is the sum of the squares of the elements
                                                                                                            • Sx is the sample standard deviation, as returned by stdDev(
                                                                                                            • σx is population standard deviation
                                                                                                            • n is the number of elements in the list, as returned by dim(
                                                                                                            • minX is the minimum value, as returned by min(
                                                                                                            • Q1 is the first quartile
                                                                                                            • Med is the median, as returned by median(
                                                                                                            • Q3 is the third quartile
                                                                                                            • maxX is the maximum value, as returned by max(

                                                                                                            1-Var Stats will not work with "reserved" list names that the calculator uses internally. The only known such reserved list is the list RESID, and there's no reason to suspect there are any others. Ans, TblInput, and any expression which resolves to a list, are also not appropriate for this command: store all of these to a list before doing 1-Var Stats on them.

                                                                                                            Optimization

                                                                                                            Aside from statistical analysis, 1-Var Stats can also be used when you want to use the values it calculates more than once. This will save on size, since, for example Σx takes up less space than sum(L1), but considering how many calculations 1-Var Stats makes, it will usually be slower. Here's a short example which saves 1 byte:

                                                                                                            :Disp "RANGE:",max(L1)-min(L1
can be
:1-Var Stats
:Disp "RANGE:",maxX-minX

                                                                                                            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

                                                                                                            History

                                                                                                            Calculator OS Version Description
                                                                                                            TI-82 1.0 Added
                                                                                                            Property Value
                                                                                                            Hex Value $F3
                                                                                                            Categories
                                                                                                            Localizations
                                                                                                            • FR: Stats 2-Var

                                                                                                            2-Var Stats

                                                                                                            Overview

                                                                                                            Performs two-variable analysis on the data in Xlistname and Ylistname with frequency freqlist.

                                                                                                            Availability: Token available everywhere.

                                                                                                            Syntax

                                                                                                            2-VarStats [Xlistname,Ylistname,freqlist]

                                                                                                            Arguments

                                                                                                            NameTypeOptional
                                                                                                            XlistnamelistYes
                                                                                                            YlistnamelistYes
                                                                                                            freqlistlistYes

                                                                                                            Location

                                                                                                            stat, CALC, 2:2-Var Stats

                                                                                                            Description

                                                                                                            This command calculates a bunch of common (and a few uncommon) statistics for a pair of lists (it uses L1 and L2 by default, but you can use any list by supplying it as an argument). You have to store the lists to variables first, though, before calculating statistics for them. For example:

                                                                                                            :{5,12,7,8,4,9→L1
:{1,0,2,5,7,4→L2
:2-Var Stats

                                                                                                            The calculator treats the two lists as a list of ordered pairs. Some of the statistics calculated assume that this is the case, and the two lists are the same size: an error will occur if the lists don't match.

                                                                                                            Like other statistical commands, you can use a frequency list as well, for cases where one element occurs more times than another (you can do this with a normal list, too, but that might be inconvenient when an element occurs very many times). There is only one frequency list for both data lists, and the frequency applies to the ordered pair formed by an element taken from each list. For example:

                                                                                                            :{1,2,3→L1
:{1,2,3→L2
:{5,3,2→L3
:2-Var Stats L1,L2,L3

                                                                                                            is the frequency-list equivalent of:

                                                                                                            :{1,1,1,1,1,2,2,2,3,3→L1
:{1,1,1,1,1,2,2,2,3,3→L2
:2-Var Stats

                                                                                                            When you're running it from the home screen, 2-Var Stats will display the statistics; this won't happen if you do it inside a program. Either way, it will also store what it calculated to the statistics variables found in VARS>Statistics… The variables 2-Var Stats affects are:

                                                                                                            • \(\definecolor{darkgreen}{rgb}{0.90,0.91,0.859}\pagecolor{darkgreen} \overline{\textrm{x}}\) is the mean (average) of the first list
                                                                                                            • Σx is the sum of the first list
                                                                                                            • Σx² is the sum of the squares of the first list
                                                                                                            • Sx is the sample standard deviation of the first list
                                                                                                            • σx is population standard deviation of the first list
                                                                                                            • minX is the minimum element of the first list
                                                                                                            • maxX is the maximum element of the first list
                                                                                                            • \(\definecolor{darkgreen}{rgb}{0.90,0.91,0.859}\pagecolor{darkgreen} \overline{\textrm{y}}\) is the mean (average) of the second list
                                                                                                            • Σy is the sum of the second list
                                                                                                            • Σy² is the sum of the squares of the second list
                                                                                                            • Sy is the sample standard deviation of the second list
                                                                                                            • σy is population standard deviation of the second list
                                                                                                            • minY is the minimum element of the second list
                                                                                                            • maxY is the maximum element of the second list
                                                                                                            • Σxy is the sum of products of each matching pair of elements in the lists
                                                                                                            • n is the number of elements in both lists

                                                                                                            2-Var Stats will not work with "reserved" list names that the calculator uses internally. The only known such reserved list is the list RESID, and there's no reason to suspect there are any others. Ans, TblInput, and any expression which resolves to a list, are also not appropriate for this command: store all of these to a list before doing 2-Var Stats on them.

                                                                                                            Advanced uses

                                                                                                            If you consider the two lists to be vectors, then Σxy is their dot product, and Σx² and Σy² are the squares of their norms; math done with these and other statistics can produce the shortest (but not necessarily quickest) way to calculate many vector operations.

                                                                                                            Optimization

                                                                                                            Aside from statistical analysis, 2-Var Stats can also be used when you want to use the values it calculates more than once. This will save on size, since, for example Σx takes up less space than sum(L1), but considering how many calculations 2-Var Stats makes, it will usually be slower.

                                                                                                            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Timothy Foster.

                                                                                                            History

                                                                                                            Calculator OS Version Description
                                                                                                            TI-82 1.0 Added
                                                                                                            Property Value
                                                                                                            Hex Value $F4
                                                                                                            Categories
                                                                                                            Localizations
                                                                                                            • FR: RegLin(a+bx)

                                                                                                            LinReg(a+bx)

                                                                                                            Overview

                                                                                                            Fits a linear regression model toXlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ.

                                                                                                            Availability: Token available everywhere.

                                                                                                            Syntax

                                                                                                            LinReg(a+bx) [Xlistname,Ylistname,freqlist,regequ]

                                                                                                            Arguments

                                                                                                            NameTypeOptional
                                                                                                            XlistnamelistYes
                                                                                                            YlistnamelistYes
                                                                                                            freqlistlistYes
                                                                                                            regequYes

                                                                                                            Location

                                                                                                            stat, CALC, 8:LinReg(a+bx)

                                                                                                            Description

                                                                                                            The LinReg(a+bx) command is one of several that can calculate the line of best fit through a set of points (it differs from LinReg(ax+b) only in the format of its output). To use it, you must first store the points to two lists: one of the x-coordinates and one of the y-coordinates, ordered so that the nth element of one list matches up with the nth element of the other list. L₁ and L₂ are the default lists to use, and the List Editor (STAT > Edit…) is a useful window for entering the points.

                                                                                                            In its simplest form, LinReg(a+bx) takes no arguments, and calculates a best fit line through the points in L₁ and L₂:

                                                                                                            :{9,13,21,30,31,31,34→L₁
:{260,320,420,530,560,550,590→L₂
:LinReg(a+bx)

                                                                                                            On the home screen, or as the last line of a program, this will display the equation of the line of best fit: you'll be shown the format, y=a+bx, and the values of a and b. It will also be stored in the RegEQ variable, but you won't be able to use this variable in a program - accessing it just pastes the equation wherever your cursor was. Finally, the statistical variables a, b, r, and r² will be set as well. These latter two variables will be displayed only if "Diagnostic Mode" is turned on (see DiagnosticOn and DiagnosticOff).

                                                                                                            You don't have to do the regression on L₁ and L₂, but if you don't you'll have to enter the names of the lists after the command. For example:

                                                                                                            :{9,13,21,30,31,31,34→FAT
:{260,320,420,530,560,550,590→CALS
:LinReg(a+bx) ʟFAT,ʟCALS

                                                                                                            You can attach frequencies to points, for when a point occurs more than once, by supplying an additional argument - the frequency list. This list does not have to contain integer frequencies. If you add a frequency list, you must supply the names of the x-list and y-list as well, even when they're L₁ and L₂.

                                                                                                            Finally, you can enter an equation variable (such as Y₁) after the command, so that the line of best fit is stored to this equation automatically. This doesn't require you to supply the names of the lists, but if you do, the equation variable must come last. You can use polar, parametric, or sequential variables as well, but since the line of best fit will be in terms of X anyway, this doesn't make much sense.

                                                                                                            An example of LinReg(a+bx) with all the optional arguments:

                                                                                                            :{9,13,21,30,31,31,34→FAT
:{260,320,420,530,560,550,590→CALS
:{2,1,1,1,2,1,1→FREQ
:LinReg(a+bx) ʟFAT,ʟCALS,ʟFREQ,Y₁

                                                                                                            Advanced Uses (for programmers)

                                                                                                            LinReg(a+bx), along with LinReg(ax+b), can be used to convert a number to a string.

                                                                                                            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, jojo40605, thornahawk, Timothy Foster.

                                                                                                            History

                                                                                                            Calculator OS Version Description
                                                                                                            TI-82 1.0 Added
                                                                                                            Property Value
                                                                                                            Hex Value $F5
                                                                                                            Categories
                                                                                                            Localizations
                                                                                                            • FR: RegExp

                                                                                                            ExpReg

                                                                                                            Overview

                                                                                                            Fits an exponential regression model to Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ.

                                                                                                            Availability: Token available everywhere.

                                                                                                            Syntax

                                                                                                            ExpReg [Xlistname,Ylistname,freqlist,regequ]

                                                                                                            Arguments

                                                                                                            NameTypeOptional
                                                                                                            XlistnamelistYes
                                                                                                            YlistnamelistYes
                                                                                                            freqlistlistYes
                                                                                                            regequYes

                                                                                                            Location

                                                                                                            stat, CALC, 0:ExpReg

                                                                                                            Description

                                                                                                            ExpReg tries to fit an exponential curve (y=a*bx) through a set of points. To use it, you must first store the points to two lists: one of the x-coordinates and one of the y-coordinates ordered so that the Nth element of one list matches up with the Nth element of the other list. L₁ and L₂ are the default lists to use, and the List Editor (STAT > Edit…) is a useful window for entering the points.

                                                                                                            The calculator does this regression by taking the natural log ln( of the y-coordinates (this isn't stored anywhere) and then doing a linear regression. The result, ln(y)=ln(a)+x*ln(b), is transformed into y=eln(a)(eln(b))x, which is an exponential curve. This algorithm shows that if any y-coordinates are negative or 0, the calculator will instantly quit with ERR:DOMAIN.

                                                                                                            In its simplest form, ExpReg takes no arguments, and fits an exponential curve through the points in L₁ and L₂:

                                                                                                            :{9,13,21,30,31,31,34→L₁
:{260,320,420,530,560,550,590→L₂
:LnReg

                                                                                                            On the home screen, or as the last line of a program, this will display the equation of the curve: you'll be shown the format, y=a*b^x, and the values of a and b. It will also be stored in the RegEQ variable, but you won't be able to use this variable in a program - accessing it just pastes the equation wherever your cursor was. Finally, the statistical variables a, b, r, and r² will be set as well. These latter two variables will be displayed only if "Diagnostic Mode" is turned on (see DiagnosticOn and DiagnosticOff).

                                                                                                            You don't have to do the regression on L₁ and L₂, but if you don't you'll have to enter the names of the lists after the command. For example:

                                                                                                            :{9,13,21,30,31,31,34→FAT
:{260,320,420,530,560,550,590→CALS
:ExpReg ʟFAT,ʟCALS

                                                                                                            You can attach frequencies to points, for when a point occurs more than once, by supplying an additional argument - the frequency list. This list does not have to contain integer frequencies. If you add a frequency list, you must supply the names of the x-list and y-list as well, even when they're L₁ and L₂.

                                                                                                            Finally, you can enter an equation variable (such as Y₁) after the command, so that the curve's equation is stored in this variable automatically. This doesn't require you to supply the names of the lists, but if you do, the equation variable must come last. You can use polar, parametric, or sequential variables as well, but since the equation will be in terms of X anyway, this doesn't make much sense.

                                                                                                            An example of ExpReg with all the optional arguments:

                                                                                                            :{9,13,21,30,31,31,34→FAT
:{260,320,420,530,560,550,590→CALS
:{2,1,1,1,2,1,1→FREQ
:ExpReg ʟFAT,ʟCALS,ʟFREQ,Y1

                                                                                                            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Myles_Zadok, thornahawk, Timothy Foster.

                                                                                                            History

                                                                                                            Calculator OS Version Description
                                                                                                            TI-82 1.0 Added
                                                                                                            Property Value
                                                                                                            Hex Value $F6
                                                                                                            Categories
                                                                                                            Localizations
                                                                                                            • FR: RegLn

                                                                                                            LnReg

                                                                                                            Overview

                                                                                                            Fits a logarithmic regression model to Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ.

                                                                                                            Availability: Token available everywhere.

                                                                                                            Syntax

                                                                                                            LnReg [Xlistname,Ylistname,freqlist,regequ]

                                                                                                            Arguments

                                                                                                            NameTypeOptional
                                                                                                            XlistnamelistYes
                                                                                                            YlistnamelistYes
                                                                                                            freqlistlistYes
                                                                                                            regequYes

                                                                                                            Location

                                                                                                            stat, CALC, 9:LnReg

                                                                                                            Description

                                                                                                            LnReg tries to fit a logarithmic curve (y=a+b*lnx) through a set of points. To use it, you must first store the points to two lists: one of the x-coordinates and one of the y-coordinates, ordered so that the nth element of one list matches up with the nth element of the other list. L₁ and L₂ are the default lists to use, and the List Editor (STAT > Edit…) is a useful window for entering the points.

                                                                                                            The calculator does this regression by taking the natural log ln( of the x-coordinates (this isn't stored anywhere) and then doing a linear regression. This means that if any x-coordinates are negative or 0, the calculator will instantly quit with ERR:DOMAIN.

                                                                                                            In its simplest form, LnReg takes no arguments, and fits a logarithmic curve through the points in L₁ and L₂:

                                                                                                            :{9,13,21,30,31,31,34→L₁
:{260,320,420,530,560,550,590→L₂
:LnReg

                                                                                                            On the home screen, or as the last line of a program, this will display the equation of the curve: you'll be shown the format, y=a+b*ln(x), and the values of a and b. It will also be stored in the RegEQ variable, but you won't be able to use this variable in a program - accessing it just pastes the equation wherever your cursor was. Finally, the statistical variables a, b, r, and r² will be set as well. These latter two variables will be displayed only if "Diagnostic Mode" is turned on (see DiagnosticOn and DiagnosticOff).

                                                                                                            You don't have to do the regression on L₁ and L₂, but if you don't you'll have to enter the names of the lists after the command. For example:

                                                                                                            :{9,13,21,30,31,31,34→FAT
:{260,320,420,530,560,550,590→CALS
:LnReg ʟFAT,ʟCALS

                                                                                                            You can attach frequencies to points, for when a point occurs more than once, by supplying an additional argument - the frequency list. This list does not have to contain integer frequencies. If you add a frequency list, you must supply the names of the x-list and y-list as well, even when they're L₁ and L₂.

                                                                                                            Finally, you can enter an equation variable (such as Y₁) after the command, so that the curve's equation is stored to this variable automatically. This doesn't require you to supply the names of the lists, but if you do, the equation variable must come last. You can use polar, parametric, or sequential variables as well, but since the equation will be in terms of X anyway, this doesn't make much sense.

                                                                                                            An example of LnReg with all the optional arguments:

                                                                                                            :{9,13,21,30,31,31,34→FAT
:{260,320,420,530,560,550,590→CALS
:{2,1,1,1,2,1,1→FREQ
:LnReg ʟFAT,ʟCALS,ʟFREQ,Y₁

                                                                                                            Error Conditions

                                                                                                            • ERR:DOMAIN is thrown if any x-coordinates are negative or 0.

                                                                                                            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, thornahawk, Timothy Foster.

                                                                                                            History

                                                                                                            Calculator OS Version Description
                                                                                                            TI-82 1.0 Added
                                                                                                            Property Value
                                                                                                            Hex Value $F7
                                                                                                            Categories
                                                                                                            Localizations
                                                                                                            • FR: RegPuiss

                                                                                                            PwrReg

                                                                                                            Overview

                                                                                                            Fits a power regression model to Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ.

                                                                                                            Availability: Token available everywhere.

                                                                                                            Syntax

                                                                                                            PwrReg [Xlistname,Ylistname,freqlist,regequ]

                                                                                                            Arguments

                                                                                                            NameTypeOptional
                                                                                                            XlistnamelistYes
                                                                                                            YlistnamelistYes
                                                                                                            freqlistlistYes
                                                                                                            regequYes

                                                                                                            Location

                                                                                                            stat, CALC, A:PwrReg

                                                                                                            Description

                                                                                                            PwrReg tries to fit a power curve (y=a*xb) through a set of points. To use it, you must first store the points to two lists: one of the x-coordinates and one of the y-coordinates, ordered so that the nth element of one list matches up with the nth element of the other list. L₁ and L₂ are the default lists to use, and the List Editor (STAT > Edit…) is a useful window for entering the points.

                                                                                                            The calculator does this regression by taking the natural log ln( of the x- and of the y-coordinates (this isn't stored anywhere) and then doing a linear regression. The result, ln(y)=bln(x)+ln(a), is transformed into y=eln(a)xb, which is a power curve. This algorithm shows that if any coordinates are negative or 0, the calculator will instantly quit with ERR:DOMAIN.

                                                                                                            In its simplest form, PwrReg takes no arguments, and fits a power curve through the points in L₁ and L₂:

                                                                                                            :{9,13,21,30,31,31,34→L₁
:{260,320,420,530,560,550,590→L₂
:LnReg

                                                                                                            On the home screen, or as the last line of a program, this will display the equation of the curve: you'll be shown the format, y=a*x^b, and the values of a and b. It will also be stored in the RegEQ variable, but you won't be able to use this variable in a program - accessing it just pastes the equation wherever your cursor was. Finally, the statistical variables a, b, r, and r² will be set as well. These latter two variables will be displayed only if "Diagnostic Mode" is turned on (see DiagnosticOn and DiagnosticOff).

                                                                                                            You don't have to do the regression on L₁ and L₂, but if you don't you'll have to enter the names of the lists after the command. For example:

                                                                                                            :{9,13,21,30,31,31,34→FAT
:{260,320,420,530,560,550,590→CALS
:PwrReg ʟFAT,ʟCALS

                                                                                                            You can attach frequencies to points, for when a point occurs more than once, by supplying an additional argument - the frequency list. This list does not have to contain integer frequencies. If you add a frequency list, you must supply the names of the x-list and y-list as well, even when they're L₁ and L₂.

                                                                                                            Finally, you can enter an equation variable (such as Y₁) after the command, so that the curve's equation is stored to this variable automatically. This doesn't require you to supply the names of the lists, but if you do, the equation variable must come last. You can use polar, parametric, or sequential variables as well, but since the equation will be in terms of X anyway, this doesn't make much sense.

                                                                                                            An example of PwrReg with all the optional arguments:

                                                                                                            :{9,13,21,30,31,31,34→FAT
:{260,320,420,530,560,550,590→CALS
:{2,1,1,1,2,1,1→FREQ
:PwrReg ʟFAT,ʟCALS,ʟFREQ,Y1

                                                                                                            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, thornahawk, Timothy Foster.

                                                                                                            History

                                                                                                            Calculator OS Version Description
                                                                                                            TI-82 1.0 Added
                                                                                                            Property Value
                                                                                                            Hex Value $F8
                                                                                                            Categories
                                                                                                            Localizations
                                                                                                            • FR: Med-Med

                                                                                                            Med-Med

                                                                                                            Overview

                                                                                                            Fits a median-median model to Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ.

                                                                                                            Availability: Token available everywhere.

                                                                                                            Syntax

                                                                                                            Med-Med [Xlistname,Ylistname,freqlist,regequ]

                                                                                                            Arguments

                                                                                                            NameTypeOptional
                                                                                                            XlistnamelistYes
                                                                                                            YlistnamelistYes
                                                                                                            freqlistlistYes
                                                                                                            regequYes

                                                                                                            Location

                                                                                                            stat, CALC, 3:Med-Med

                                                                                                            Description

                                                                                                            The Med-Med command is one of several that can calculate a line of best fit through a set of points. However, unlike the LinReg(ax+b) and LinReg(a+bx) commands, which generate the same result in different formats, Med-Med produces a different line entirely, known as the 'median fit line' or the 'median-median model'. This model is more resistant to outliers than the best-fit line produced by LinReg(ax+b)-type commands, in much the same way that the median of a set of data is more resistant to outliers than the mean. The process of calculating a median fit line is roughly as follows (reference):

                                                                                                            1. Divide the data into three equal groups by their x-values (the smallest third, the middle third, and the largest third)
                                                                                                            2. Find the "median point" for each group by pairing the median x-value in the group with the median y-value (this need not be an actual data point).
                                                                                                            3. These points are stored to (x₁,y₁), (x₂,y₂), and (x₃,y₃) on the calculator.
                                                                                                            4. Find the line passing through the median point for the first and third group.
                                                                                                            5. Shift this line one-third of the way toward the median point of the second group.

                                                                                                            To use the Med-Med command, you must first store the points to two lists: one of the x-coordinates and one of the y-coordinates, ordered so that the nth element of one list matches up with the nth element of the other list. L₁ and L₂ are the default lists to use, and the List Editor (STAT > Edit…) is a useful window for entering the points. As you can see from the steps shown above, Med-Med requires at least three points with different x-values to work with.

                                                                                                            In its simplest form, Med-Med takes no arguments, and calculates a regression line through the points in L₁ and L₂:

                                                                                                            :{9,13,21,30,31,31,34→L₁
:{260,320,420,530,560,550,590→L₂
:Med-Med

                                                                                                            On the home screen, or as the last line of a program, this will display the equation of the regression line: you'll be shown the format, y=ax+b, and the values of a and b. It will also be stored in the RegEQ variable, but you won't be able to use this variable in a program - accessing it just pastes the equation wherever your cursor was. Finally, the statistical variables a and b will be set as well. There are no diagnostics available for the Med-Med command, so r and r² will not be calculated or displayed even if you run DiagnosticOn.

                                                                                                            You don't have to do the regression on L₁ and L₂, but if you don't you'll have to enter the names of the lists after the command. For example:

                                                                                                            :{9,13,21,30,31,31,34→FAT
:{260,320,420,530,560,550,590→CALS
:Med-Med ʟFAT,ʟCALS

                                                                                                            You can attach frequencies to points, for when a point occurs more than once, by supplying an additional argument - the frequency list. This list does not have to contain integer frequencies. If you add a frequency list, you must supply the names of the x-list and y-list as well, even when they're L₁ and L₂.

                                                                                                            Finally, you can enter an equation variable (such as Y₁) after the command, so that the line of best fit is stored to this equation automatically. This doesn't require you to supply the names of the lists, but if you do, the equation variable must come last. You can use polar, parametric, or sequential variables as well, but since the line of best fit will be in terms of X anyway, this doesn't make much sense.

                                                                                                            An example of Med-Med with all the optional arguments:

                                                                                                            :{9,13,21,30,31,31,34→FAT
:{260,320,420,530,560,550,590→CALS
:{2,1,1,1,2,1,1→FREQ
:Med-Med ʟFAT,ʟCALS,ʟFREQ,Y₁

                                                                                                            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, thornahawk, Timothy Foster.

                                                                                                            History

                                                                                                            Calculator OS Version Description
                                                                                                            TI-82 1.0 Added
                                                                                                            Property Value
                                                                                                            Hex Value $F9
                                                                                                            Categories
                                                                                                            Localizations
                                                                                                            • FR: RegQuad

                                                                                                            QuadReg

                                                                                                            Overview

                                                                                                            Fits a quadratic regression model toXlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ.

                                                                                                            Availability: Token available everywhere.

                                                                                                            Syntax

                                                                                                            QuadReg [Xlistname,Ylistname,freqlist,regequ]

                                                                                                            Arguments

                                                                                                            NameTypeOptional
                                                                                                            XlistnamelistYes
                                                                                                            YlistnamelistYes
                                                                                                            freqlistlistYes
                                                                                                            regequYes

                                                                                                            Location

                                                                                                            stat, CALC, 5:QuadReg

                                                                                                            Description

                                                                                                            The QuadReg command can calculate the best fit quadratic through a set of points. To use it, you must first store the points to two lists: one of the x-coordinates and one of the y-coordinates, ordered so that the nth element of one list matches up with the nth element of the other list. L₁ and L₂ are the default lists to use, and the List Editor (STAT > Edit…) is a useful window for entering the points. You must have at least 3 points, because there are infinitely many quadratics that can go through 2 points or 1 point.

                                                                                                            In its simplest form, QuadReg takes no arguments, and calculates a quadratic through the points in L₁ and L₂:

                                                                                                            :{9,13,21,30,31,31,34→L₁
:{260,320,420,530,560,550,590→L₂
:QuadReg

                                                                                                            On the home screen, or as the last line of a program, this will display the equation of the quadratic: you'll be shown the format, y=ax²+bx+c, and the values of a, b, and c. It will also be stored in the RegEQ variable, but you won't be able to use this variable in a program - accessing it just pastes the equation wherever your cursor was. Finally, the statistical variables a, b, c, and R² will be set as well. This latter variable will be displayed only if "Diagnostic Mode" is turned on (see DiagnosticOn and DiagnosticOff).

                                                                                                            You don't have to do the regression on L₁ and L₂, but if you don't you'll have to enter the names of the lists after the command. For example:

                                                                                                            :{9,13,21,30,31,31,34→FAT
:{260,320,420,530,560,550,590→CALS
:QuadReg ʟFAT,ʟCALS

                                                                                                            You can attach frequencies to points, for when a point occurs more than once, by supplying an additional argument - the frequency list. This list does not have to contain integer frequencies. If you add a frequency list, you must supply the names of the x-list and y-list as well, even when they're L₁ and L₂.

                                                                                                            Finally, you can enter an equation variable (such as Y₁) after the command, so that the quadratic is stored to this equation automatically. This doesn't require you to supply the names of the lists, but if you do, the equation variable must come last. You can use polar, parametric, or sequential variables as well, but since the quadratic will be in terms of X anyway, this doesn't make much sense.

                                                                                                            An example of QuadReg with all the optional arguments:

                                                                                                            :{9,13,21,30,31,31,34→FAT
:{260,320,420,530,560,550,590→CALS
:{2,1,1,1,2,1,1→FREQ
:QuadReg ʟFAT,ʟCALS,ʟFREQ,Y₁

                                                                                                            Advanced

                                                                                                            Note that even if a relationship is actually linear, since a quadratic regression has all the freedom of a linear regression and more, it will produce a better R² value, especially if the number of terms is small, and may lead you to (falsely) believe that a relationship is quadratic when it actually isn't. Take the correlation constant with a grain of salt, and consider if the fit is really that much better at the expense of added complexity, and if there's any reason to believe the relationship between the variables may be quadratic.

                                                                                                            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, thornahawk, Timothy Foster.

                                                                                                            History

                                                                                                            Calculator OS Version Description
                                                                                                            TI-82 1.0 Added
                                                                                                            Property Value
                                                                                                            Hex Value $FA
                                                                                                            Categories
                                                                                                            Localizations
                                                                                                            • FR: EffListe

                                                                                                            ClrList

                                                                                                            Overview

                                                                                                            Sets the dimension of one or more listnames to 0.

                                                                                                            Availability: Token available everywhere.

                                                                                                            Syntax

                                                                                                            ClrListlistname1[,listname2, ...,listname n]

                                                                                                            Arguments

                                                                                                            NameTypeOptional
                                                                                                            listname1listName
                                                                                                            listname2listNameYes
                                                                                                            listname nlistYes

                                                                                                            Location

                                                                                                            stat, EDIT, 4:ClrList

                                                                                                            Description

                                                                                                            ClrList sets the length of a list (or several lists) to 0. This is virtually equivalent to deleting the list, except for several differences:

                                                                                                            • The list still exists — it will be shown in the memory management menu and the list menu
                                                                                                            • Calling the dim( command on it will return 0, rather than an error.
                                                                                                            • ClrList can clear multiple lists at the same time

                                                                                                            Advanced Uses

                                                                                                            You might use ClrList when building up a list element by element and using dim( in the process:

                                                                                                            :ClrList L1
:While 10>dim(L1
:Input X
:X→L1(1+dim(L1
:End

                                                                                                            Optimization

                                                                                                            Using DelVar instead of ClrList allows you to save a tiny bit of memory (between 12 and 16 bytes) that ClrList doesn't delete, while keeping almost every aspect of the list clearing the same. If you are clearing several lists, you can separate them with commas as the arguments to ClrList, which can save space. Using ClrList is also substantially faster than DelVar if the list is going to be cleared many times.

                                                                                                            Error Conditions

                                                                                                            • ERR:SYNTAX is thrown if you leave off the ʟ symbol when referring to a custom list (i.e., ClrList B will not work; you have to use ClrList ʟB).

                                                                                                            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, jonbush, Myles_Zadok, Timothy Foster.

                                                                                                            History

                                                                                                            Calculator OS Version Description
                                                                                                            TI-82 1.0 Added
                                                                                                            Property Value
                                                                                                            Hex Value $FB
                                                                                                            Categories
                                                                                                            Localizations
                                                                                                            • FR: EffTable

                                                                                                            ClrTable

                                                                                                            Overview

                                                                                                            Clears all values from the table.

                                                                                                            Availability: Token only available from within the Basic editor.

                                                                                                            Syntax

                                                                                                            ClrTable

                                                                                                            Location

                                                                                                            prgm, I/O, 9:ClrTable

                                                                                                            Description

                                                                                                            The ClrTable command clears all calculations for the table screen shown if you press 2nd TABLE. That is, all already-calculated values in the table are cleared, and TblInput is deleted. In IndpntAuto and DependAuto mode, this usually isn't noticeable because the table will be recalculated almost immediately when you next look at it (unless one of the entered functions is so complicated it takes a while to calculate). This mainly has an effect in IndpntAsk or DependAsk mode, where the corresponding parts of the table will be cleared entirely.

                                                                                                            Advanced Uses

                                                                                                            As a side effect, ClrTable seems to have all the effects of ClrDraw — it clears the graph screen, and any equations or plots will be regraphed the next time the graph screen is displayed.

                                                                                                            Command Timings

                                                                                                            ClrTable and ClrDraw take the same amount of time to clear the screen.

                                                                                                            Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Myles_Zadok.

                                                                                                            History

                                                                                                            Calculator OS Version Description
                                                                                                            TI-82 1.0 Added
                                                                                                            Property Value
                                                                                                            Hex Value $FC
                                                                                                            Categories
                                                                                                            Localizations
                                                                                                            • FR: Histogramme

                                                                                                            Histogram

                                                                                                            Overview

                                                                                                            Used as the "type" argument in the command
                                                                                                            Where # gives Plot1, Plot2 or Plot3.

                                                                                                            Availability: Token only available from within the Basic editor.

                                                                                                            Syntax

                                                                                                            Plot#(type,Xlist[,freqlist,color#])

                                                                                                            Arguments

                                                                                                            NameTypeOptional
                                                                                                            typeHistogram token
                                                                                                            Xlistlist
                                                                                                            freqlistlist
                                                                                                            color#colorNum

                                                                                                            Location

                                                                                                            2nd, stat plot, TYPE

                                                                                                            Description

                                                                                                            The commands Plot1(, Plot2(, and Plot3(, which are identical except for which stat plot (1, 2, or 3) they affect, define their corresponding stat plot. When the stat plot is defined, it is also turned on so no PlotsOn command is necessary.

                                                                                                            The first argument of the commands is always the type of plot, and is one of Scatter, xyLine, Histogram, Boxplot, ModBoxplot, and NormProbPlot - these types are found in the TYPE submenu of the stat plot menu. The other arguments vary. For all but Histogram and Boxplot, there is a mark argument - this is a dot, a cross, or a box, symbols that can be found in the MARK submenu of the stat plot menu. On color calculators, there is an optional final argument to specify the color of the plot.

                                                                                                            Scatter plot

                                                                                                            Plot#(Scatter, x-list, y-list, mark) defines a scatter plot. The points defined by x-list and y-list are plotted using mark on the graph screen.

                                                                                                            x-list and y-list must be the same length.

                                                                                                            xyLine plot

                                                                                                            Plot#(xyLine, x-list, y-list, mark) defines an xyLine plot. Similarly to a scatter plot, the points defined by x-list and y-list are plotted using mark on the graph screen, but with an xyLine plot they are also connected by a line, in the order that they occur in the lists.

                                                                                                            x-list and y-list must be the same length.

                                                                                                            Histogram plot

                                                                                                            Plot#(Histogram, x-list, freq list) defines a Histogram plot. The x-axis is divided into intervals that are Xscl wide. A bar is drawn in in each interval whose height corresponds to the number of points in the interval. Points that are not between Xmin and Xmax are not tallied.

                                                                                                            Xscl must not be too small - it can divide the screen into no more than 47 different bars.

                                                                                                            Box plot

                                                                                                            Plot#(Boxplot, x-list, freq list) defines a box plot. A rectangular box is drawn whose left edge is Q1 (the first quartile) of the data, and whose right edge is Q3 (the third quartile). A vertical segment is drawn within the box at the median, and 'whiskers' are drawn from the box to the minimum and maximum data points.

                                                                                                            The box plot ignores the Ymax and Ymin dimensions of the screen, and any plots that aren't box plots or modified box plots. Each box plot takes approximately 1/3 of the screen in height, and if more than one are plotted, they will take up different areas of the screen.

                                                                                                            Modified box plot

                                                                                                            Plot#(ModBoxplot, x-list, freq list, mark) defines a modified box plot. This is almost entirely like the normal box plot, except that it also draws outliers. Whiskers are only drawn to the furthers point within 1.5 times the interquartile range (Q3-Q1) of the box. Beyond this point, data points are drawn individually, using mark.

                                                                                                            The box plot ignores the Ymax and Ymin dimensions of the screen, and any plots that aren't box plots or modified box plots. Each box plot takes approximately 1/3 of the screen in height, and if more than one are plotted, they will take up different areas of the screen.

                                                                                                            Normal probability plot

                                                                                                            Plot#(NormProbPlot, data list, data axis, mark) defines a normal probability plot. The mean and standard deviation of the data are calculated. Then for each point, the number of standard deviations it is from the mean is calculated, and the point is plotted against this number using mark. data axis can be either X or Y: it determines whether the value of a point determines it's x-coordinate or y-coordinate.

                                                                                                            The point behind this rather convoluted process is to test the extent to which the data is normally distributed. If it follows the normal distribution closely, then the result will be close to a straight line - otherwise it will be curved.

                                                                                                            Advanced Uses

                                                                                                            After doing a regression, a scatter plot of ʟRESID against the x-list is a useful measure of the effectiveness of the regression. If the plot appears random, this is a good sign; if there is a pattern to the plot, this means it's likely that a better regression model exists.

                                                                                                            Optimization

                                                                                                            The ʟ symbol at the beginning of list names can be omitted everywhere in this command.

                                                                                                            In addition, every element except the plot type and the data list or data lists are optional, and take on the following default values:

                                                                                                            • freq list is 1 by default, meaning that all frequencies are 1.
                                                                                                            • mark is the box by default.
                                                                                                            • data axis is X by default.

                                                                                                            Error Conditions

                                                                                                            • ERR:DIM MISMATCH is thrown if the x and y lists, or the data and frequency lists, have different dimensions.
                                                                                                            • ERR:STAT is thrown if Xscl is too small in the case of a Histogram.

                                                                                                            All errors are thrown when plotting the stat plot, as opposed to when the command is executed, and do not provide a 2:Goto option.

                                                                                                            Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Myles_Zadok.

                                                                                                            History

                                                                                                            Calculator OS Version Description
                                                                                                            TI-82 1.0 Added
                                                                                                            Property Value
                                                                                                            Hex Value $FD
                                                                                                            Categories
                                                                                                            Localizations
                                                                                                            • FR: Polygone

                                                                                                            xyLine

                                                                                                            Overview

                                                                                                            Used as the "type" argument in the command
                                                                                                            Where # gives Plot1, Plot2 or Plot3.

                                                                                                            Availability: Token available everywhere.

                                                                                                            Syntax

                                                                                                            Plot#(type,Xlist[,freqlist,color#])

                                                                                                            Arguments

                                                                                                            NameTypeOptional
                                                                                                            typexyLine token
                                                                                                            Xlistlist
                                                                                                            freqlistlist
                                                                                                            color#colorNum

                                                                                                            Location

                                                                                                            2nd, stat plot, TYPE

                                                                                                            Description

                                                                                                            The commands Plot1(, Plot2(, and Plot3(, which are identical except for which stat plot (1, 2, or 3) they affect, define their corresponding stat plot. When the stat plot is defined, it is also turned on so no PlotsOn command is necessary.

                                                                                                            The first argument of the commands is always the type of plot, and is one of Scatter, xyLine, Histogram, Boxplot, ModBoxplot, and NormProbPlot - these types are found in the TYPE submenu of the stat plot menu. The other arguments vary. For all but Histogram and Boxplot, there is a mark argument - this is a dot, a cross, or a box, symbols that can be found in the MARK submenu of the stat plot menu. On color calculators, there is an optional final argument to specify the color of the plot.

                                                                                                            Scatter plot

                                                                                                            Plot#(Scatter, x-list, y-list, mark) defines a scatter plot. The points defined by x-list and y-list are plotted using mark on the graph screen.

                                                                                                            x-list and y-list must be the same length.

                                                                                                            xyLine plot

                                                                                                            Plot#(xyLine, x-list, y-list, mark) defines an xyLine plot. Similarly to a scatter plot, the points defined by x-list and y-list are plotted using mark on the graph screen, but with an xyLine plot they are also connected by a line, in the order that they occur in the lists.

                                                                                                            x-list and y-list must be the same length.

                                                                                                            Histogram plot

                                                                                                            Plot#(Histogram, x-list, freq list) defines a Histogram plot. The x-axis is divided into intervals that are Xscl wide. A bar is drawn in in each interval whose height corresponds to the number of points in the interval. Points that are not between Xmin and Xmax are not tallied.

                                                                                                            Xscl must not be too small - it can divide the screen into no more than 47 different bars.

                                                                                                            Box plot

                                                                                                            Plot#(Boxplot, x-list, freq list) defines a box plot. A rectangular box is drawn whose left edge is Q1 (the first quartile) of the data, and whose right edge is Q3 (the third quartile). A vertical segment is drawn within the box at the median, and 'whiskers' are drawn from the box to the minimum and maximum data points.

                                                                                                            The box plot ignores the Ymax and Ymin dimensions of the screen, and any plots that aren't box plots or modified box plots. Each box plot takes approximately 1/3 of the screen in height, and if more than one are plotted, they will take up different areas of the screen.

                                                                                                            Modified box plot

                                                                                                            Plot#(ModBoxplot, x-list, freq list, mark) defines a modified box plot. This is almost entirely like the normal box plot, except that it also draws outliers. Whiskers are only drawn to the furthers point within 1.5 times the interquartile range (Q3-Q1) of the box. Beyond this point, data points are drawn individually, using mark.

                                                                                                            The box plot ignores the Ymax and Ymin dimensions of the screen, and any plots that aren't box plots or modified box plots. Each box plot takes approximately 1/3 of the screen in height, and if more than one are plotted, they will take up different areas of the screen.

                                                                                                            Normal probability plot

                                                                                                            Plot#(NormProbPlot, data list, data axis, mark) defines a normal probability plot. The mean and standard deviation of the data are calculated. Then for each point, the number of standard deviations it is from the mean is calculated, and the point is plotted against this number using mark. data axis can be either X or Y: it determines whether the value of a point determines it's x-coordinate or y-coordinate.

                                                                                                            The point behind this rather convoluted process is to test the extent to which the data is normally distributed. If it follows the normal distribution closely, then the result will be close to a straight line - otherwise it will be curved.

                                                                                                            Advanced Uses

                                                                                                            After doing a regression, a scatter plot of ʟRESID against the x-list is a useful measure of the effectiveness of the regression. If the plot appears random, this is a good sign; if there is a pattern to the plot, this means it's likely that a better regression model exists.

                                                                                                            Optimization

                                                                                                            The ʟ symbol at the beginning of list names can be omitted everywhere in this command.

                                                                                                            In addition, every element except the plot type and the data list or data lists are optional, and take on the following default values:

                                                                                                            • freq list is 1 by default, meaning that all frequencies are 1.
                                                                                                            • mark is the box by default.
                                                                                                            • data axis is X by default.

                                                                                                            Error Conditions

                                                                                                            • ERR:DIM MISMATCH is thrown if the x and y lists, or the data and frequency lists, have different dimensions.
                                                                                                            • ERR:STAT is thrown if Xscl is too small in the case of a Histogram.

                                                                                                            All errors are thrown when plotting the stat plot, as opposed to when the command is executed, and do not provide a 2:Goto option.

                                                                                                            Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Myles_Zadok.

                                                                                                            History

                                                                                                            Calculator OS Version Description
                                                                                                            TI-82 1.0 Added
                                                                                                            Property Value
                                                                                                            Hex Value $FE
                                                                                                            Categories
                                                                                                            Localizations
                                                                                                            • FR: Nuage

                                                                                                            Scatter

                                                                                                            Overview

                                                                                                            Used as the "type" argument in the command
                                                                                                            Where # gives Plot1, Plot2 or Plot3.

                                                                                                            Availability: Token only available from within the Basic editor.

                                                                                                            Syntax

                                                                                                            Plot#(type,Xlist[,freqlist,color#])

                                                                                                            Arguments

                                                                                                            NameTypeOptional
                                                                                                            typeScatter token
                                                                                                            Xlistlist
                                                                                                            freqlistlist
                                                                                                            color#colorNum

                                                                                                            Location

                                                                                                            2nd, stat plot, TYPE

                                                                                                            Description

                                                                                                            The commands Plot1(, Plot2(, and Plot3(, which are identical except for which stat plot (1, 2, or 3) they affect, define their corresponding stat plot. When the stat plot is defined, it is also turned on so no PlotsOn command is necessary.

                                                                                                            The first argument of the commands is always the type of plot, and is one of Scatter, xyLine, Histogram, Boxplot, ModBoxplot, and NormProbPlot - these types are found in the TYPE submenu of the stat plot menu. The other arguments vary. For all but Histogram and Boxplot, there is a mark argument - this is a dot, a cross, or a box, symbols that can be found in the MARK submenu of the stat plot menu. On color calculators, there is an optional final argument to specify the color of the plot.

                                                                                                            Scatter plot

                                                                                                            Plot#(Scatter, x-list, y-list, mark) defines a scatter plot. The points defined by x-list and y-list are plotted using mark on the graph screen.

                                                                                                            x-list and y-list must be the same length.

                                                                                                            xyLine plot

                                                                                                            Plot#(xyLine, x-list, y-list, mark) defines an xyLine plot. Similarly to a scatter plot, the points defined by x-list and y-list are plotted using mark on the graph screen, but with an xyLine plot they are also connected by a line, in the order that they occur in the lists.

                                                                                                            x-list and y-list must be the same length.

                                                                                                            Histogram plot

                                                                                                            Plot#(Histogram, x-list, freq list) defines a Histogram plot. The x-axis is divided into intervals that are Xscl wide. A bar is drawn in in each interval whose height corresponds to the number of points in the interval. Points that are not between Xmin and Xmax are not tallied.

                                                                                                            Xscl must not be too small - it can divide the screen into no more than 47 different bars.

                                                                                                            Box plot

                                                                                                            Plot#(Boxplot, x-list, freq list) defines a box plot. A rectangular box is drawn whose left edge is Q1 (the first quartile) of the data, and whose right edge is Q3 (the third quartile). A vertical segment is drawn within the box at the median, and 'whiskers' are drawn from the box to the minimum and maximum data points.

                                                                                                            The box plot ignores the Ymax and Ymin dimensions of the screen, and any plots that aren't box plots or modified box plots. Each box plot takes approximately 1/3 of the screen in height, and if more than one are plotted, they will take up different areas of the screen.

                                                                                                            Modified box plot

                                                                                                            Plot#(ModBoxplot, x-list, freq list, mark) defines a modified box plot. This is almost entirely like the normal box plot, except that it also draws outliers. Whiskers are only drawn to the furthers point within 1.5 times the interquartile range (Q3-Q1) of the box. Beyond this point, data points are drawn individually, using mark.

                                                                                                            The box plot ignores the Ymax and Ymin dimensions of the screen, and any plots that aren't box plots or modified box plots. Each box plot takes approximately 1/3 of the screen in height, and if more than one are plotted, they will take up different areas of the screen.

                                                                                                            Normal probability plot

                                                                                                            Plot#(NormProbPlot, data list, data axis, mark) defines a normal probability plot. The mean and standard deviation of the data are calculated. Then for each point, the number of standard deviations it is from the mean is calculated, and the point is plotted against this number using mark. data axis can be either X or Y: it determines whether the value of a point determines it's x-coordinate or y-coordinate.

                                                                                                            The point behind this rather convoluted process is to test the extent to which the data is normally distributed. If it follows the normal distribution closely, then the result will be close to a straight line - otherwise it will be curved.

                                                                                                            Advanced Uses

                                                                                                            After doing a regression, a scatter plot of ʟRESID against the x-list is a useful measure of the effectiveness of the regression. If the plot appears random, this is a good sign; if there is a pattern to the plot, this means it's likely that a better regression model exists.

                                                                                                            Optimization

                                                                                                            The ʟ symbol at the beginning of list names can be omitted everywhere in this command.

                                                                                                            In addition, every element except the plot type and the data list or data lists are optional, and take on the following default values:

                                                                                                            • freq list is 1 by default, meaning that all frequencies are 1.
                                                                                                            • mark is the box by default.
                                                                                                            • data axis is X by default.

                                                                                                            Error Conditions

                                                                                                            • ERR:DIM MISMATCH is thrown if the x and y lists, or the data and frequency lists, have different dimensions.
                                                                                                            • ERR:STAT is thrown if Xscl is too small in the case of a Histogram.

                                                                                                            All errors are thrown when plotting the stat plot, as opposed to when the command is executed, and do not provide a 2:Goto option.

                                                                                                            Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Myles_Zadok.

                                                                                                            History

                                                                                                            Calculator OS Version Description
                                                                                                            TI-82 1.0 Added
                                                                                                            Property Value
                                                                                                            Hex Value $FF
                                                                                                            Categories
                                                                                                            Localizations
                                                                                                            • FR: RegLin(ax+b)

                                                                                                            LinReg(ax+b)

                                                                                                            Overview

                                                                                                            Fits a linear regression model toXlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ.

                                                                                                            Availability: Token available everywhere.

                                                                                                            Syntax

                                                                                                            LinReg(ax+b) [Xlistname,Ylistname,freqlist,regequ]

                                                                                                            Arguments

                                                                                                            NameTypeOptional
                                                                                                            XlistnamelistYes
                                                                                                            YlistnamelistYes
                                                                                                            freqlistlistYes
                                                                                                            regequYes

                                                                                                            Location

                                                                                                            stat, CALC, 4:LinReg(ax+b)

                                                                                                            Description

                                                                                                            The LinReg(ax+b) is one of several commands that can calculate the line of best fit through a set of points. To use it, you must first store the points to two lists: one of the x-coordinates and one of the y-coordinates, ordered so that the nth element of one list matches up with the nth element of the other list. L₁ and L₂ are the default lists to use, and the List Editor (STAT > Edit…) is a useful window for entering the points.

                                                                                                            In its simplest form, LinReg(ax+b) takes no arguments, and calculates a best fit line through the points in L₁ and L₂:

                                                                                                            :{9,13,21,30,31,31,34→L₁
:{260,320,420,530,560,550,590→L₂
:LinReg(ax+b)

                                                                                                            On the home screen, or as the last line of a program, this will display the equation of the line of best fit: you'll be shown the format, y=ax+b, and the values of a and b. It will also be stored in the RegEQ variable, but you won't be able to use this variable in a program - accessing it just pastes the equation wherever your cursor was. Finally, the statistical variables a, b, r, and r² will be set as well. These latter two variables will be displayed only if "Diagnostic Mode" is turned on (see DiagnosticOn and DiagnosticOff).

                                                                                                            You don't have to do the regression on L₁ and L₂, but if you don't you'll have to enter the names of the lists after the command. For example:

                                                                                                            :{9,13,21,30,31,31,34→FAT
:{260,320,420,530,560,550,590→CALS
:LinReg(ax+b) ʟFAT,ʟCALS

                                                                                                            You can attach frequencies to points, for when a point occurs more than once, by supplying an additional argument - the frequency list. This list does not have to contain integer frequencies. If you add a frequency list, you must supply the names of the x-list and y-list as well, even when they're L₁ and L₂.

                                                                                                            Finally, you can enter an equation variable (such as Y₁) after the command, so that the line of best fit is stored to this equation automatically. This doesn't require you to supply the names of the lists, but if you do, the equation variable must come last. You can use polar, parametric, or sequential variables as well, but since the line of best fit will be in terms of X anyway, this doesn't make much sense.

                                                                                                            An example of LinReg(ax+b) with all the optional arguments:

                                                                                                            :{9,13,21,30,31,31,34→FAT
:{260,320,420,530,560,550,590→CALS
:{2,1,1,1,2,1,1→FREQ
:LinReg(ax+b) ʟFAT,ʟCALS,ʟFREQ,Y₁

                                                                                                            Advanced Uses (for programmers)

                                                                                                            LinReg(ax+b), along with LinReg(a+bx) and Med-Med, can be used to convert a number to a string.

                                                                                                            Source: parts of this page were written by the following TI|BD contributors: Apersoma, burr, DarkerLine, GoVegan, thornahawk, Timothy Foster.

                                                                                                            History

                                                                                                            Calculator OS Version Description
                                                                                                            TI-82 1.0 Added
                                                                                                            Property Value
                                                                                                            Hex Value $BB43
                                                                                                            Categories
                                                                                                            Localizations
                                                                                                            • FR: 1-PropZInt(

                                                                                                            1-PropZInt(

                                                                                                            Overview

                                                                                                            Computes a one-proportion z confidence interval.

                                                                                                            Availability: Token only available from within the Basic editor.

                                                                                                            Syntax

                                                                                                            1-PropZInt(x,n[,confidence level])

                                                                                                            Arguments

                                                                                                            NameTypeOptional
                                                                                                            x
                                                                                                            n
                                                                                                            confidence levelYes

                                                                                                            Location

                                                                                                            stat, TESTS, A:1-PropZInt(

                                                                                                            Description

                                                                                                            The 1-PropZInt( command calculates a confidence interval for a proportion, at a specific confidence level: for example, if the confidence level is 95%, you are 95% certain that the proportion lies within the interval you get. The command assumes that the sample is large enough that the normal approximation to binomial distributions is valid: this is true if, in the sample you take, the positive and negative counts are both >5.

                                                                                                            The 1-PropZInt( command takes 3 arguments. The first, x, is the positive count in the sample. The second, n, is the total size of the sample. (So the sample proportion is equal to x out of n). The third argument is the confidence level, which defaults to 95.

                                                                                                            The output gives you a confidence interval of the form (a,b), meaning that the true proportion π is most likely in the range a<π<b, and the value of x__/n.

                                                                                                            Sample Problem

                                                                                                            You want to know the proportion of students at your school that support a particular political candidate. You take a random sample of 50 students, and find that 22 of them support that candidate. 22, the positive count, and 50-22=28, the negative count, are both >5, so the assumption is satisfied.

                                                                                                            Using 22 for x, and 50 for n, you decide to find a 95% confidence interval. The syntax for that is:

                                                                                                            :1-PropZInt(22,50,95
which can also be
:1-PropZInt(22,50,.95

                                                                                                            The output if you run the above code will look approximately like this:

                                                                                                            1-PropZInt
 (.30241,.57759)
 p=.44
 n=50

                                                                                                            This tells you that between about 30.2% and about 57.8% of the students at your school are in support of the political candidate.

                                                                                                            Optimization

                                                                                                            If the confidence level is 95%, you can omit the final 95, since that is the default value:

                                                                                                            :1-PropZInt(22,50,95
can be
:1-PropZInt(22,50

                                                                                                            Error Conditions

                                                                                                            • ERR:DOMAIN is thrown if the sample proportion is not between 0 and 1, any argument is negative, or the confidence level is 100 or more.

                                                                                                            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

                                                                                                            History

                                                                                                            Calculator OS Version Description
                                                                                                            TI-83 0.01013 Added
                                                                                                            Property Value
                                                                                                            Hex Value $BB3E
                                                                                                            Categories
                                                                                                            Localizations
                                                                                                            • FR: 1-PropZTest(

                                                                                                            1-PropZTest(

                                                                                                            Overview

                                                                                                            Computes a one-proportion z test. alternative=-1 is <; alternative=0 is ≠; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results.
                                                                                                            Color#: 10 - 24 or color name pasted from [vars] COLOR.

                                                                                                            Availability: Token only available from within the Basic editor.

                                                                                                            Syntax

                                                                                                            1-PropZTest(p0,x,n[,alternative,drawflag, color#])

                                                                                                            Arguments

                                                                                                            NameTypeOptional
                                                                                                            p0
                                                                                                            x
                                                                                                            n
                                                                                                            alternativeYes
                                                                                                            drawflagYes
                                                                                                            color#colorNumYes

                                                                                                            Location

                                                                                                            stat, TESTS, 5:1-PropZTest(

                                                                                                            Description

                                                                                                            1-PropZTest performs an z-test to compare a population proportion to a hypothesis value. This test is valid for sufficiently large samples: only when the number of successes (x in the command syntax) and the number of failures (n-x) are both >5.

                                                                                                            The logic behind the test is as follows: we want to test the hypothesis that the true proportion is equal to some value p0 (the null hypothesis). To do this, we assume that this "null hypothesis" is true, and calculate the probability that the (usually, somewhat different) actual proportion occurred, under this assumption. If this probability is sufficiently low (usually, 5% is the cutoff point), we conclude that since it's so unlikely that the data could have occurred under the null hypothesis, the null hypothesis must be false, and therefore the true proportion is not equal to p0. If, on the other hand, the probability is not too low, we conclude that the data may well have occurred under the null hypothesis, and therefore there's no reason to reject it.

                                                                                                            Commonly used notation has the letter π being used for the true population proportion (making the null hypothesis be π=p0). TI must have been afraid that this would be confused with the real number π, so on the calculator, "prop" is used everywhere instead.

                                                                                                            In addition to the null hypothesis, we must have an alternative hypothesis as well - usually this is simply that the proportion is not equal to p0. However, in certain cases, our alternative hypothesis may be that the proportion is greater or less than p0.

                                                                                                            The arguments to 1-PropZTest( are as follows:

                                                                                                            • p0 - the value for the null hypothesis (the proportion you're testing for)
                                                                                                            • x - the success count in the sample
                                                                                                            • n - the total size of the sample (so the sample proportion would be x__/n)
                                                                                                            • alternative (optional if you don't include draw?) - determines the alternative hypothesis
                                                                                                              • 0 (default value) - prop≠p0
                                                                                                              • -1 (or any negative value) - prop<p0
                                                                                                              • 1 (or any positive value) - prop>p0
                                                                                                            • draw? (optional) set this to 1 if you want a graphical rather than numeric result

                                                                                                            Although you can access the 1-PropZTest command on the home screen, via the catalog, there's no need: the 1-PropZTest… interactive solver, found in the statistics menu, is much more intuitive to use - you don't have to memorize the syntax.

                                                                                                            In either case, it's important to understand the output of 1-PropZTest. Here are the meanings of each line:

                                                                                                            • The first line, involving "prop" and p0, is the alternative hypothesis.
                                                                                                            • z is the test statistic. If the null hypothesis is true, it should be close to 0.
                                                                                                            • p is the probability that the difference between the proportion and p0 would occur if the null hypothesis is true. When the value is sufficiently small, we reject the null hypothesis and conclude that the alternative hypothesis is true. You should have a cutoff value ready, such as 5% or 1%. If p is lower, you "reject the null hypothesis on a 5% (or 1%) level" in technical terms.
                                                                                                            • p-hat is the sample proportion, x__/n.
                                                                                                            • n is the sample size.

                                                                                                            Advanced Uses

                                                                                                            The final optional argument of 1-PropZTest, draw?, will display the results in a graphical manner if you put in "1" for it. The calculator will draw the standard normal distribution, and shade the area of the graph that corresponds to the probability p. In addition, the value of z and the value of p will be displayed. You would make your conclusions in the same way as for the regular output.

                                                                                                            Optimization

                                                                                                            Some of the arguments of the 1-PropZTest command have default values, and the argument can be omitted if this value is used.

                                                                                                            • The draw? argument can be omitted if you don't want graphical output, although you could put "0" in as well.
                                                                                                            • If the above argument is omitted, and you're doing a two sided test, you may omit the alternative argument.

                                                                                                            Example:

                                                                                                            :1-PropZTest(.5,22,50,0,0
can be
:1-PropZTest(.5,22,50

                                                                                                            Error Conditions

                                                                                                            • ERR:DOMAIN is thrown if p0 or x__/n are not between 0 and 1, or x is negative or greater than n (however, any real value for alternative and draw? will work)

                                                                                                            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

                                                                                                            History

                                                                                                            Calculator OS Version Description
                                                                                                            TI-83 0.01013 Added
                                                                                                            Property Value
                                                                                                            Hex Value $F2
                                                                                                            Categories
                                                                                                            Localizations
                                                                                                            • FR: Stats 1-Var

                                                                                                            1-Var Stats

                                                                                                            Overview

                                                                                                            Performs one-variable analysis on the data in Xlistname with frequency freqlist.

                                                                                                            Availability: Token available everywhere.

                                                                                                            Syntax

                                                                                                            1-VarStats [Xlistname,freqlist]

                                                                                                            Arguments

                                                                                                            NameTypeOptional
                                                                                                            XlistnamelistYes
                                                                                                            freqlistlistYes

                                                                                                            Location

                                                                                                            stat, CALC, 1:1-Var Stats

                                                                                                            Description

                                                                                                            This command calculates a bunch of common (and a few uncommon) statistics for a list (it uses L1 by default, but you can use any list by supplying it as an argument). You have to store the list to a variable first, though, before calculating statistics for it. For example:

                                                                                                            :{5,12,7,8,4,9→L1
:1-Var Stats

                                                                                                            Like other statistical commands, you can use a frequency list as well, for cases where one element occurs more times than another (you can do this with a normal list, too, but that might be inconvenient when an element occurs very many times). For example:

                                                                                                            :{1,2,3→L1
:{5,3,2→L2
:1-Var Stats L1,L2

                                                                                                            is the frequency-list equivalent of:

                                                                                                            :{1,1,1,1,1,2,2,2,3,3→L1
:1-Var Stats

                                                                                                            When you're running it from the home screen, 1-Var Stats will display the statistics; this won't happen if you do it inside a program. Either way, it will also store what it calculated to the statistics variables found in VARS>Statistics… The variables 1-Var Stats affects are:

                                                                                                            • \(\overline{\textrm{x}}\) is the mean (average) of the elements, as returned by mean(
                                                                                                            • Σx is the sum of the elements, as returned by sum(
                                                                                                            • Σx² is the sum of the squares of the elements
                                                                                                            • Sx is the sample standard deviation, as returned by stdDev(
                                                                                                            • σx is population standard deviation
                                                                                                            • n is the number of elements in the list, as returned by dim(
                                                                                                            • minX is the minimum value, as returned by min(
                                                                                                            • Q1 is the first quartile
                                                                                                            • Med is the median, as returned by median(
                                                                                                            • Q3 is the third quartile
                                                                                                            • maxX is the maximum value, as returned by max(

                                                                                                            1-Var Stats will not work with "reserved" list names that the calculator uses internally. The only known such reserved list is the list RESID, and there's no reason to suspect there are any others. Ans, TblInput, and any expression which resolves to a list, are also not appropriate for this command: store all of these to a list before doing 1-Var Stats on them.

                                                                                                            Optimization

                                                                                                            Aside from statistical analysis, 1-Var Stats can also be used when you want to use the values it calculates more than once. This will save on size, since, for example Σx takes up less space than sum(L1), but considering how many calculations 1-Var Stats makes, it will usually be slower. Here's a short example which saves 1 byte:

                                                                                                            :Disp "RANGE:",max(L1)-min(L1
can be
:1-Var Stats
:Disp "RANGE:",maxX-minX

                                                                                                            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

                                                                                                            History

                                                                                                            Calculator OS Version Description
                                                                                                            TI-82 1.0 Added
                                                                                                            Property Value
                                                                                                            Hex Value $31
                                                                                                            Categories
                                                                                                            Localizations
                                                                                                            • FR: 1
                                                                                                            1

                                                                                                            Overview

                                                                                                            Availability: Token available everywhere.

                                                                                                            Syntax

                                                                                                            1

                                                                                                            Description

                                                                                                            Examples

                                                                                                            Explanation 1

                                                                                                            code 1

                                                                                                            Explanation 2

                                                                                                            code 2

                                                                                                            Error Conditions

                                                                                                            Advanced Notes

                                                                                                            History

                                                                                                            Calculator OS Version Description
                                                                                                            TI-82 1.0 Added
                                                                                                            Property Value
                                                                                                            Hex Value $C1
                                                                                                            Categories
                                                                                                            Localizations
                                                                                                            • FR: ₁₀^(

                                                                                                            ₁₀^(

                                                                                                            Overview

                                                                                                            Availability: Token available everywhere.

                                                                                                            Syntax

                                                                                                            ₁₀^(

                                                                                                            Description

                                                                                                            Examples

                                                                                                            Explanation 1

                                                                                                            code 1

                                                                                                            Explanation 2

                                                                                                            code 2

                                                                                                            Error Conditions

                                                                                                            Advanced Notes

                                                                                                            History

                                                                                                            Calculator OS Version Description
                                                                                                            TI-82 1.0 ₁₀^ added
                                                                                                            TI-83 0.01013 Renamed ₁₀^ to ₁₀^(
                                                                                                            Property Value
                                                                                                            Hex Value $BB44
                                                                                                            Categories
                                                                                                            Localizations
                                                                                                            • FR: 2-PropZInt(

                                                                                                            2-PropZInt(

                                                                                                            Overview

                                                                                                            Computes a two-proportion z confidence interval.

                                                                                                            Availability: Token only available from within the Basic editor.

                                                                                                            Syntax

                                                                                                            2-PropZInt(x1,n1,x2,n2[,confidence level])

                                                                                                            Arguments

                                                                                                            NameTypeOptional
                                                                                                            x1
                                                                                                            n1
                                                                                                            x2
                                                                                                            n2
                                                                                                            confidence levelYes

                                                                                                            Location

                                                                                                            stat, TESTS, B:2-PropZInt(

                                                                                                            Description

                                                                                                            The 2-PropZInt( command calculates a confidence interval for the difference between two proportions, at a specific confidence level: for example, if the confidence level is 95%, you are 95% certain that the difference lies within the interval you get. The command assumes that the sample is large enough that the normal approximation to binomial distributions is valid: this is true if, in both samples involved, the positive and negative counts are both >5.

                                                                                                            The 1-PropZInt( command takes 5 arguments. The first two, x1 and n1 are the positive count and total count in the first sample (so the estimated value of the first proportion is x1 out of n1. The next two arguments, x2 and n2, are the positive count and total count in the second sample.

                                                                                                            The output gives you a confidence interval of the form (a,b), which is the range of values for the difference π1-π2 (where π1 and π2 are the first and second proportions respectively). If you were looking for the difference π2-π1 all you have to do is switch two sides and negate the numbers in the interval.

                                                                                                            Sample Problem

                                                                                                            You want to compare the proportion of students at your school and at a friend's school. that support a particular political candidate. You take a random sample of 50 students, and find that 22 of them support that candidate. Your friend took a random sample of 75 students at his school, and found that 28 supported the candidate.

                                                                                                            The first proportion is the proportion of supporters at your school. 22 out of 50 students support the candidate, so x1=22 and n1=50.
                                                                                                            The second proportion is the proportion of supporters at your friend's school. 28 out of 75 students support the candidate, so x2=28 and n2=75.
                                                                                                            If you decided to do a 95% confidence interval, you would add the argument 95 after all these, so the syntax would be as follows:

                                                                                                            :2-PropZInt(22,50,28,75,95
which can also be
:2-PropZInt(22,50,28,75,.95

                                                                                                            The output if you run the above code will look approximately like this:

                                                                                                            1-PropZInt
 (-.1092,.24249)
 p1=.44
 p2=.3733333333
 n1=50
 n2=75

                                                                                                            This tells you that between about the difference betwen the proportions is between about -0.11 (your school's proportion being about 0.11 less than your friend's school's proportion) to about 0.24 (your school's proportion being about 0.24 greater than your friend's school's proportion).

                                                                                                            Optimization

                                                                                                            If the confidence level is 95%, you can omit the final 95, since that is the default value:

                                                                                                            :2-PropZInt(22,50,28,75,95
can be
:2-PropZInt(22,50,28,75

                                                                                                            Error Conditions

                                                                                                            • ERR:DOMAIN is thrown if either proportion is not between 0 and 1, or xi is negative or greater than ni, or the confidence level is negative or at least 100.

                                                                                                            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

                                                                                                            History

                                                                                                            Calculator OS Version Description
                                                                                                            TI-83 0.01013 Added
                                                                                                            Property Value
                                                                                                            Hex Value $BB3F
                                                                                                            Categories
                                                                                                            Localizations
                                                                                                            • FR: 2-PropZTest(

                                                                                                            2-PropZTest(

                                                                                                            Overview

                                                                                                            Computes a two-proportion z test. alternative=-1 is <; alternative=0 is ≠; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results.
                                                                                                            Color#: 10 - 24 or color name pasted from [vars] COLOR.

                                                                                                            Availability: Token only available from within the Basic editor.

                                                                                                            Syntax

                                                                                                            2-PropZTest(x1,n1,x2,n2[,alternative,drawflag, color#])

                                                                                                            Arguments

                                                                                                            NameTypeOptional
                                                                                                            x1
                                                                                                            n1
                                                                                                            x2
                                                                                                            n2
                                                                                                            alternativeYes
                                                                                                            drawflagYes
                                                                                                            color#colorNumYes

                                                                                                            Location

                                                                                                            stat, TESTS, 6:2-PropZTest(

                                                                                                            Description

                                                                                                            2-PropZTest( performs a_z_-test to compare two population proportions. This test is valid for sufficiently large samples: only when the number of successes (x in the command syntax) and the number of failures (n-x) are both >5, for both populations.

                                                                                                            The logic behind the test is as follows: we want to test the hypothesis that the proportions are equal (the null hypothesis). To do this, we assume that this "null hypothesis" is true, and calculate the probability that the differences between the two proportions occurred, under this assumption. If this probability is sufficiently low (usually, 5% is the cutoff point), we conclude that since it's so unlikely that the data could have occurred under the null hypothesis, the null hypothesis must be false, and therefore the proportions are not equal. If, on the other hand, the probability is not too low, we conclude that the data may well have occurred under the null hypothesis, and therefore there's no reason to reject it.

                                                                                                            Commonly used notation has the letters π1 and π2 being used for the true population proportions (making the null hypothesis be π1=π2). TI must have been afraid that this would be confused with the real number π, so on the calculator, "p1" and "p2" are used everywhere instead.

                                                                                                            In addition to the null hypothesis, we must have an alternative hypothesis as well - usually, this is simply that the proportions are not equal. However, in certain cases, our alternative hypothesis may be that one proportion is greater or less than the other.

                                                                                                            The arguments to 2-PropZTest( (which must be integers, or the calculator will generate a domain error) are as follows:

                                                                                                            • x1 - the success count in the first sample
                                                                                                            • n1 - the total size of the first sample (so the sample proportion would be x1__/n1)
                                                                                                            • x2 - the success count in the second sample
                                                                                                            • n2 - the total size of the second sample (so the sample proportion would be x2__/n2)
                                                                                                            • alternative (optional if you don't include draw?) - determines the alternative hypothesis
                                                                                                              • 0 (default value) - p1≠p2
                                                                                                              • -1 (or any negative value) - p1<p2
                                                                                                              • 1 (or any positive value) - p1>p2
                                                                                                            • draw? (optional) set this to 1 if you want a graphical rather than numeric result

                                                                                                            Although you can access the 2-PropZTest( command on the home screen, via the catalog, there's no need: the 2-PropZTest(… interactive solver, found in the statistics menu, is much more intuitive to use - you don't have to memorize the syntax.

                                                                                                            In either case, it's important to understand the output of 2-PropZTest(. Here are the meanings of each line:

                                                                                                            • The first line, involving p1 and p2, is the alternative hypothesis.
                                                                                                            • z is the test statistic. If the null hypothesis is true, it should be close to 0.
                                                                                                            • p is the probability that the difference between the two proportions would occur if the null hypothesis is true. When the value is sufficiently small, we reject the null hypothesis and conclude that the alternative hypothesis is true. You should have a cutoff value ready, such as 5% or 1%. If p is lower, you "reject the null hypothesis on a 5% (or 1%) level" in technical terms.
                                                                                                            • p-hat1 is the sample proportion x1__/n1.
                                                                                                            • p-hat2 is the sample proportion x2__/n2.
                                                                                                            • p-hat is the total sample proportion
                                                                                                            • n1 is the first sample size.
                                                                                                            • n2 is the second sample size.

                                                                                                            Advanced Uses

                                                                                                            The final optional argument of 2-PropZTest(, draw?, will display the results in a graphical manner if you put in "1" for it. The calculator will draw the standard normal distribution, and shade the area of the graph that corresponds to the probability p. In addition, the value of z and the value of p will be displayed. You would make your conclusions in the same way as for the regular output.

                                                                                                            Optimization

                                                                                                            Some of the arguments of the 2-PropZTest( command have default values, and the argument can be omitted if this value is used.

                                                                                                            • The draw? argument can be omitted if you don't want graphical output, although you could put "0" in as well.
                                                                                                            • If the above argument is omitted, and you're doing a two-sided test, you may omit the alternative argument.

                                                                                                            Example:

                                                                                                            :2-PropZTest(22,50,48,100,0,0
can be
:2-PropZTest(22,50,48,100

                                                                                                            Error Conditions

                                                                                                            • ERR:DOMAIN is thrown if the values of the arguments entered are not integers.

                                                                                                            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Myles_Zadok.

                                                                                                            History

                                                                                                            Calculator OS Version Description
                                                                                                            TI-83 0.01013 Added
                                                                                                            Property Value
                                                                                                            Hex Value $BB47
                                                                                                            Categories
                                                                                                            Localizations
                                                                                                            • FR: 2-Comp𝐅Test(

                                                                                                            2-Samp𝐅Test

                                                                                                            Overview

                                                                                                            Performs a two-sample 𝐅 test. alternative=-1 is <; alternative=0 is ≠; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results.
                                                                                                            Color#: 10 - 24 or color name pasted from [vars] COLOR.

                                                                                                            Availability: Token only available from within the Basic editor.

                                                                                                            Syntax

                                                                                                            2-Samp𝐅Test[listname1,listname2,freqlist1,freqlist2,alternative,drawflag,color#]

                                                                                                            Arguments

                                                                                                            NameTypeOptional
                                                                                                            𝐅Yes
                                                                                                            listname1listNameYes
                                                                                                            listname2listNameYes
                                                                                                            freqlist1listYes
                                                                                                            freqlist2listYes
                                                                                                            alternativeYes
                                                                                                            drawflagYes
                                                                                                            color#colorNumYes

                                                                                                            Location

                                                                                                            stat, TESTS, E:2-Samp, Test

                                                                                                            Overview

                                                                                                            Performs a two-sample 𝐅 test. alternative=-1 is <; alternative=0 is ≠; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results.
                                                                                                            Color#: 10 - 24 or color name pasted from [vars] COLOR.

                                                                                                            Availability: Token only available from within the Basic editor.

                                                                                                            Syntax

                                                                                                            2-Samp𝐅TestSx1,n1,Sx2,n2[,alternative,drawflag,color#]

                                                                                                            Arguments

                                                                                                            NameTypeOptional
                                                                                                            𝐅
                                                                                                            Sx1
                                                                                                            n1
                                                                                                            Sx2
                                                                                                            n2Yes
                                                                                                            alternativeYes
                                                                                                            drawflagYes
                                                                                                            color#colorNumYes

                                                                                                            Location

                                                                                                            stat, TESTS, E:2-Samp, Test

                                                                                                            Description

                                                                                                            Examples

                                                                                                            Explanation 1

                                                                                                            code 1

                                                                                                            Explanation 2

                                                                                                            code 2

                                                                                                            Error Conditions

                                                                                                            Advanced Notes

                                                                                                            History

                                                                                                            Calculator OS Version Description
                                                                                                            TI-83 0.01013 Added
                                                                                                            Property Value
                                                                                                            Hex Value $BB49
                                                                                                            Categories
                                                                                                            Localizations
                                                                                                            • FR: 2-CompTIntC(

                                                                                                            2-SampTInt

                                                                                                            Overview

                                                                                                            Computes a two-sample t confidence interval. pooled=1 pools variances; pooled=0 does not pool variances.

                                                                                                            Comment:Data list input

                                                                                                            Availability: Token only available from within the Basic editor.

                                                                                                            Syntax

                                                                                                            2-SampTInt[listname1,listname2,freqlist1,freqlist2,confidence level,pooled]

                                                                                                            Arguments

                                                                                                            NameTypeOptional
                                                                                                            listname1listNameYes
                                                                                                            listname2listNameYes
                                                                                                            freqlist1listYes
                                                                                                            freqlist2listYes
                                                                                                            confidence levelYes
                                                                                                            pooledYes

                                                                                                            Location

                                                                                                            stat, TESTS, 0:2-SampTInt

                                                                                                            Overview

                                                                                                            Computes a two-sample t confidence interval. pooled=1 pools variances; pooled=0 does not pool variances.

                                                                                                            Comment:Summary stats input

                                                                                                            Availability: Token only available from within the Basic editor.

                                                                                                            Syntax

                                                                                                            2-SampTIntx̄1,Sx1,n1,x̄2,Sx2,n2[,confidence  level,pooled]

                                                                                                            Arguments

                                                                                                            NameTypeOptional
                                                                                                            x̄
                                                                                                            1
                                                                                                            Sx1
                                                                                                            n1
                                                                                                            x̄
                                                                                                            2
                                                                                                            Sx2
                                                                                                            n2Yes
                                                                                                            confidenceYes
                                                                                                            levelYes
                                                                                                            pooledYes

                                                                                                            Location

                                                                                                            stat, TESTS, 0:2-SampTInt

                                                                                                            Description

                                                                                                            The 2-SampTInt command uses the techniques of T Intervals to compute an interval for the difference between the means of two independent populations, at a specified confidence level. Use 2-SampTInt( when you have two independent variables to compare, and you don't know their standard deviations. The 2-SampTInt command assumes that both your variables are normally distributed, but it will work for other distributions if the sample size is large enough.

                                                                                                            There are two ways to call this command: by supplying it with needed sample statistics (mean, standard deviation, and sample size, for both data sets), or by entering two lists and letting the calculator work the statistics out. In either case, you will need to enter the desired confidence level as well.

                                                                                                            In the summary stats syntax, x1 and x2 the two sample means, s1 and s2 are the two sample standard deviations, and n1 and n2 the two sample sizes.

                                                                                                            The output will contain an open interval (a, b) that is your answer: the difference between the two means will lie in this interval. Specifically, it is the second mean subtracted from the first - μ1-μ2. If you're interested in the reverse difference, just flip the signs on the interval.

                                                                                                            Tip: don't use this command in a matched-pairs setting when you can match the two samples up by units or subjects. Instead, take the difference between the two samples in each matched pair, and use a regular TInterval.

                                                                                                            Sample Problem

                                                                                                            You want to compare the average height of a freshman and a senior at your school. You haven't asked everyone, but you took a random sample of 40 people from each class and found out their heights (and stored them to L1 and L2). You've decided to use a 95% confidence interval.

                                                                                                            Based on the data list syntax for a 2-SampTInt, here is your code:

                                                                                                            :2-SampTInt L1,L2,95
you can also use
:2-SampTInt L1,L2,.95

                                                                                                            Alternatively, you could calculate the mean and sample size and enter those instead. The sample size in this case is 40 for both data sets; let's say the means were 57 inches and 67 inches and the standard deviations 5.2 and 7.1 inches. You now have all the needed statistics:

                                                                                                            • x1 is the mean height of freshmen: 57 inches
                                                                                                            • s1 is the sample standard deviation for freshmen: 5.2 inches
                                                                                                            • n1 is the number of freshmen in the sample: 40
                                                                                                            • x2 is the mean height of seniors: 67 inches
                                                                                                            • s2 is the sample standard deviation for seniors: 7.1 inches
                                                                                                            • n2 is the number of seniors in the sample: 40

                                                                                                            This means that the code is:

                                                                                                            :2-SampTInt 57,5.2,40,67,7.1,40,95
you can also use
:2-SampTInt 57,5.2,40,67,7.1,40,.95

                                                                                                            Of course, the main use of the 2-SampTInt command is in a program. While you can enter the command on the home screen as well (just look in the catalog for it), it would probably be easier to select 2-SampTInt… from the STAT>TEST menu (see the sidebar), since you don't have to remember the syntax.

                                                                                                            Advanced Uses

                                                                                                            As with most other statistical commands, you can add frequencies to the lists (only with the data list syntax, of course); if you do, both lists must have frequencies, and the arguments go in the order first data list, second data list, first freq. list, second freq. list. Each frequency list must contain non-negative real numbers, which can't be all 0.

                                                                                                            There is a final argument to 2-SampTInt: pooled. It can be either 0 or 1 (although any argument that isn't 0 will get treated as a 1); the default value is 0. If the value is 1, then then the variances will be pooled: that is, the calculator will assume that the variances of the two populations are equal, and use a combined form of the two standard deviations in place of each population's individual standard deviation. Set this flag if you have reason to believe that the standard deviations are equal.

                                                                                                            Optimization

                                                                                                            Using the data list syntax, all items are optional: the calculator will assume you want to use L1 and L2 for your data unless other lists are supplied, and that the confidence level you want is 95% unless you give another one. Using the summary stats syntax, the confidence level is also optional - again, the calculator will assume 95%. This means we can rewrite our code above in a simpler manner:

                                                                                                            :2-SampTInt L1,L2,95
can be
:2-SampTInt

                                                                                                            :2-SampTInt 57,5.2,40,67,7.1,40,95
can be
:2-SampTInt 57,5.2,40,67,7.1,40

                                                                                                            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

                                                                                                            History

                                                                                                            Calculator OS Version Description
                                                                                                            TI-83 0.01013 Added
                                                                                                            Property Value
                                                                                                            Hex Value $BB46
                                                                                                            Categories
                                                                                                            Localizations
                                                                                                            • FR: 2-CompTTest(

                                                                                                            2-SampTTest

                                                                                                            Overview

                                                                                                            Computes a two-sample t test. alternative=-1 is <; alternative=0 is ≠; alternative=1 is >. pooled=1 pools variances; pooled=0 does not pool variances. drawflag=1 draws results; drawflag=0 calculates results.
                                                                                                            Color#: 10 - 24 or color name pasted from [vars] COLOR.

                                                                                                            Availability: Token only available from within the Basic editor.

                                                                                                            Syntax

                                                                                                            2-SampTTest [listname1,listname2,freqlist1,freqlist2,alternative,pooled,drawflag,color#])

                                                                                                            Arguments

                                                                                                            NameTypeOptional
                                                                                                            listname1listNameYes
                                                                                                            listname2listNameYes
                                                                                                            freqlist1listYes
                                                                                                            freqlist2listYes
                                                                                                            alternativeYes
                                                                                                            pooledYes
                                                                                                            drawflagYes
                                                                                                            color#colorNumYes

                                                                                                            Location

                                                                                                            stat, TESTS, 4:2-SampTTest

                                                                                                            Overview

                                                                                                            Computes a two-sample t test. alternative=-1 is <; alternative=0 is ≠; alternative=1 is >. pooled=1 pools variances; pooled=0 does not pool variances. drawflag=1 draws results; drawflag=0 calculates results.
                                                                                                            Color#: 10 - 24 or color name pasted from [vars] COLOR.

                                                                                                            Availability: Token only available from within the Basic editor.

                                                                                                            Syntax

                                                                                                            2-SampTTestx̄1,Sx1,n1,v2,Sx2,n2[,alternative,pooled,drawflag,color#])

                                                                                                            Arguments

                                                                                                            NameTypeOptional
                                                                                                            x̄
                                                                                                            1
                                                                                                            Sx1
                                                                                                            n1
                                                                                                            v2
                                                                                                            Sx2
                                                                                                            n2Yes
                                                                                                            alternativeYes
                                                                                                            pooledYes
                                                                                                            drawflagYes
                                                                                                            color#colorNumYes

                                                                                                            Location

                                                                                                            stat, TESTS, 4:2-SampTTest

                                                                                                            Description

                                                                                                            2-SampTTest performs a t significance test to compare the means of two populations. This test is valid for simple random samples from populations with unknown standard deviations. In addition, either the populations must be normally distributed, or the sample sizes have to be sufficiently large (usually, greater than 10).

                                                                                                            The logic behind the test is as follows: we want to test the hypothesis that the true means of the two populations are equal (the null hypothesis). The letter μ is used for a population mean, so this is usually written as μ1=μ2. To do this, we assume that this "null hypothesis" is true, and calculate the probability that the difference between the two means occurred, under this assumption. If this probability is sufficiently low (usually, 5% is the cutoff point), we conclude that since it's so unlikely that the data could have occurred under the null hypothesis, the null hypothesis must be false, and therefore the means are not equal. If, on the other hand, the probability is not too low, we conclude that the data may well have occurred under the null hypothesis, and therefore there's no reason to reject it.

                                                                                                            In addition to the null hypothesis, we must have an alternative hypothesis as well - usually this is simply that the two means are not equal. However, in certain cases when we have reason to suspect that one mean is greater than the other (such as when we are trying to verify a claim that one mean is greater), our alternative hypothesis may be that the first mean is greater than the second (μ1>μ2) or less (μ1<μ2).

                                                                                                            As for the 2-SampTTest command itself, there are two ways of calling it: you may give it a list of all the sample data, or the necessary statistics about the list (x1 and x2 are the sample means, s1 and s2 the sample standard deviations, and n1 and n2 the sample sizes). In either case, you can indicate what the alternate hypothesis is, by a value of 0, -1, or 1 for the alternative argument. 0 indicates a two-sided hypothesis of μ1≠μ2, -1 indicates μ1<μ2, and 1 indicates μ1>μ2. (In fact, the calculator will treat any negative value as -1, and any positive value as 1).

                                                                                                            Although you can access the 2-SampTTest command on the home screen, via the catalog, there's no need: the 2-SampTTest… interactive solver, found in the statistics menu, is much more intuitive to use - you don't have to memorize the syntax.

                                                                                                            In either case, it's important to understand the output of 2-SampTTest. Here are the meanings of each line:

                                                                                                            • The first line, involving μ1 and μ2, is the alternative hypothesis.
                                                                                                            • t is the test statistic, the standardized difference between the means. If the null hypothesis is true, it should be close to 0.
                                                                                                            • p is the probability that the difference between μ1 and μ2 (the two means) would occur if the null hypothesis is true. When the value is sufficiently small, we reject the null hypothesis and conclude that the alternative hypothesis is true. You should have a cutoff value ready, such as 5% or 1%. If p is lower, you "reject the null hypothesis on a 5% (or 1%) level" in technical terms.
                                                                                                            • x-bar1 and x-bar2 are the two sample means.
                                                                                                            • Sx1 and Sx2 are the two sample standard deviations.
                                                                                                            • n1 and n2 are the sample sizes.

                                                                                                            Sample Problem

                                                                                                            Your school claims that the average SAT score of students at the school is higher than at a rival school. You took samples of SAT scores from students at both schools (and stored them to L1 and L2).
                                                                                                            Since the school's claim is that your school's score is higher, that will be your alternative hypothesis (μ1>μ2), which corresponds to a value of 1. The code you'd use is:

                                                                                                            :2-SampTTest L1,L2,1

                                                                                                            Alternatively, you could calculate the mean, standard deviation, and size of your samples, and put those into the command instead. Suppose you obtained SAT scores from 60 students at your school and 40 students at the rival school, the means were 1737 and 1623, and the standard deviation 211 and 218. Then your code is:

                                                                                                            :2-SampTTest 1737,211,60,1623,218,40,1

                                                                                                            You will see the following output:

                                                                                                            2-SampTTest
 μ1>μ2
 z=2.594854858
 p=.0056059824
 x1=1737
 x2=1623
 Sx1=211
 Sx2=218
 n1=60
 n2=40

                                                                                                            The most important part of this output is "p=.0056059824". This value of p is smaller than 1% or 0.01. This is significant on the 1% level, so we reject the null hypothesis and conclude that the alternative hypothesis is true: μ1>μ2, that is, your school's average SAT score is indeed higher.

                                                                                                            Advanced Uses

                                                                                                            The final optional argument of 2-SampTTest, draw?, will display the results in a graphical manner if you put in "1" for it. The calculator will draw the distribution, and shade the area of the graph beyound the t statistic. In addition, the value of t and the value of p will be displayed (the value of p corresponds to the shaded area). You would make your conclusions in the same way as for the regular output.

                                                                                                            The optional argument pooled?, if given a nonzero value, will pool the standard deviations to find a combined value which will then be used for both populations. Use this feature if you have reason to believe that the two populations have the same standard deviation.

                                                                                                            As with most other statistical commands, you may use a frequency list in your input (when using the data list syntax). If you do, then both lists must have frequencies, and the order of the arguments would be list1, list2, frequency1, frequency2.

                                                                                                            Optimization

                                                                                                            Some of the arguments of the 2-SampTTest command have default values, and the argument can be omitted if this value is accepted.

                                                                                                            • The draw? argument can be omitted if you don't want graphical output, although you could put "0" in as well.
                                                                                                            • If the draw? argument is omitted, you can omit the pooled? argument if you do not want your standard deviations pooled.
                                                                                                            • If both the above arguments are omitted, and you're doing a two sided test, you may omit the alternative argument.
                                                                                                            • With data list input, you can always omit the frequency lists if you won't be using them.
                                                                                                            • With data list input, if the flags that go at the end are omitted, and you're using the default lists L1 and L2, you may omit those as well.

                                                                                                            The code in the sample problem above can't be optimized, because the alternative argument is 1:

                                                                                                            :2-SampTTest L1,L2,1

                                                                                                            However, if we were doing a two-sided test, we could omit the alternative argument as well as the lists:

                                                                                                            :2-SampTTest L1,L2,0
can be just
:2-SampTTest

                                                                                                            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Timothy Foster.

                                                                                                            History

                                                                                                            Calculator OS Version Description
                                                                                                            TI-83 0.01013 Added
                                                                                                            Property Value
                                                                                                            Hex Value $BB42
                                                                                                            Categories
                                                                                                            Localizations
                                                                                                            • FR: 2-CompZIntC(

                                                                                                            2-SampZInt(

                                                                                                            Overview

                                                                                                            Computes a two-sample z confidence interval.

                                                                                                            Comment:Data list input

                                                                                                            Availability: Token only available from within the Basic editor.

                                                                                                            Syntax

                                                                                                            2-SampZInt(σ1,σ2[,listname1,listname2,freqlist1,freqlist2,confidence level])

                                                                                                            Arguments

                                                                                                            NameTypeOptional
                                                                                                            σ
                                                                                                            1Yes
                                                                                                            σYes
                                                                                                            2Yes
                                                                                                            listname1listNameYes
                                                                                                            listname2listNameYes
                                                                                                            freqlist1listYes
                                                                                                            freqlist2listYes
                                                                                                            confidence levelYes

                                                                                                            Location

                                                                                                            stat, TESTS, 9:2-SampZInt(

                                                                                                            Overview

                                                                                                            Computes a two-sample z confidence interval.

                                                                                                            Comment:Summary stats input

                                                                                                            Availability: Token only available from within the Basic editor.

                                                                                                            Syntax

                                                                                                            2-SampZInt(σ1,σ2,x̄1,n1,x̄2,n2[,confidence level])

                                                                                                            Arguments

                                                                                                            NameTypeOptional
                                                                                                            σ
                                                                                                            1
                                                                                                            σ
                                                                                                            2
                                                                                                            x̄
                                                                                                            1
                                                                                                            n1Yes
                                                                                                            x̄Yes
                                                                                                            2Yes
                                                                                                            n2Yes
                                                                                                            confidence levelYes

                                                                                                            Location

                                                                                                            stat, TESTS, 9:2-SampZInt(

                                                                                                            Description

                                                                                                            The 2-SampZInt( command uses the techniques of Z Intervals to compute an interval for the difference between the means of two independent populations, at a specified confidence level. Use 2-SampZInt( when you have two independent variables to compare, and you already know their standard deviations. The 2-SampZInt( command assumes that both variables are distributed normally, but it will work for other distributions if the sample size is large enough.

                                                                                                            There are two ways to call this command: by supplying it with needed sample statistics (mean and sample size, for both data sets), or by entering two lists and letting the calculator work the statistics out. In either case, you will need to enter the standard deviation and desired confidence level as well.

                                                                                                            In the data list syntax, σ1 and σ2 are the two standard deviations.
                                                                                                            In the summary stats syntax, σ1 and σ2 are the two standard deviations, x1 and x2 the two sample means, and n1 and n2 the two sample sizes.

                                                                                                            The output will contain an open interval (a, b) that is your answer: the difference between the two means will lie in this interval. Specifically, it is the second mean subtracted from the first - μ1-μ2. If you're interested in the reverse difference, just flip the signs on the interval.

                                                                                                            Tip: don't use this command in a matched-pairs setting when you can match the two samples up by units or subjects. Instead, take the difference between the two samples in each matched pair, and use a regular ZInterval.

                                                                                                            Sample Problem

                                                                                                            You want to compare the average height of a freshman and a senior at your school. You haven't asked everyone, but you took a random sample of 40 people from each class and found out their heights (and stored them to L1 and L2). You've read in your textbook that the standard deviation of teenagers' heights is usually 6 inches. You've decided to use a 95% confidence interval.

                                                                                                            Based on the data list syntax for a 2-SampZInt(, here is your code:

                                                                                                            :2-SampZInt(6,6,L1,L2,95
you can also use
:2-SampZInt(6,6,L1,L2,.95

                                                                                                            Alternatively, you could calculate the mean and sample size and enter those instead. The sample size in this case is 40 for both data sets; let's say the means were 57 inches and 67 inches. You now have all the needed statistics:

                                                                                                            • σ1 is the standard deviation for freshmen: 6 inches
                                                                                                            • σ2 is the standard deviation for seniors: also 6 inches
                                                                                                            • x1 is the mean height of freshmen: 57 inches
                                                                                                            • n1 is the number of freshmen in the sample: 40
                                                                                                            • x2 is the mean height of seniors: 67 inches
                                                                                                            • n2 is the number of seniors in the sample: 40

                                                                                                            This means that the code is:

                                                                                                            :2-SampZInt(6,6,57,40,67,40,95
you can also use
:2-SampZInt(6,6,57,40,67,40,.95

                                                                                                            Of course, the main use of the 2-SampZInt( command is in a program. While you can enter the command on the home screen as well (just look in the catalog for it), it would probably be easier to select 2-SampZInt… from the STAT>TEST menu (see the sidebar), since you don't have to remember the syntax.

                                                                                                            Advanced Uses

                                                                                                            As with most other statistical commands, you can add frequencies to the lists (only with the data list syntax, of course); if you do, both lists must have frequencies, and the arguments go in the order first data list, second data list, first freq. list, second freq. list. Each frequency list must contain non-negative real numbers, which can't be all 0.

                                                                                                            Optimization

                                                                                                            Using the data list syntax, all items but the standard deviations are optional: the calculator will assume you want to use L1 and L2 for your data unless other lists are supplied, and that the confidence level you want is 95% unless you give another one. Using the summary stats syntax, the confidence level is also optional - again, the calculator will assume 95%. This means we can rewrite our code above in a simpler manner:

                                                                                                            :2-SampZInt(6,6,L1,L2,95
can be
:2-SampZInt(6,6

                                                                                                            :2-SampZInt(6,6,57,40,67,40,95
can be
:2-SampZInt(6,6,57,40,67,40

                                                                                                            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Timothy Foster.

                                                                                                            History

                                                                                                            Calculator OS Version Description
                                                                                                            TI-83 0.01013 Added
                                                                                                            Property Value
                                                                                                            Hex Value $BB3D
                                                                                                            Categories
                                                                                                            Localizations
                                                                                                            • FR: 2-CompZTest(

                                                                                                            2-SampZTest(

                                                                                                            Overview

                                                                                                            Computes a two-sample z test. alternative=-1 is <; alternative=0 is ≠; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results.
                                                                                                            Color#: 10 - 24 or color name pasted from [vars] COLOR.

                                                                                                            Availability: Token only available from within the Basic editor.

                                                                                                            Syntax

                                                                                                            2-SampZTest( σ1,σ2[,listname1,listname2,freqlist1,freqlist2,alternative,drawflag,color#])

                                                                                                            Arguments

                                                                                                            NameTypeOptional
                                                                                                            σ
                                                                                                            1Yes
                                                                                                            σYes
                                                                                                            2Yes
                                                                                                            listname1listNameYes
                                                                                                            listname2listNameYes
                                                                                                            freqlist1listYes
                                                                                                            freqlist2listYes
                                                                                                            alternativeYes
                                                                                                            drawflagYes
                                                                                                            color#colorNumYes

                                                                                                            Location

                                                                                                            stat, TESTS, 3:2-SampZTest(

                                                                                                            Overview

                                                                                                            Computes a two-sample z test. alternative=-1 is <; alternative=0 is ≠; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results.
                                                                                                            Color#: 10 - 24 or color name pasted from [vars] COLOR.

                                                                                                            Availability: Token only available from within the Basic editor.

                                                                                                            Syntax

                                                                                                            2-SampZTest(σ1,σ2,x̄1,n1,x̄2,n2[,alternative,drawflag,color#])

                                                                                                            Arguments

                                                                                                            NameTypeOptional
                                                                                                            σ
                                                                                                            1
                                                                                                            σ
                                                                                                            2
                                                                                                            x̄
                                                                                                            1
                                                                                                            n1Yes
                                                                                                            x̄Yes
                                                                                                            2Yes
                                                                                                            n2Yes
                                                                                                            alternativeYes
                                                                                                            drawflagYes
                                                                                                            color#colorNumYes

                                                                                                            Location

                                                                                                            stat, TESTS, 3:2-SampZTest(

                                                                                                            Description

                                                                                                            2-SampZTest( performs a z significance test to compare the means of two populations. This test is valid for simple random samples from populations with known standard deviations. In addition, either the populations must be normally distributed, or the sample sizes have to be sufficiently large (usually, greater than 10).

                                                                                                            The logic behind the test is as follows: we want to test the hypothesis that the true means of the two populations are equal (the null hypothesis). The letter μ is used for a population mean, so this is usually written as μ1=μ2. To do this, we assume that this "null hypothesis" is true, and calculate the probability that the difference between the two means occurred, under this assumption. If this probability is sufficiently low (usually, 5% is the cutoff point), we conclude that since it's so unlikely that the data could have occurred under the null hypothesis, the null hypothesis must be false, and therefore the means are not equal. If, on the other hand, the probability is not too low, we conclude that the data may well have occurred under the null hypothesis, and therefore there's no reason to reject it.

                                                                                                            In addition to the null hypothesis, we must have an alternative hypothesis as well - usually this is simply that the two means are not equal. However, in certain cases when we have reason to suspect that one mean is greater than the other (such as when we are trying to verify a claim that one mean is greater), our alternative hypothesis may be that the first mean is greater than the second (μ1>μ2) or less (μ1<μ2).

                                                                                                            As for the 2-SampZTest( command itself, there are two ways of calling it: after giving the two standard deviations, you may give it a list of all the sample data, or the necessary statistics about the list (x1 and x2 are the sample means, and n1 and n2 are the sample sizes). In either case, you can indicate what the alternate hypothesis is, by a value of 0, -1, or 1 for the alternative argument. 0 indicates a two-sided hypothesis of μ1≠μ2, -1 indicates μ1<μ2, and 1 indicates μ1>μ2. (In fact, the calculator will treat any negative value as -1, and any positive value as 1).

                                                                                                            Although you can access the 2-SampZTest( command on the home screen, via the catalog, there's no need: the 2-SampZTest… interactive solver, found in the statistics menu, is much more intuitive to use - you don't have to memorize the syntax.

                                                                                                            In either case, it's important to understand the output of 2-SampZTest. Here are the meanings of each line:

                                                                                                            • The first line, involving μ1 and μ2, is the alternative hypothesis.
                                                                                                            • z is the test statistic, the standardized difference between the means. If the null hypothesis is true, it should be close to 0.
                                                                                                            • p is the probability that the difference between μ1 and μ2 (the two means) would occur if the null hypothesis is true. When the value is sufficiently small, we reject the null hypothesis and conclude that the alternative hypothesis is true. You should have a cutoff value ready, such as 5% or 1%. If p is lower, you "reject the null hypothesis on a 5% (or 1%) level" in technical terms.
                                                                                                            • x-bar1 and x-bar2 are the two sample means.
                                                                                                            • n1 and n2 are the sample sizes.

                                                                                                            Sample Problem

                                                                                                            Your school claims that the average SAT score of students at the school is higher than at a rival school. You took samples of SAT scores from students at both schools (and stored them to L1 and L2). Although you didn't know the standard deviations, you decided to use the value 200 that you found online as an estimate.

                                                                                                            You now have all the data. You're assuming σ1 and σ2 are both 200; the two data lists are L1 and L2. Since the school's claim is that your school's score is higher, that will be your alternative hypothesis (μ1>μ2), which corresponds to a value of 1. The code you'd use is:

                                                                                                            :2-SampZTest(200,200,L1,L2,1

                                                                                                            Alternatively, you could calculate the mean and sample size of your sample, and put those into the command instead. Suppose you obtained SAT scores from 60 students at your school and 40 students at the rival school, and that the means were 1737 and 1623. Then your code is:

                                                                                                            :2-SampZTest(200,200,1737,60,1623,40,1

                                                                                                            You will see the following output:

                                                                                                            Z-Test
 μ1>μ2
 z=2.792418307
 p=.0026158434
 x1=1737
 x2=1623
 n1=60
 n2=40

                                                                                                            The most important part of this output is "p=.0026158434". This value of p is much smaller than 1% or 0.01. This is significant on the 1% level, so we reject the null hypothesis and conclude that the alternative hypothesis is true: μ1>μ2, that is, your school's average SAT score is indeed higher.

                                                                                                            Advanced Uses

                                                                                                            The final argument of 2-SampZTest(, draw?, will display the results in a graphical manner if you put in "1" for it. The calculator will draw the standard normal curve, and shade the area of the graph beyond the z statistic. In addition, the value of z and the value of p will be displayed (the value of p corresponds to the shaded area). You would make your conclusions in the same way as for the regular output.

                                                                                                            As with most other statistical commands, you may use a frequency list in your input (when using the data list syntax). If you do, then both lists must have frequencies, and the order of the arguments would be list1, list2, frequency1, frequency2.

                                                                                                            Optimization

                                                                                                            Most of the arguments of the 2-SampZTest( command have default values, and the argument can be omitted if this value is accepted.

                                                                                                            • The draw? argument can be omitted if you don't want graphical output, although you could put "0" in as well.
                                                                                                            • If the draw? argument is omitted, you can omit the alternative argument to use a two-sided test (μ1≠μ2). If you include the draw? argument, you have to include this - otherwise there will be confusion as to what the 5th argument means.
                                                                                                            • With data list input, you can always omit the frequency lists if you won't be using them.
                                                                                                            • With data list input, if the draw? and alternative arguments are omitted, and your data is in L1 and L2 (and you're not using frequency lists), you may omit L1 and L2 - those are default parameters. However, if alternative or draw? is present, you have to include it, or else the syntax may be confused with the syntax for summary stats input.

                                                                                                            The code in the sample problem above can't be optimized, because the alternative argument is 1:

                                                                                                            :2-SampZTest(200,200,L1,L2,1

                                                                                                            However, if we were doing a two-sided test, we could omit the alternative argument as well as the lists:

                                                                                                            :2-SampZTest(200,200,L1,L2,0
can be
:2-SampZTest(200,200

                                                                                                            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

                                                                                                            History

                                                                                                            Calculator OS Version Description
                                                                                                            TI-83 0.01013 Added
                                                                                                            Property Value
                                                                                                            Hex Value $BB47
                                                                                                            Categories
                                                                                                            Localizations
                                                                                                            • FR: 2-Comp𝐅Test(

                                                                                                            2-Samp𝐅Test

                                                                                                            Overview

                                                                                                            Performs a two-sample 𝐅 test. alternative=-1 is <; alternative=0 is ≠; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results.
                                                                                                            Color#: 10 - 24 or color name pasted from [vars] COLOR.

                                                                                                            Availability: Token only available from within the Basic editor.

                                                                                                            Syntax

                                                                                                            2-Samp𝐅Test[listname1,listname2,freqlist1,freqlist2,alternative,drawflag,color#]

                                                                                                            Arguments

                                                                                                            NameTypeOptional
                                                                                                            𝐅Yes
                                                                                                            listname1listNameYes
                                                                                                            listname2listNameYes
                                                                                                            freqlist1listYes
                                                                                                            freqlist2listYes
                                                                                                            alternativeYes
                                                                                                            drawflagYes
                                                                                                            color#colorNumYes

                                                                                                            Location

                                                                                                            stat, TESTS, E:2-Samp, Test

                                                                                                            Overview

                                                                                                            Performs a two-sample 𝐅 test. alternative=-1 is <; alternative=0 is ≠; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results.
                                                                                                            Color#: 10 - 24 or color name pasted from [vars] COLOR.

                                                                                                            Availability: Token only available from within the Basic editor.

                                                                                                            Syntax

                                                                                                            2-Samp𝐅TestSx1,n1,Sx2,n2[,alternative,drawflag,color#]

                                                                                                            Arguments

                                                                                                            NameTypeOptional
                                                                                                            𝐅
                                                                                                            Sx1
                                                                                                            n1
                                                                                                            Sx2
                                                                                                            n2Yes
                                                                                                            alternativeYes
                                                                                                            drawflagYes
                                                                                                            color#colorNumYes

                                                                                                            Location

                                                                                                            stat, TESTS, E:2-Samp, Test

                                                                                                            Description

                                                                                                            Examples

                                                                                                            Explanation 1

                                                                                                            code 1

                                                                                                            Explanation 2

                                                                                                            code 2

                                                                                                            Error Conditions

                                                                                                            Advanced Notes

                                                                                                            History

                                                                                                            Calculator OS Version Description
                                                                                                            TI-83 0.01013 Added
                                                                                                            Property Value
                                                                                                            Hex Value $F3
                                                                                                            Categories
                                                                                                            Localizations
                                                                                                            • FR: Stats 2-Var

                                                                                                            2-Var Stats

                                                                                                            Overview

                                                                                                            Performs two-variable analysis on the data in Xlistname and Ylistname with frequency freqlist.

                                                                                                            Availability: Token available everywhere.

                                                                                                            Syntax

                                                                                                            2-VarStats [Xlistname,Ylistname,freqlist]

                                                                                                            Arguments

                                                                                                            NameTypeOptional
                                                                                                            XlistnamelistYes
                                                                                                            YlistnamelistYes
                                                                                                            freqlistlistYes

                                                                                                            Location

                                                                                                            stat, CALC, 2:2-Var Stats

                                                                                                            Description

                                                                                                            This command calculates a bunch of common (and a few uncommon) statistics for a pair of lists (it uses L1 and L2 by default, but you can use any list by supplying it as an argument). You have to store the lists to variables first, though, before calculating statistics for them. For example:

                                                                                                            :{5,12,7,8,4,9→L1
:{1,0,2,5,7,4→L2
:2-Var Stats

                                                                                                            The calculator treats the two lists as a list of ordered pairs. Some of the statistics calculated assume that this is the case, and the two lists are the same size: an error will occur if the lists don't match.

                                                                                                            Like other statistical commands, you can use a frequency list as well, for cases where one element occurs more times than another (you can do this with a normal list, too, but that might be inconvenient when an element occurs very many times). There is only one frequency list for both data lists, and the frequency applies to the ordered pair formed by an element taken from each list. For example:

                                                                                                            :{1,2,3→L1
:{1,2,3→L2
:{5,3,2→L3
:2-Var Stats L1,L2,L3

                                                                                                            is the frequency-list equivalent of:

                                                                                                            :{1,1,1,1,1,2,2,2,3,3→L1
:{1,1,1,1,1,2,2,2,3,3→L2
:2-Var Stats

                                                                                                            When you're running it from the home screen, 2-Var Stats will display the statistics; this won't happen if you do it inside a program. Either way, it will also store what it calculated to the statistics variables found in VARS>Statistics… The variables 2-Var Stats affects are:

                                                                                                            • \(\definecolor{darkgreen}{rgb}{0.90,0.91,0.859}\pagecolor{darkgreen} \overline{\textrm{x}}\) is the mean (average) of the first list
                                                                                                            • Σx is the sum of the first list
                                                                                                            • Σx² is the sum of the squares of the first list
                                                                                                            • Sx is the sample standard deviation of the first list
                                                                                                            • σx is population standard deviation of the first list
                                                                                                            • minX is the minimum element of the first list
                                                                                                            • maxX is the maximum element of the first list
                                                                                                            • \(\definecolor{darkgreen}{rgb}{0.90,0.91,0.859}\pagecolor{darkgreen} \overline{\textrm{y}}\) is the mean (average) of the second list
                                                                                                            • Σy is the sum of the second list
                                                                                                            • Σy² is the sum of the squares of the second list
                                                                                                            • Sy is the sample standard deviation of the second list
                                                                                                            • σy is population standard deviation of the second list
                                                                                                            • minY is the minimum element of the second list
                                                                                                            • maxY is the maximum element of the second list
                                                                                                            • Σxy is the sum of products of each matching pair of elements in the lists
                                                                                                            • n is the number of elements in both lists

                                                                                                            2-Var Stats will not work with "reserved" list names that the calculator uses internally. The only known such reserved list is the list RESID, and there's no reason to suspect there are any others. Ans, TblInput, and any expression which resolves to a list, are also not appropriate for this command: store all of these to a list before doing 2-Var Stats on them.

                                                                                                            Advanced uses

                                                                                                            If you consider the two lists to be vectors, then Σxy is their dot product, and Σx² and Σy² are the squares of their norms; math done with these and other statistics can produce the shortest (but not necessarily quickest) way to calculate many vector operations.

                                                                                                            Optimization

                                                                                                            Aside from statistical analysis, 2-Var Stats can also be used when you want to use the values it calculates more than once. This will save on size, since, for example Σx takes up less space than sum(L1), but considering how many calculations 2-Var Stats makes, it will usually be slower.

                                                                                                            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Timothy Foster.

                                                                                                            History

                                                                                                            Calculator OS Version Description
                                                                                                            TI-82 1.0 Added
                                                                                                            Property Value
                                                                                                            Hex Value $32
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                                                                                                            • FR: 2

                                                                                                            2

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                                                                                                            Availability: Token available everywhere.

                                                                                                            Syntax

                                                                                                            2

                                                                                                            Description

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                                                                                                            Explanation 1

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                                                                                                            Calculator OS Version Description
                                                                                                            TI-82 1.0 Added
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                                                                                                            • FR: 3

                                                                                                            3

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                                                                                                            Availability: Token available everywhere.

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                                                                                                            Calculator OS Version Description
                                                                                                            TI-82 1.0 Added
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                                                                                                            • FR: 4

                                                                                                            4

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                                                                                                            Availability: Token available everywhere.

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                                                                                                            Calculator OS Version Description
                                                                                                            TI-82 1.0 Added
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                                                                                                            • FR: 5

                                                                                                            5

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                                                                                                            Availability: Token available everywhere.

                                                                                                            Syntax

                                                                                                            5

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                                                                                                            Explanation 1

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                                                                                                            code 2

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                                                                                                            Advanced Notes

                                                                                                            History

                                                                                                            Calculator OS Version Description
                                                                                                            TI-82 1.0 Added
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                                                                                                            Hex Value $36
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                                                                                                            • FR: 6

                                                                                                            6

                                                                                                            Overview

                                                                                                            Availability: Token available everywhere.

                                                                                                            Syntax

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                                                                                                            Explanation 1

                                                                                                            code 1

                                                                                                            Explanation 2

                                                                                                            code 2

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                                                                                                            History

                                                                                                            Calculator OS Version Description
                                                                                                            TI-82 1.0 Added
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                                                                                                            Hex Value $37
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                                                                                                            • FR: 7

                                                                                                            7

                                                                                                            Overview

                                                                                                            Availability: Token available everywhere.

                                                                                                            Syntax

                                                                                                            7

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                                                                                                            Explanation 1

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                                                                                                            Explanation 2

                                                                                                            code 2

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                                                                                                            History

                                                                                                            Calculator OS Version Description
                                                                                                            TI-82 1.0 Added
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                                                                                                            Hex Value $38
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                                                                                                            • FR: 8

                                                                                                            8

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                                                                                                            Availability: Token available everywhere.

                                                                                                            Syntax

                                                                                                            8

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                                                                                                            Explanation 1

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                                                                                                            Calculator OS Version Description
                                                                                                            TI-82 1.0 Added
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                                                                                                            Hex Value $39
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                                                                                                            • FR: 9

                                                                                                            9

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                                                                                                            Availability: Token available everywhere.

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                                                                                                            code 1

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                                                                                                            Calculator OS Version Description
                                                                                                            TI-82 1.0 Added
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                                                                                                            Hex Value $BBD6
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                                                                                                            • FR: ;

                                                                                                            ;

                                                                                                            Overview

                                                                                                            Availability: Token available everywhere.

                                                                                                            Syntax

                                                                                                            ;

                                                                                                            Description

                                                                                                            Examples

                                                                                                            Explanation 1

                                                                                                            code 1

                                                                                                            Explanation 2

                                                                                                            code 2

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                                                                                                            Calculator OS Version Description
                                                                                                            TI-83+ 1.15 Added
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                                                                                                            Hex Value $6A
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                                                                                                            • FR: =

                                                                                                            =

                                                                                                            Overview

                                                                                                            Availability: Token available everywhere.

                                                                                                            Syntax

                                                                                                            =

                                                                                                            Description

                                                                                                            Examples

                                                                                                            Explanation 1

                                                                                                            code 1

                                                                                                            Explanation 2

                                                                                                            code 2

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                                                                                                            History

                                                                                                            Calculator OS Version Description
                                                                                                            TI-82 1.0 Added
                                                                                                            Property Value
                                                                                                            Hex Value $6D
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                                                                                                            • FR: ≤

                                                                                                            ≤

                                                                                                            Overview

                                                                                                            Availability: Token available everywhere.

                                                                                                            Syntax

                                                                                                            ≤

                                                                                                            Description

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                                                                                                            Explanation 1

                                                                                                            code 1

                                                                                                            Explanation 2

                                                                                                            code 2

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                                                                                                            History

                                                                                                            Calculator OS Version Description
                                                                                                            TI-82 1.0 Added
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                                                                                                            Hex Value $BBD1
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                                                                                                            • FR: @

                                                                                                            @

                                                                                                            Overview

                                                                                                            Availability: Token available everywhere.

                                                                                                            Syntax

                                                                                                            @

                                                                                                            Description

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                                                                                                            Explanation 1

                                                                                                            code 1

                                                                                                            Explanation 2

                                                                                                            code 2

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                                                                                                            Advanced Notes

                                                                                                            History

                                                                                                            Calculator OS Version Description
                                                                                                            TI-83+ 1.15 Added
                                                                                                            Property Value
                                                                                                            Hex Value $41
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                                                                                                            • FR: A

                                                                                                            A

                                                                                                            Overview

                                                                                                            Availability: Token available everywhere.

                                                                                                            Syntax

                                                                                                            A

                                                                                                            Description

                                                                                                            Examples

                                                                                                            Explanation 1

                                                                                                            code 1

                                                                                                            Explanation 2

                                                                                                            code 2

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                                                                                                            Advanced Notes

                                                                                                            History

                                                                                                            Calculator OS Version Description
                                                                                                            TI-82 1.0 Added
                                                                                                            Property Value
                                                                                                            Hex Value $BB59
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                                                                                                            • FR: ANUVA(

                                                                                                            ANOVA(

                                                                                                            Overview

                                                                                                            Performs a one-way analysis of variance for comparing the means of two to 20 populations.

                                                                                                            Availability: Token available everywhere.

                                                                                                            Syntax

                                                                                                            ANOVA(list1,list2[,list3,...,list20])

                                                                                                            Arguments

                                                                                                            NameTypeOptional
                                                                                                            list1list
                                                                                                            list2list
                                                                                                            list3listYes
                                                                                                            ...Yes
                                                                                                            list20listYes

                                                                                                            Location

                                                                                                            stat, TESTS, H:ANOVA(

                                                                                                            Description

                                                                                                            The ANOVA (analysis of variance) command is used to test if there is a significant difference between the means of several populations (this is an extension of the two-sample t-test which compares only two populations). The calculator assumes the null hypothesis, that all means are equal, and returns a probability value, p, of the differences in the data occurring if the null hypothesis were true. If p is small (usually, if it's less than .05), then it's unlikely we'd get such differences just by chance if the null hypothesis were true, so we reject it and conclude that at least one of the means is different.

                                                                                                            There are two reasons why we don't test the means in pairs using a simpler test. First of all, it would take a long time: there's so many pairs to compare. Second of all, when you're doing many tests, there's a high probability you'll get a low p-value by chance. Imagine that you're doing 10 tests. If the probability of getting a low p-value on one test is .05, then the probability that at least one test will return one is 1-.9510: about 0.4 - this is quite likely to happen. The ANOVA test avoids this by having only one null hypothesis to test.

                                                                                                            If you're only interested in the result of the test, the only thing you'll need in the output is the second line: "p=…" This is your p-value, and determines whether you should reject the null hypothesis or not. If you need more detail, here are the meanings of the other variables:

                                                                                                            • F is the test statistic. If the null hypothesis is true, it should follow Snedecor's F distribution, and Fcdf( can be used to determine the p-value.
                                                                                                            • For both Factor and Error:
                                                                                                              • MS is the mean squares (SS/df). If the null hypothesis is true, Factor MS should be roughly equal to Error MS
                                                                                                              • SS is the sum of squares - see the TI-83+ Manual for formulas
                                                                                                              • df is the number of degrees of freedom - for Factor, it's the df between the categorical variables, and for Error, it's the sum of df between each variable.
                                                                                                            • Sxp is the pooled variation.

                                                                                                            Advanced Uses

                                                                                                            The statistics F, p, and Sxp will be stored to the appropriate variables after this test. The other six statistics do not have a normal variable associated with them. However, the two-byte tokens 0x6237 through 0x623C are, in fact, used to store the values of Factor MS, Factor SS, Factor df, Error MS, Error SS, and Error df respectively. They can't be accessed through a menu, but if you use a hex editor to paste them into your program, you will be able to use them just like any other variable.

                                                                                                            However, be careful because the Factor and Error tokens look exactly alike (even though they refer to different variables), and can be confused. Also, there is a chance that future OS versions will change the behavior of ANOVA(, though this is unlikely, and this trick will no longer work.

                                                                                                            Error Conditions

                                                                                                            • ERR:ARGUMENT is thrown if one of the lists is blank, only one list is used, or the function is completely blank.
                                                                                                            • ERR:SYNTAX is thrown if you do not use lists (Matrixes, numbers,etc)
                                                                                                              • ERR:INVALID DIM is thrown if you use a list that has 0 or a negative number.
                                                                                                              • ERR:DATA TYPE is thrown by using "l" or a list with a different set of data.

                                                                                                            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583, Myles_Zadok, nap386, Trenly.

                                                                                                            History

                                                                                                            Calculator OS Version Description
                                                                                                            TI-83 0.01013 Added
                                                                                                            Property Value
                                                                                                            Hex Value $EF3B
                                                                                                            Categories
                                                                                                              Localizations
                                                                                                              • FR: AUTO

                                                                                                              AUTO

                                                                                                              Overview

                                                                                                              Displays answers in a similar format as the input.

                                                                                                              Availability: Token available everywhere.

                                                                                                              Syntax

                                                                                                              AUTO

                                                                                                              Location

                                                                                                              mode, Answers: AUTO

                                                                                                              Description

                                                                                                              Examples

                                                                                                              Explanation 1

                                                                                                              code 1

                                                                                                              Explanation 2

                                                                                                              code 2

                                                                                                              Error Conditions

                                                                                                              Advanced Notes

                                                                                                              History

                                                                                                              Calculator OS Version Description
                                                                                                              TI-84+ 2.53 Added
                                                                                                              Property Value
                                                                                                              Hex Value $72
                                                                                                              Categories
                                                                                                              Localizations
                                                                                                              • FR: Rep

                                                                                                              Ans

                                                                                                              Overview

                                                                                                              Returns the last answer.

                                                                                                              Availability: Token available everywhere.

                                                                                                              Syntax

                                                                                                              Ans

                                                                                                              Location

                                                                                                              2nd, ans

                                                                                                              Description

                                                                                                              The Ans variable holds the last answer that was stored in the calculator. Because Ans is stored in a special storage area built-in to the calculator, and it is extensively used by the calculator, you cannot delete it. Ans is also useful; it can make your programs both smaller and faster:

                                                                                                              • Unlike other variables which have a value type hard-coded in (i.e., a string can only hold text, and lists and matrices can only hold numbers), Ans can take on whatever value you want: a real or complex, list, matrix, or string are all acceptable.

                                                                                                              • Along with the finance variables, Ans is faster than the real, complex, list, matrix, and string variables; and subsequently, you should try to use it as much as possible.

                                                                                                              One of the most common places to use Ans is in place of storing a value to a variable. Just paste the Ans variable to the location where the variable was called, and then when the expression is evaluated, the calculator will use the current value of Ans. Using the Ans variable allows you to eliminate the variable, which helps save a little or a lot of memory (depending on the type of variable and its size).

                                                                                                              Instead of:

                                                                                                              30+5A→B
Disp 25A,B

                                                                                                              A shorter version would be:

                                                                                                              30+5A
Disp 25A,Ans

                                                                                                              (Since the Ans token is only 1 byte, you've just saved two bytes. In longer programs the savings can add up!)

                                                                                                              The one major drawback to using Ans is that its current value is only temporary.

                                                                                                              What commands modify Ans?

                                                                                                              Whenever you:

                                                                                                              • Store a value to a variable, such as 1→X

                                                                                                              • Place an expression or string on a line by itself, such as 1+2 or "Hello"

                                                                                                              • Use the optional argument of the Pause command such as Pause X. Ans will be updated to the new value.

                                                                                                              If you're performing multiple calculations across multiple variables, you might be better off storing each in a separate variable.

                                                                                                              What commands do NOT modify Ans?

                                                                                                              There are several cases in which changing the value of a variable does not modify Ans, thus preserving its current value for later use:

                                                                                                              • Asking a user for input via Prompt X or Input "X:",X

                                                                                                              • Storing to an equation variable such as "X+1"→Y₁

                                                                                                              • Using DelVar to delete a variable (i.e. set its value to zero, if it's a real variable)

                                                                                                              • For( loops

                                                                                                              • Changing the value with IS>( or DS<(

                                                                                                              Also most other commands that do not modify variables will preserve Ans, including:

                                                                                                              • ClrHome
                                                                                                              • If … Then … Else … End
                                                                                                              • Disp
                                                                                                              • Output()
                                                                                                              • Repeat
                                                                                                              • While
                                                                                                              • Lbl
                                                                                                              • Goto
                                                                                                              • Menu()
                                                                                                              • Pause (when there's no parameter following it, otherwise the parameter will be stored in Ans!)

                                                                                                              Knowing these cases can be very useful, allowing you to make efficient use of Ans to store a result and re-use it in later lines rather than create a temporary variable for it.

                                                                                                              Using Ans with Lists

                                                                                                              Ans can be used to store lists and access individual items. Take the following example:

                                                                                                              10→A
{11,22,33}
Disp Ans(1),Ans(2)

                                                                                                              In this example, the calculator is smart enough to know that Ans is currently holding a list, and so will interpret the (1) and (2) as accessing items from the list. As such it will display 11 and 22. Trying to access Ans(4) will display an error.

                                                                                                              However if we removed line 2 from the code above, Ans would instead be holding the value 10, and as such Ans would be multiplied by 1 and 2, resulting in 10 and 20.

                                                                                                              The augment() function can also be used with Ans to add additional items to your list, for example:

                                                                                                              {1,2}
augment(Ans,{3,4})
Disp Ans

                                                                                                              This will display {1 2 3 4}

                                                                                                              Timing

                                                                                                              Storing a real value into Ans takes approximately 1.0 ms. This does not include the time needed to compute or retrieve the value, which may be significant.

                                                                                                              Source: parts of this page were written by the following TI|BD contributors: alexrudd, burr, DarkerLine, GoVegan, kg583, lirtosiast, Myles_Zadok, rileyp, Timothy Foster, Trenly.

                                                                                                              History

                                                                                                              Calculator OS Version Description
                                                                                                              TI-82 1.0 Added
                                                                                                              Property Value
                                                                                                              Hex Value $BB68
                                                                                                              Categories
                                                                                                              Localizations
                                                                                                              • FR: Archive

                                                                                                              Archive

                                                                                                              Overview

                                                                                                              Moves the specified variable from RAM to the user data archive memory.

                                                                                                              Availability: Token available everywhere.

                                                                                                              Syntax

                                                                                                              Archive variables

                                                                                                              Arguments

                                                                                                              NameTypeOptional
                                                                                                              variables

                                                                                                              Location

                                                                                                              2nd, mem, 5:Archive

                                                                                                              Description

                                                                                                              The Archive command moves a variable from RAM to the archive (also known as ROM). A quick synopsis of the difference between the two:

                                                                                                              • Data in the archive cannot be accessed, but it's protected from RAM clears (which may occur during battery removal if not done carefully); also, the archive can hold much more data.
                                                                                                              • Data in RAM can be accessed for calculations, but it can also be deleted during a RAM clear or accidentally overwritten by another program.

                                                                                                              Nothing happens if the variable in question is already archived.

                                                                                                              You might want to use this command to protect data such as saved games from being accidentally deleted. It's not, in general, a good idea to archive commonly used variables, such as the real variables A-Z, since programs usually expect to be able to access these variables without problems, and won't check if they're archived.

                                                                                                              Also, some variables cannot be archived. These include:

                                                                                                              • The real variables R, T, X, Y, θ, and n (due to their use in graphing)
                                                                                                              • The equation variables Yn, XnT, YnT, rn, u, v, and w
                                                                                                              • The stat plots Plot_#_
                                                                                                              • Window, table, and zoom variables such as TblInput or Xmin
                                                                                                              • Statistical variables and the list ʟRESID
                                                                                                              • Finance variables

                                                                                                              Finally, the Archive command does not work on programs when using it from a program (it does, however, archive programs from the home screen). However, an assembly program can be executed as a subroutine so that Archive and UnArchive can be used within a program. The program should however be run again afterwards.

                                                                                                              Advanced Uses

                                                                                                              As archived variables (and programs) can not be accessed by the calculator's inbuilt OS, archiving programs can be quite problematic when trying to execute them. However; by enabling your programs to be viewable in assembly shells, you can execute your programs without needing to unarchive them first. This is because the assembly shell copies the program to the RAM automatically, and is then executed. Closing the program will automatically remove the copy from the RAM, so no RAM is lost in the end.

                                                                                                              Error Conditions

                                                                                                              • ERR:ARCHIVE FULL is thrown when there isn't enough space in the archive for the variable.
                                                                                                              • ERR:INVALID is thrown when trying to archive a program from within a program.
                                                                                                              • ERR:VARIABLE is thrown when trying to archive a variable that cannot be archived.

                                                                                                              Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Myles_Zadok, thornahawk, Trenly.

                                                                                                              History

                                                                                                              Calculator OS Version Description
                                                                                                              TI-83+ 0.103 Added
                                                                                                              Property Value
                                                                                                              Hex Value $BB6A
                                                                                                              Categories
                                                                                                              Localizations
                                                                                                              • FR: Asm(

                                                                                                              Asm(

                                                                                                              Overview

                                                                                                              Availability: Token available everywhere.

                                                                                                              Syntax

                                                                                                              Asm(

                                                                                                              Description

                                                                                                              The Asm( command is used for running an assembly program. Unlike TI-Basic programs, assembly programs are written in the calculator's machine code directly, which makes them more powerful in both speed and functionality. However, it also means that if they crash, they crash hard — there is no built-in error menu to protect you.

                                                                                                              Keep in mind that many assembly programs these days are written for a shell such as Ion or MirageOS. If you're dealing with one of those programs, calling Asm( on it will do nothing; you need to get the appropriate shell and run that instead.

                                                                                                              With the AsmPrgm and AsmComp( commands, you can create small assembly programs yourself, directly on the calculator. If you are using at TI-84+CE with OS 5.3, the Asm( is unnecessary to run such programs.

                                                                                                              Error Conditions

                                                                                                              • ERR:INVALID is thrown if the program isn't an assembly program.

                                                                                                              See Also

                                                                                                              Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583, Myles_Zadok, Trenly.

                                                                                                              History

                                                                                                              Calculator OS Version Description
                                                                                                              TI-83+ 0.103 Added
                                                                                                              Property Value
                                                                                                              Hex Value $EF7A
                                                                                                              Categories
                                                                                                              Localizations
                                                                                                              • FR: Asm84CEPrgm

                                                                                                              Asm84CEPrgm

                                                                                                              Overview

                                                                                                              Comment:Asm83CEPrgm on the TI-83 Premium CE

                                                                                                              Syntax

                                                                                                              Asm84CEPrgm

                                                                                                              Description

                                                                                                              Please see the AsmPrgm page. The functionality and use are the same between both commands. However, the Asm84CEPrgm is only available on the TI-84+CE calculator. Keep in mind that hexadecimal for the monochrome calculators may not work on color calculators. This token does not work on OS 5.3.1, it has been deprecated by Texas Instruments for no good reason. Even uploading a program with this token in it will not work as it will throw an INVALID error.

                                                                                                              There is a workaround to this problem. A sendable program containing the command can be found here.

                                                                                                              To run assembly programs on the calculator, recall the command from the program you sent. Type your hex code in the editor. When you're done, quit the program. Type the following on the homescreen:

                                                                                                              AsmComp(prgmNAME1,prgmNAME2

                                                                                                              Then, find the program you compressed and run it with either the Asm( command or like a normal BASIC progam.

                                                                                                              Source: parts of this page were written by the following TI|BD contributors: jonbush, Myles_Zadok, Trenly, VoxelPrismatic.

                                                                                                              History

                                                                                                              Calculator OS Version Description
                                                                                                              TI-84+CE 5.0.0 Added
                                                                                                              Property Value
                                                                                                              Hex Value $EF68
                                                                                                              Categories
                                                                                                              Localizations
                                                                                                              • FR: Asm84CPrgm

                                                                                                              Asm84CPrgm

                                                                                                              Overview

                                                                                                              Syntax

                                                                                                              Asm84CPrgm

                                                                                                              Description

                                                                                                              Please see the AsmPrgm page. The functionality and use is the same between both commands. However, the Asm84CPrgm is only available on the TI-84+CSE calculator. Keep in mind that hexadecimal for the monochrome calculators may not work on color calculators.

                                                                                                              Source: parts of this page were written by the following TI|BD contributors: Electromagnet8, jonbush, Myles_Zadok, Trenly.

                                                                                                              History

                                                                                                              Calculator OS Version Description
                                                                                                              TI-84+CSE 4.0 Added
                                                                                                              Property Value
                                                                                                              Hex Value $BB6B
                                                                                                              Categories
                                                                                                              Localizations
                                                                                                              • FR: AsmComp(

                                                                                                              AsmComp(

                                                                                                              Overview

                                                                                                              Availability: Token available everywhere.

                                                                                                              Syntax

                                                                                                              AsmComp(

                                                                                                              Description

                                                                                                              This command is used to compress an assembly program written using AsmPrgm into an "assembled" assembly program. This will make the program about twice as small, and protect it from being edited, in addition to making execution faster.

                                                                                                              To use AsmComp(, give it the ASCII represented assembly program, followed by the name you want the assembled program to have. That name can't be already taken. Since it's not easy to rename an assembled assembly program, if you want to write a program called prgmGAME, you type the ASCII represented code in a program with a different name (e.g. GAMEA) and then do AsmComp((prgmGAMEA,prgmGAME).

                                                                                                              Assembly programs can be run with Asm(.

                                                                                                              Error Conditions

                                                                                                              • ERR:DUPLICATE is thrown if prgm_RESULT_ is an already used program name;
                                                                                                              • ERR:INVALID is thrown if prgm_ORIGINAL_ doesn't start with AsmPrgm;
                                                                                                              • ERR:SYNTAX is thrown if prgm_ORIGINAL_ is not an assembly program.

                                                                                                              Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, MateoConLechuga, Myles_Zadok, Trenly.

                                                                                                              History

                                                                                                              Calculator OS Version Description
                                                                                                              TI-83+ 0.103 Added
                                                                                                              Property Value
                                                                                                              Hex Value $BB6C
                                                                                                              Categories
                                                                                                              Localizations
                                                                                                              • FR: AsmPrgm

                                                                                                              AsmPrgm

                                                                                                              Overview

                                                                                                              Availability: Token available everywhere.

                                                                                                              Syntax

                                                                                                              AsmPrgm

                                                                                                              Description

                                                                                                              Examples

                                                                                                              Explanation 1

                                                                                                              code 1

                                                                                                              Explanation 2

                                                                                                              code 2

                                                                                                              Error Conditions

                                                                                                              Advanced Notes

                                                                                                              History

                                                                                                              Calculator OS Version Description
                                                                                                              TI-83+ 0.103 Added
                                                                                                              Property Value
                                                                                                              Hex Value $7E09
                                                                                                              Categories
                                                                                                              Localizations
                                                                                                              • FR: AxesNAff

                                                                                                              AxesOff

                                                                                                              Overview

                                                                                                              Turns off the graph axes.

                                                                                                              Availability: Token only available from within the Basic editor.

                                                                                                              Syntax

                                                                                                              AxesOff

                                                                                                              Location

                                                                                                              2nd, format, AxesOff

                                                                                                              Description

                                                                                                              The AxesOff command disables the X and Y axes on the graph screen, so that they aren't drawn. They can be enabled again with the AxesOn command.

                                                                                                              (the y=x line that is drawn when both Seq and Web modes are enabled is also controlled by this command)

                                                                                                              Generally, the AxesOff command should be used at the beginning of the program to disable the axes if the program is going to use the graph screen, since the axes get in the way. However, you should consider using StoreGDB and RecallGDB to save this setting if that's the case.

                                                                                                              Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Myles_Zadok, Trenly.

                                                                                                              History

                                                                                                              Calculator OS Version Description
                                                                                                              TI-82 1.0 Added
                                                                                                              Property Value
                                                                                                              Hex Value $7E08
                                                                                                              Categories
                                                                                                              Localizations
                                                                                                              • FR: AxesAff

                                                                                                              AxesOn

                                                                                                              Overview

                                                                                                              Turns on the graph axes with color. The coloroption allows the color of the axes to be specified.
                                                                                                              Color#: 10 - 24 or color name pasted from [vars] COLOR..

                                                                                                              Availability: Token only available from within the Basic editor.

                                                                                                              Syntax

                                                                                                              AxesOn[color#]

                                                                                                              Arguments

                                                                                                              NameTypeOptional
                                                                                                              color#colorNumYes

                                                                                                              Location

                                                                                                              2nd, format, AxesOn

                                                                                                              Description

                                                                                                              The AxesOn command enables the X and Y axes on the graph screen, so that they are drawn. They can be disabled with the AxesOff command.

                                                                                                              (the y=x line that is drawn when both Seq and Web modes are enabled is also controlled by this command)

                                                                                                              Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Myles_Zadok, Trenly.

                                                                                                              History

                                                                                                              Calculator OS Version Description
                                                                                                              TI-82 1.0 AxesOn added
                                                                                                              TI-84+CSE 4.0 Renamed AxesOn to AxesOn
                                                                                                              Property Value
                                                                                                              Hex Value $42
                                                                                                              Categories
                                                                                                              Localizations
                                                                                                              • FR: B

                                                                                                              B

                                                                                                              Overview

                                                                                                              Availability: Token available everywhere.

                                                                                                              Syntax

                                                                                                              B

                                                                                                              Description

                                                                                                              Examples

                                                                                                              Explanation 1

                                                                                                              code 1

                                                                                                              Explanation 2

                                                                                                              code 2

                                                                                                              Error Conditions

                                                                                                              Advanced Notes

                                                                                                              History

                                                                                                              Calculator OS Version Description
                                                                                                              TI-82 1.0 Added
                                                                                                              Property Value
                                                                                                              Hex Value $EF43
                                                                                                              Categories
                                                                                                              Localizations
                                                                                                              • FR: NOIR

                                                                                                              BLACK

                                                                                                              Overview

                                                                                                              Availability: Token available everywhere.

                                                                                                              Syntax

                                                                                                              BLACK

                                                                                                              Description

                                                                                                              Examples

                                                                                                              Explanation 1

                                                                                                              code 1

                                                                                                              Explanation 2

                                                                                                              code 2

                                                                                                              Error Conditions

                                                                                                              Advanced Notes

                                                                                                              History

                                                                                                              Calculator OS Version Description
                                                                                                              TI-84+CSE 4.0 Added
                                                                                                              Property Value
                                                                                                              Hex Value $EF41
                                                                                                              Categories
                                                                                                              Localizations
                                                                                                              • FR: BLEU

                                                                                                              BLUE

                                                                                                              Overview

                                                                                                              Availability: Token available everywhere.

                                                                                                              Syntax

                                                                                                              BLUE

                                                                                                              Description

                                                                                                              Examples

                                                                                                              Explanation 1

                                                                                                              code 1

                                                                                                              Explanation 2

                                                                                                              code 2

                                                                                                              Error Conditions

                                                                                                              Advanced Notes

                                                                                                              History

                                                                                                              Calculator OS Version Description
                                                                                                              TI-84+CSE 4.0 Added
                                                                                                              Property Value
                                                                                                              Hex Value $EF47
                                                                                                              Categories
                                                                                                              Localizations
                                                                                                              • FR: MARRON

                                                                                                              BROWN

                                                                                                              Overview

                                                                                                              Availability: Token available everywhere.

                                                                                                              Syntax

                                                                                                              BROWN

                                                                                                              Description

                                                                                                              Examples

                                                                                                              Explanation 1

                                                                                                              code 1

                                                                                                              Explanation 2

                                                                                                              code 2

                                                                                                              Error Conditions

                                                                                                              Advanced Notes

                                                                                                              History

                                                                                                              Calculator OS Version Description
                                                                                                              TI-84+CSE 4.0 Added
                                                                                                              Property Value
                                                                                                              Hex Value $EF64
                                                                                                              Categories
                                                                                                                Localizations
                                                                                                                • FR: ArrPlanNAff

                                                                                                                BackgroundOff

                                                                                                                Overview

                                                                                                                Turns off background image in the graph area.

                                                                                                                Availability: Token only available from within the Basic editor.

                                                                                                                Syntax

                                                                                                                BackgroundOff

                                                                                                                Location

                                                                                                                2nd, draw, BACKGROUND, 2:BackgroundOff:

                                                                                                                Description

                                                                                                                The BackgroundOff command has only one purpose: turn the background off. Run the command on its own line in a program with no other characters or arguments.

                                                                                                                :BackgroundOn BLUE //Makes background blue
:BackgroundOff //Makes background white again

                                                                                                                Optimization

                                                                                                                BackgroundOff does essentially the same thing as turning the background on to the color white, as shown below.

                                                                                                                :BackgroundOn WHITE
can be
:BackgroundOff

                                                                                                                Source: parts of this page were written by the following TI|BD contributors: Battlesquid, kg583, Michael2_3B, MrWompWomp, Myles_Zadok, Trenly.

                                                                                                                History

                                                                                                                Calculator OS Version Description
                                                                                                                TI-84+CSE 4.0 Added
                                                                                                                Property Value
                                                                                                                Hex Value $EF5B
                                                                                                                Categories
                                                                                                                  Localizations
                                                                                                                  • FR: ArrPlanAff

                                                                                                                  BackgroundOn

                                                                                                                  Overview

                                                                                                                  Displays a menu the Background Image Var n (Image#n) specified in the graph area.

                                                                                                                  Availability: Token only available from within the Basic editor.

                                                                                                                  Syntax

                                                                                                                  BackgroundOn n

                                                                                                                  Location

                                                                                                                  2nd, draw, BACKGROUND, 1:BackgroundOn

                                                                                                                  Description

                                                                                                                  With the introduction of color and a higher resolution screen than the monochrome calculators, the TI-84+CSE and TI-84+CE included the ability to display a background image on the graphscreen. The images variables are similar to the picture variables in that there 10 slots. In addition, functions can be drawn on top of images.

                                                                                                                  BackgroundOn recalls an image variable or color and displays it on the graphscreen.

                                                                                                                  :BackgroundOn Image1
is the same as
:BackgroundOn 1

                                                                                                                  Intrestingly, the following is a valid syntax, which fills the graphscreen with a light blue (18).

                                                                                                                  :15→B
:BackgroundOn B+3

                                                                                                                  In addition, BackgroundOn can be used to fill the graphscreen with a solid color. The color variables range from 10 to 24, blue to dark gray, as documented here. For example, BackgroundOn 12 will fill the graphscreen with black.

                                                                                                                  :BackgroundOn 12

                                                                                                                  Error Conditions

                                                                                                                  • ERR:DOMAIN is thrown if the number is not an integer between 0 and 24.

                                                                                                                  Source: parts of this page were written by the following TI|BD contributors: Battlesquid, Electromagnet8, MrWompWomp, Myles_Zadok, Trenly.

                                                                                                                  History

                                                                                                                  Calculator OS Version Description
                                                                                                                  TI-84+CSE 4.0 Added
                                                                                                                  Property Value
                                                                                                                  Hex Value $EF6C
                                                                                                                  Categories
                                                                                                                    Localizations
                                                                                                                    • FR: CouleurBord

                                                                                                                    BorderColor

                                                                                                                    Overview

                                                                                                                    Turns on a border color surrounding the graph area with the specified color. Color #:1-4.

                                                                                                                    Availability: Token only available from within the Basic editor.

                                                                                                                    Syntax

                                                                                                                    BorderColor[color#]

                                                                                                                    Arguments

                                                                                                                    NameTypeOptional
                                                                                                                    color#colorNumYes

                                                                                                                    Location

                                                                                                                    2nd, format, BorderColor

                                                                                                                    Description

                                                                                                                    Examples

                                                                                                                    Explanation 1

                                                                                                                    code 1

                                                                                                                    Explanation 2

                                                                                                                    code 2

                                                                                                                    Error Conditions

                                                                                                                    Advanced Notes

                                                                                                                    History

                                                                                                                    Calculator OS Version Description
                                                                                                                    TI-84+CSE 4.0 Added
                                                                                                                    Property Value
                                                                                                                    Hex Value $05
                                                                                                                    Categories
                                                                                                                    Localizations
                                                                                                                    • FR: Carré

                                                                                                                    Boxplot

                                                                                                                    Overview

                                                                                                                    Defines Plot# (1, 2, or 3) of type

                                                                                                                    Availability: Token only available from within the Basic editor.

                                                                                                                    Syntax

                                                                                                                    Boxplot Plot#(type,Xlist[,freqlist,color#])

                                                                                                                    Arguments

                                                                                                                    NameTypeOptional
                                                                                                                    type
                                                                                                                    Xlistlist
                                                                                                                    freqlistlistYes
                                                                                                                    color#colorNumYes

                                                                                                                    Location

                                                                                                                    2nd, stat plot

                                                                                                                    Description

                                                                                                                    The commands Plot1(, Plot2(, and Plot3(, which are identical except for which stat plot (1, 2, or 3) they affect, define their corresponding stat plot. When the stat plot is defined, it is also turned on so no PlotsOn command is necessary.

                                                                                                                    The first argument of the commands is always the type of plot, and is one of Scatter, xyLine, Histogram, Boxplot, ModBoxplot, and NormProbPlot - these types are found in the TYPE submenu of the stat plot menu. The other arguments vary. For all but Histogram and Boxplot, there is a mark argument - this is a dot, a cross, or a box, symbols that can be found in the MARK submenu of the stat plot menu. On color calculators, there is an optional final argument to specify the color of the plot.

                                                                                                                    Scatter plot

                                                                                                                    Plot#(Scatter, x-list, y-list, mark) defines a scatter plot. The points defined by x-list and y-list are plotted using mark on the graph screen.

                                                                                                                    x-list and y-list must be the same length.

                                                                                                                    xyLine plot

                                                                                                                    Plot#(xyLine, x-list, y-list, mark) defines an xyLine plot. Similarly to a scatter plot, the points defined by x-list and y-list are plotted using mark on the graph screen, but with an xyLine plot they are also connected by a line, in the order that they occur in the lists.

                                                                                                                    x-list and y-list must be the same length.

                                                                                                                    Histogram plot

                                                                                                                    Plot#(Histogram, x-list, freq list) defines a Histogram plot. The x-axis is divided into intervals that are Xscl wide. A bar is drawn in in each interval whose height corresponds to the number of points in the interval. Points that are not between Xmin and Xmax are not tallied.

                                                                                                                    Xscl must not be too small - it can divide the screen into no more than 47 different bars.

                                                                                                                    Box plot

                                                                                                                    Plot#(Boxplot, x-list, freq list) defines a box plot. A rectangular box is drawn whose left edge is Q1 (the first quartile) of the data, and whose right edge is Q3 (the third quartile). A vertical segment is drawn within the box at the median, and 'whiskers' are drawn from the box to the minimum and maximum data points.

                                                                                                                    The box plot ignores the Ymax and Ymin dimensions of the screen, and any plots that aren't box plots or modified box plots. Each box plot takes approximately 1/3 of the screen in height, and if more than one are plotted, they will take up different areas of the screen.

                                                                                                                    Modified box plot

                                                                                                                    Plot#(ModBoxplot, x-list, freq list, mark) defines a modified box plot. This is almost entirely like the normal box plot, except that it also draws outliers. Whiskers are only drawn to the furthers point within 1.5 times the interquartile range (Q3-Q1) of the box. Beyond this point, data points are drawn individually, using mark.

                                                                                                                    The box plot ignores the Ymax and Ymin dimensions of the screen, and any plots that aren't box plots or modified box plots. Each box plot takes approximately 1/3 of the screen in height, and if more than one are plotted, they will take up different areas of the screen.

                                                                                                                    Normal probability plot

                                                                                                                    Plot#(NormProbPlot, data list, data axis, mark) defines a normal probability plot. The mean and standard deviation of the data are calculated. Then for each point, the number of standard deviations it is from the mean is calculated, and the point is plotted against this number using mark. data axis can be either X or Y: it determines whether the value of a point determines it's x-coordinate or y-coordinate.

                                                                                                                    The point behind this rather convoluted process is to test the extent to which the data is normally distributed. If it follows the normal distribution closely, then the result will be close to a straight line - otherwise it will be curved.

                                                                                                                    Advanced Uses

                                                                                                                    After doing a regression, a scatter plot of ʟRESID against the x-list is a useful measure of the effectiveness of the regression. If the plot appears random, this is a good sign; if there is a pattern to the plot, this means it's likely that a better regression model exists.

                                                                                                                    Optimization

                                                                                                                    The ʟ symbol at the beginning of list names can be omitted everywhere in this command.

                                                                                                                    In addition, every element except the plot type and the data list or data lists are optional, and take on the following default values:

                                                                                                                    • freq list is 1 by default, meaning that all frequencies are 1.
                                                                                                                    • mark is the box by default.
                                                                                                                    • data axis is X by default.

                                                                                                                    Error Conditions

                                                                                                                    • ERR:DIM MISMATCH is thrown if the x and y lists, or the data and frequency lists, have different dimensions.
                                                                                                                    • ERR:STAT is thrown if Xscl is too small in the case of a Histogram.

                                                                                                                    All errors are thrown when plotting the stat plot, as opposed to when the command is executed, and do not provide a 2:Goto option.

                                                                                                                    Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Myles_Zadok.

                                                                                                                    History

                                                                                                                    Calculator OS Version Description
                                                                                                                    TI-82 1.0 Added
                                                                                                                    Property Value
                                                                                                                    Hex Value $43
                                                                                                                    Categories
                                                                                                                    Localizations
                                                                                                                    • FR: C

                                                                                                                    C

                                                                                                                    Overview

                                                                                                                    Availability: Token available everywhere.

                                                                                                                    Syntax

                                                                                                                    C

                                                                                                                    Description

                                                                                                                    Examples

                                                                                                                    Explanation 1

                                                                                                                    code 1

                                                                                                                    Explanation 2

                                                                                                                    code 2

                                                                                                                    Error Conditions

                                                                                                                    Advanced Notes

                                                                                                                    History

                                                                                                                    Calculator OS Version Description
                                                                                                                    TI-82 1.0 Added
                                                                                                                    Property Value
                                                                                                                    Hex Value $EF93
                                                                                                                    Categories
                                                                                                                      Localizations
                                                                                                                      • FR: CENTRE

                                                                                                                      CENTER

                                                                                                                      Overview

                                                                                                                      CENTER is a tail argument for the invNorm( command where the optional argument tail can be LEFT (-∞,-a), CENTER [-a,a] or RIGHT (a, ∞) for Real a.
                                                                                                                      See also invNorm(.

                                                                                                                      Comment:CE OS 5.2+

                                                                                                                      Availability: Token available everywhere.

                                                                                                                      Syntax

                                                                                                                      CENTER

                                                                                                                      Location

                                                                                                                      2nd, catalog

                                                                                                                      Description

                                                                                                                      Examples

                                                                                                                      Explanation 1

                                                                                                                      code 1

                                                                                                                      Explanation 2

                                                                                                                      code 2

                                                                                                                      Error Conditions

                                                                                                                      Advanced Notes

                                                                                                                      History

                                                                                                                      Calculator OS Version Description
                                                                                                                      TI-84+CE 5.2.0 Added
                                                                                                                      Property Value
                                                                                                                      Hex Value $EF38
                                                                                                                      Categories
                                                                                                                        Localizations
                                                                                                                        • FR: CLASSIC

                                                                                                                        CLASSIC

                                                                                                                        Overview

                                                                                                                        Displays inputs and outputs on a single line, such as 1/2+3/4.

                                                                                                                        Availability: Token available everywhere.

                                                                                                                        Syntax

                                                                                                                        CLASSIC

                                                                                                                        Location

                                                                                                                        mode, CLASSIC

                                                                                                                        Description

                                                                                                                        CLASSIC will put the calculator into Classic mode as opposed to MathPrint mode. The Classic mode will make the calculator display everything as pre-MathPrint OS would, including input. For instance, rather than superscripting exponents as MathPrint mode would, Classic mode uses the simple caret syntax (^).

                                                                                                                        MathPrint mode:
                                                                                                                        24
                                                                                                                             16

                                                                                                                        Classic mode:
                                                                                                                        2^4
                                                                                                                             16

                                                                                                                        Advanced Uses

                                                                                                                        When in Classic mode, text and numbers are displayed much faster on the home screen and the function menus load faster. This can be useful in games that use the home screen, or just with calculations in general.

                                                                                                                        Source: parts of this page were written by the following TI|BD contributors: ccrh2009, jonbush, Kydapoot, lirtosiast, Myles_Zadok, Timothy Foster.

                                                                                                                        History

                                                                                                                        Calculator OS Version Description
                                                                                                                        TI-84+ 2.53 Added
                                                                                                                        Property Value
                                                                                                                        Hex Value $EF36
                                                                                                                        Categories
                                                                                                                        Localizations
                                                                                                                        • FR: CLASSIC

                                                                                                                        CLASSIC

                                                                                                                        Overview

                                                                                                                        Comment:Alias / Old

                                                                                                                        Syntax

                                                                                                                        CLASSIC

                                                                                                                        Description

                                                                                                                        Examples

                                                                                                                        Explanation 1

                                                                                                                        code 1

                                                                                                                        Explanation 2

                                                                                                                        code 2

                                                                                                                        Error Conditions

                                                                                                                        Advanced Notes

                                                                                                                        History

                                                                                                                        Calculator OS Version Description
                                                                                                                        Property Value
                                                                                                                        Hex Value $6331
                                                                                                                        Categories
                                                                                                                        Localizations
                                                                                                                        • FR: |C/Y

                                                                                                                        |C/Y

                                                                                                                        Overview

                                                                                                                        Syntax

                                                                                                                        |C/Y

                                                                                                                        Description

                                                                                                                        Examples

                                                                                                                        Explanation 1

                                                                                                                        code 1

                                                                                                                        Explanation 2

                                                                                                                        code 2

                                                                                                                        Error Conditions

                                                                                                                        Advanced Notes

                                                                                                                        History

                                                                                                                        Calculator OS Version Description
                                                                                                                        TI-83 0.01013 Added
                                                                                                                        Property Value
                                                                                                                        Hex Value $A5
                                                                                                                        Categories
                                                                                                                        Localizations
                                                                                                                        • FR: Cercle(

                                                                                                                        Circle(

                                                                                                                        Overview

                                                                                                                        Draws a circle with center (X,Y) and radius with specified
                                                                                                                        Color#: 10 - 24 or color name pasted from [vars] COLOR.
                                                                                                                        linestyle#: 1-2.

                                                                                                                        Availability: Token available everywhere.

                                                                                                                        Syntax

                                                                                                                        Circle(X,Y,radius[,color#,linestyle#])

                                                                                                                        Arguments

                                                                                                                        NameTypeOptional
                                                                                                                        X
                                                                                                                        Y
                                                                                                                        radius
                                                                                                                        color#colorNumYes
                                                                                                                        linestyle#integerYes

                                                                                                                        Location

                                                                                                                        2nd, draw, DRAW, 9:Circle(

                                                                                                                        Description

                                                                                                                        Circle(X,Y,r) will draw a circle at (X,Y) with radius r. X and Y will be affected by the window settings. The radius will also be affected by the window settings.

                                                                                                                        :Circle(5,5,5)

                                                                                                                        Advanced Uses

                                                                                                                        The radius of a circle is affected by the window settings. This means that if the x- and y-increment is two, the radius will be two pixels. However, there is another way to take advantage of this to draw ellipses. If the x- and y-increment are different, then the shape will not be a circle. For instance, with Xmin=0, Xmax=20, Ymin=0, and Ymax=31, Circle(10,10,2) will draw an ellipse, where the width is greater than the height.

                                                                                                                        Optimization

                                                                                                                        If a complex list such as {𝑖} is passed to Circle( as the fourth argument, the "fast circle" routine is used instead, which uses the symmetries of the circle to only do 1/8 of the trig calculations. For example:

                                                                                                                        :Circle(0,0,5
can be
:Circle(0,0,5,{i

                                                                                                                        Any list of complex numbers will work as the fourth argument in the same way, but there's no benefit to using any other list.

                                                                                                                        Note: The "fast circle" routine is not available on the TI-84+CSE or TI-84+CE calculators.

                                                                                                                        Command Timings

                                                                                                                        The ordinary Circle( is extremely slow. The fast circle trick discussed above cuts the time down to only about 30% of the "slow Circle(" time! While still not instant, this is faster than any replacement routine that can be written in TI-Basic.

                                                                                                                        For small radii, replace Circle( with Pt-On( instead.

                                                                                                                        Source: parts of this page were written by the following TI|BD contributors: 15274, burr, CloudVariable, DarkerLine, GoVegan, jonbush, Myles_Zadok, Xphoenix, Zaphod Beeblebrox.

                                                                                                                        History

                                                                                                                        Calculator OS Version Description
                                                                                                                        TI-82 1.0 Added
                                                                                                                        Property Value
                                                                                                                        Hex Value $BB57
                                                                                                                        Categories
                                                                                                                        Localizations
                                                                                                                        • FR: Efface entrées

                                                                                                                        Clear Entries

                                                                                                                        Overview

                                                                                                                        Clears the contents of the Last Entry storage area.

                                                                                                                        Availability: Token available everywhere.

                                                                                                                        Syntax

                                                                                                                        Clear Entries

                                                                                                                        Location

                                                                                                                        2nd, mem, MEMORY, 3:Clear Entries

                                                                                                                        Description

                                                                                                                        Normally, by pressing 2nd ENTER repeatedly, you can cycle through some of the recent entries on the home screen. With the Clear Entries command, this history is cleared (only Clear Entries remains in the history).

                                                                                                                        This can be used to free some memory, although it's recommended not to do this in a program (because clearing things without asking first isn't nice). Aside from that, maybe the only reason to use Clear Entries is to protect your privacy — although someone looking at your entries will know you cleared something, so it's not that effective.

                                                                                                                        Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Myles_Zadok.

                                                                                                                        History

                                                                                                                        Calculator OS Version Description
                                                                                                                        TI-83 0.01013 Added
                                                                                                                        Property Value
                                                                                                                        Hex Value $EF0F
                                                                                                                        Categories
                                                                                                                        Localizations
                                                                                                                        • FR: HorlNAff

                                                                                                                        ClockOff

                                                                                                                        Overview

                                                                                                                        Turns off the clock display in the mode screen.

                                                                                                                        Availability: Token available everywhere.

                                                                                                                        Syntax

                                                                                                                        ClockOff

                                                                                                                        Location

                                                                                                                        2nd, catalog, ClockOff

                                                                                                                        Description

                                                                                                                        The ClockOff command turns off the clock display at the bottom of the mode screen on the TI-84+/SE calculators. You can turn the clock back on by using the ClockOn command, or by selecting 'TURN CLOCK ON' ,displayed in place of the clock on the mode screen.

                                                                                                                        The ClockOff command does not actually turn the clock off. The time can still be accessed through use of the getTime and getDate commands, and all their cousins.

                                                                                                                        Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Jonathan King, Myles_Zadok.

                                                                                                                        History

                                                                                                                        Calculator OS Version Description
                                                                                                                        TI-84+ 0.01 Added
                                                                                                                        Property Value
                                                                                                                        Hex Value $EF10
                                                                                                                        Categories
                                                                                                                        Localizations
                                                                                                                        • FR: HorlAff

                                                                                                                        ClockOn

                                                                                                                        Overview

                                                                                                                        Turns on the clock display in the mode screen.

                                                                                                                        Availability: Token available everywhere.

                                                                                                                        Syntax

                                                                                                                        ClockOn

                                                                                                                        Location

                                                                                                                        2nd, catalog, ClockOn

                                                                                                                        Description

                                                                                                                        The ClockOn command turns on the clock display at the bottom of the mode screen on the TI-84+/SE calculators. Alternatively, you can scroll down to the 'TURN CLOCK ON' message that is displayed in place of the clock on the mode screen and press ENTER twice. You can turn the clock off by using the ClockOff command.

                                                                                                                        Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Myles_Zadok.

                                                                                                                        History

                                                                                                                        Calculator OS Version Description
                                                                                                                        TI-84+ 0.01 Added
                                                                                                                        Property Value
                                                                                                                        Hex Value $BB52
                                                                                                                        Categories
                                                                                                                        Localizations
                                                                                                                        • FR: EffToutListes

                                                                                                                        ClrAllLists

                                                                                                                        Overview

                                                                                                                        Sets to 0 the dimension of all lists in memory.

                                                                                                                        Availability: Token available everywhere.

                                                                                                                        Syntax

                                                                                                                        ClrAllLists

                                                                                                                        Location

                                                                                                                        2nd, mem, MEMORY, 4:ClrAllLists

                                                                                                                        Description

                                                                                                                        The ClrAllLists command sets the dimension (length) of all lists to zero. This is virtually equivalent to deleting the lists, except for two differences:

                                                                                                                        • The lists still exist and will show up in the list menu and the memory management menu.
                                                                                                                        • The dim( command will return 0 for a cleared list, rather than an error.

                                                                                                                        However, accessing a cleared list in any other way will return an error, just as for a deleted list.

                                                                                                                        The ClrAllLists command should never be used in a program you give to someone else or upload - unless the user is aware of this effect, they might lose important data stored in one of their lists. There is no way to limit the effect of ClrAllLists, so a program should use ClrList instead to avoid affecting unrelated lists (this is assuming you already want to use this questionably-useful effect).

                                                                                                                        Outside a program (or in a program for personal use), you might use this command to clear the contents of your lists to free up memory, while still not deleting the lists. This might possibly be convenient. Maybe.

                                                                                                                        Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Myles_Zadok.

                                                                                                                        History

                                                                                                                        Calculator OS Version Description
                                                                                                                        TI-83 0.01013 Added
                                                                                                                        Property Value
                                                                                                                        Hex Value $85
                                                                                                                        Categories
                                                                                                                        Localizations
                                                                                                                        • FR: EffDessin

                                                                                                                        ClrDraw

                                                                                                                        Overview

                                                                                                                        Clears all drawn elements from a graph or drawing.

                                                                                                                        Availability: Token available everywhere.

                                                                                                                        Syntax

                                                                                                                        ClrDraw

                                                                                                                        Location

                                                                                                                        2nd, draw, DRAW, 1:ClrDraw

                                                                                                                        Description

                                                                                                                        The ClrDraw command is useful clearing away something drawn on the graph screen; in particular, you want to do this at the beginning of a program that uses the graph screen, to get rid of anything that might be on it initially. If there are functions, plots, axes, labels, or grid enabled, these will be redrawn even after you ClrDraw. If you don't want these, you should turn them off before the ClrDraw command.

                                                                                                                        Like many other drawing commands, if you're outside a program and on the graph screen, you can use this command directly, without going to the home screen. Just select ClrDraw from the menu, and the screen will be cleared immediately.

                                                                                                                        Advanced Uses

                                                                                                                        Unless the final state of the graph screen is the intended effect of the program, you want to use ClrDraw at the end of the program so that the user doesn't have to deal with it.

                                                                                                                        Caution: if the graph screen is displayed even before you execute ClrDraw, the user variable Y will be reset to 0. This might be useful as a side effect, but it's more likely to turn out to be a nuisance if you were relying on Y to store something useful. Also, such a wacky effect might get removed in later OS versions1, so it's a gamble relying on it to work for all users.

                                                                                                                        The RecallPic command does not erase what is previously on the graph screen when recalling a picture. Unless this is what you intend, use ClrDraw to erase the graph screen's old contents before recalling a picture.

                                                                                                                        Optimization

                                                                                                                        The ClrDraw command is not the only way to clear the screen. If something changes about the state of the functions or plots plotted on the graph, about the window dimensions, or the axes, grid, and labels, the graph screen will be marked as 'dirty' by the calculator, and will be cleared the next time you display it.

                                                                                                                        Don't be too confident about relying on this however. For example, if you cleared Y1 before displaying the graph, and Y1 previously contained something, the graph will be redrawn. However, if Y1 never existed, then you haven't changed anything, and the graph will remain.

                                                                                                                        A lot of people choose their preferred window settings using the following two commands, which sets the window to X= -47..47, Y= -31..31:

                                                                                                                        ZStandard:ZInteger

                                                                                                                        Since this actually switches two window settings, at least one will be different from the previous settings, so the next time the graph screen is shown, it will be cleared without a ClrDraw command. There are other friendly window settings that you can use as well.

                                                                                                                        See Also

                                                                                                                        Footnotes

                                                                                                                        1. Fixed on the TI-84+CSE

                                                                                                                        Source: parts of this page were written by the following TI|BD contributors: Austin 332000, burr, DarkerLine, GoVegan, kg583.

                                                                                                                        History

                                                                                                                        Calculator OS Version Description
                                                                                                                        TI-82 1.0 Added
                                                                                                                        Property Value
                                                                                                                        Hex Value $E1
                                                                                                                        Categories
                                                                                                                        Localizations
                                                                                                                        • FR: EffEcran

                                                                                                                        ClrHome

                                                                                                                        Overview

                                                                                                                        Clears the home screen.

                                                                                                                        Availability: Token only available from within the Basic editor.

                                                                                                                        Syntax

                                                                                                                        ClrHome

                                                                                                                        Location

                                                                                                                        prgm, I/O, 8:ClrHome

                                                                                                                        Description

                                                                                                                        There are numerous times in a program that you need a clear screen, so that you can display whatever text you want without it being interrupted. One place, in particular, is at the beginning of a program, since the previous program call(s) and any other text is typically still displayed on the screen. The simple ClrHome command is the command you use to clear the home screen.

                                                                                                                        When you use the ClrHome, it resets the cursor position to the top left corner of the home screen. This is what the Disp and Pause commands use as the reference for what line to display their text on, but it does not have any effect on Output(.

                                                                                                                        Advanced Uses

                                                                                                                        You want to make sure to clear the home screen when exiting programs (at the end of a program). This ensures that the next program that the user runs will not have to deal with whatever text your program left behind. It also helps the user, because they will not have to manually clear the home screen by pressing the CLEAR key; you have already done it for them.

                                                                                                                        Error Conditions

                                                                                                                        • ERR:INVALID occurs if this statement is used outside a program.

                                                                                                                        See Also

                                                                                                                        Source: parts of this page were written by the following TI|BD contributors: alexrudd, burr, CloudVariable, DarkerLine, GoVegan, kg583, Trenly.

                                                                                                                        History

                                                                                                                        Calculator OS Version Description
                                                                                                                        TI-82 1.0 Added
                                                                                                                        Property Value
                                                                                                                        Hex Value $FA
                                                                                                                        Categories
                                                                                                                        Localizations
                                                                                                                        • FR: EffListe

                                                                                                                        ClrList

                                                                                                                        Overview

                                                                                                                        Sets the dimension of one or more listnames to 0.

                                                                                                                        Availability: Token available everywhere.

                                                                                                                        Syntax

                                                                                                                        ClrListlistname1[,listname2, ...,listname n]

                                                                                                                        Arguments

                                                                                                                        NameTypeOptional
                                                                                                                        listname1listName
                                                                                                                        listname2listNameYes
                                                                                                                        listname nlistYes

                                                                                                                        Location

                                                                                                                        stat, EDIT, 4:ClrList

                                                                                                                        Description

                                                                                                                        ClrList sets the length of a list (or several lists) to 0. This is virtually equivalent to deleting the list, except for several differences:

                                                                                                                        • The list still exists — it will be shown in the memory management menu and the list menu
                                                                                                                        • Calling the dim( command on it will return 0, rather than an error.
                                                                                                                        • ClrList can clear multiple lists at the same time

                                                                                                                        Advanced Uses

                                                                                                                        You might use ClrList when building up a list element by element and using dim( in the process:

                                                                                                                        :ClrList L1
:While 10>dim(L1
:Input X
:X→L1(1+dim(L1
:End

                                                                                                                        Optimization

                                                                                                                        Using DelVar instead of ClrList allows you to save a tiny bit of memory (between 12 and 16 bytes) that ClrList doesn't delete, while keeping almost every aspect of the list clearing the same. If you are clearing several lists, you can separate them with commas as the arguments to ClrList, which can save space. Using ClrList is also substantially faster than DelVar if the list is going to be cleared many times.

                                                                                                                        Error Conditions

                                                                                                                        • ERR:SYNTAX is thrown if you leave off the ʟ symbol when referring to a custom list (i.e., ClrList B will not work; you have to use ClrList ʟB).

                                                                                                                        Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, jonbush, Myles_Zadok, Timothy Foster.

                                                                                                                        History

                                                                                                                        Calculator OS Version Description
                                                                                                                        TI-82 1.0 Added
                                                                                                                        Property Value
                                                                                                                        Hex Value $FB
                                                                                                                        Categories
                                                                                                                        Localizations
                                                                                                                        • FR: EffTable

                                                                                                                        ClrTable

                                                                                                                        Overview

                                                                                                                        Clears all values from the table.

                                                                                                                        Availability: Token only available from within the Basic editor.

                                                                                                                        Syntax

                                                                                                                        ClrTable

                                                                                                                        Location

                                                                                                                        prgm, I/O, 9:ClrTable

                                                                                                                        Description

                                                                                                                        The ClrTable command clears all calculations for the table screen shown if you press 2nd TABLE. That is, all already-calculated values in the table are cleared, and TblInput is deleted. In IndpntAuto and DependAuto mode, this usually isn't noticeable because the table will be recalculated almost immediately when you next look at it (unless one of the entered functions is so complicated it takes a while to calculate). This mainly has an effect in IndpntAsk or DependAsk mode, where the corresponding parts of the table will be cleared entirely.

                                                                                                                        Advanced Uses

                                                                                                                        As a side effect, ClrTable seems to have all the effects of ClrDraw — it clears the graph screen, and any equations or plots will be regraphed the next time the graph screen is displayed.

                                                                                                                        Command Timings

                                                                                                                        ClrTable and ClrDraw take the same amount of time to clear the screen.

                                                                                                                        Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Myles_Zadok.

                                                                                                                        History

                                                                                                                        Calculator OS Version Description
                                                                                                                        TI-82 1.0 Added
                                                                                                                        Property Value
                                                                                                                        Hex Value $7E05
                                                                                                                        Categories
                                                                                                                        Localizations
                                                                                                                        • FR: CoordNAff

                                                                                                                        CoordOff

                                                                                                                        Overview

                                                                                                                        Turns off cursor coordinate value display.

                                                                                                                        Availability: Token only available from within the Basic editor.

                                                                                                                        Syntax

                                                                                                                        CoordOff

                                                                                                                        Location

                                                                                                                        2nd, format, CoordOff

                                                                                                                        Description

                                                                                                                        When moving a cursor on a screen, it's possible for the calculator to display the coordinates of the current point (either polar or rectangular coordinates, depending on which of RectGC or PolarGC is set). The CoordOff command turns off this option.

                                                                                                                        To turn it on, use the CoordOn command.

                                                                                                                        Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, iPhoenixOnTIBD, Myles_Zadok.

                                                                                                                        History

                                                                                                                        Calculator OS Version Description
                                                                                                                        TI-82 1.0 Added
                                                                                                                        Property Value
                                                                                                                        Hex Value $7E04
                                                                                                                        Categories
                                                                                                                        Localizations
                                                                                                                        • FR: CoordAff

                                                                                                                        CoordOn

                                                                                                                        Overview

                                                                                                                        Turns on cursor coordinate value display.

                                                                                                                        Availability: Token only available from within the Basic editor.

                                                                                                                        Syntax

                                                                                                                        CoordOn

                                                                                                                        Location

                                                                                                                        2nd, format, CoordOn

                                                                                                                        Description

                                                                                                                        When moving a cursor on a screen, it's possible for the calculator to display the coordinates of the current point (either polar or rectangular coordinates, depending on which of RectGC or PolarGC is set). The CoordOn command turns on this option (to disable it, use the CoordOff command).

                                                                                                                        The coordinates are displayed in practically every situation when you're moving a cursor on the graph screen, even including the Trace, Input or Select( commands in a program. The interactive mode of Text( and the Pen tool are the exceptions — this is because these two situations involve a pixel coordinate, and not a point.

                                                                                                                        Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Myles_Zadok.

                                                                                                                        History

                                                                                                                        Calculator OS Version Description
                                                                                                                        TI-82 1.0 Added
                                                                                                                        Property Value
                                                                                                                        Hex Value $EFA2
                                                                                                                        Categories
                                                                                                                        Localizations
                                                                                                                        • FR: Copier ligne

                                                                                                                        Copy Line

                                                                                                                        Overview

                                                                                                                        Comment:CE OS 5.3+

                                                                                                                        Syntax

                                                                                                                        Copy Line

                                                                                                                        Description

                                                                                                                        Examples

                                                                                                                        Explanation 1

                                                                                                                        code 1

                                                                                                                        Explanation 2

                                                                                                                        code 2

                                                                                                                        Error Conditions

                                                                                                                        Advanced Notes

                                                                                                                        History

                                                                                                                        Calculator OS Version Description
                                                                                                                        TI-84+CE 5.3.0 Added
                                                                                                                        Property Value
                                                                                                                        Hex Value $2E
                                                                                                                        Categories
                                                                                                                        Localizations
                                                                                                                        • FR: RegCubique

                                                                                                                        CubicReg

                                                                                                                        Overview

                                                                                                                        Fits a cubic regression model to Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ.

                                                                                                                        Availability: Token available everywhere.

                                                                                                                        Syntax

                                                                                                                        CubicReg [Xlistname,Ylistname,freqlist,regequ]

                                                                                                                        Arguments

                                                                                                                        NameTypeOptional
                                                                                                                        XlistnamelistYes
                                                                                                                        YlistnamelistYes
                                                                                                                        freqlistlistYes
                                                                                                                        regequYes

                                                                                                                        Location

                                                                                                                        stat, CALC, 6:CubicReg

                                                                                                                        Description

                                                                                                                        The CubicReg command can calculate the best fit cubic function through a set of points. To use it, you must first store the points to two lists: one of the x-coordinates and one of the y-coordinates, ordered so that the nth element of one list matches up with the nth element of the other list. L₁ and L₂ are the default lists to use, and the List Editor (STAT > Edit…) is a useful window for entering the points. You must have at least 4 points because there are infinitely many cubics that can go through 3 points or less.

                                                                                                                        In its simplest form, CubicReg takes no arguments, and calculates a cubic through the points in L₁ and L₂:

                                                                                                                        :{9,13,21,30,31,31,34→L₁
:{260,320,420,530,560,550,590→L₂
:CubicReg

                                                                                                                        On the home screen, or as the last line of a program, this will display the equation of the quadratic: you'll be shown the format, y=ax³+bx²+cx+d, and the values of a, b, c, and d. It will also be stored in the RegEQ variable, but you won't be able to use this variable in a program — accessing it just pastes the equation wherever your cursor was. Finally, the statistical variables a, b, c, d, and R² will be set as well. This latter variable will be displayed only if "Diagnostic Mode" is turned on (see DiagnosticOn and DiagnosticOff).

                                                                                                                        You don't have to do the regression on L₁ and L₂, but if you don't you'll have to enter the names of the lists after the command. For example:

                                                                                                                        :{9,13,21,30,31,31,34→FAT
:{260,320,420,530,560,550,590→CALS
:CubicReg ʟFAT,ʟCALS

                                                                                                                        You can attach frequencies to points, for when a point occurs more than once, by supplying an additional argument — the frequency list. This list does not have to contain integer frequencies. If you add a frequency list, you must supply the names of the x-list and y-list as well, even when they're L₁ and L₂.

                                                                                                                        Finally, you can enter an equation variable (such as Y₁) after the command, so that the equation is stored in this variable automatically. This doesn't require you to supply the names of the lists, but if you do, the equation variable must come last. You can use polar, parametric, or sequential variables as well, but since the quadratic will be in terms of X anyway, this doesn't make much sense.

                                                                                                                        An example of CubicReg with all the optional arguments:

                                                                                                                        :{9,13,21,30,31,31,34→FAT
:{260,320,420,530,560,550,590→CALS
:{2,1,1,1,2,1,1→FREQ
:CubicReg ʟFAT,ʟCALS,ʟFREQ,Y₁

                                                                                                                        Advanced

                                                                                                                        Note that even if a relationship is actually linear or quadratic, since a cubic regression has all the freedom of a linear regression and more, it will produce a better R² value, especially if the number of points is small, and may lead you to (falsely) believe that a relationship is cubic when it actually isn't. Take the correlation constant with a grain of salt, and consider if the fit is really that much better at the expense of doubling the complexity and if there's any reason to believe the relationship between the variables may be cubic.

                                                                                                                        Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Myles_Zadok, thornahawk, Timothy Foster.

                                                                                                                        History

                                                                                                                        Calculator OS Version Description
                                                                                                                        TI-82 1.0 Added
                                                                                                                        Property Value
                                                                                                                        Hex Value $EFA1
                                                                                                                        Categories
                                                                                                                        Localizations
                                                                                                                        • FR: Couper ligne

                                                                                                                        Cut Line

                                                                                                                        Overview

                                                                                                                        Comment:CE OS 5.3+

                                                                                                                        Syntax

                                                                                                                        Cut Line

                                                                                                                        Description

                                                                                                                        Examples

                                                                                                                        Explanation 1

                                                                                                                        code 1

                                                                                                                        Explanation 2

                                                                                                                        code 2

                                                                                                                        Error Conditions

                                                                                                                        Advanced Notes

                                                                                                                        History

                                                                                                                        Calculator OS Version Description
                                                                                                                        TI-84+CE 5.3.0 Added
                                                                                                                        Property Value
                                                                                                                        Hex Value $44
                                                                                                                        Categories
                                                                                                                        Localizations
                                                                                                                        • FR: D

                                                                                                                        D

                                                                                                                        Overview

                                                                                                                        Availability: Token available everywhere.

                                                                                                                        Syntax

                                                                                                                        D

                                                                                                                        Description

                                                                                                                        Examples

                                                                                                                        Explanation 1

                                                                                                                        code 1

                                                                                                                        Explanation 2

                                                                                                                        code 2

                                                                                                                        Error Conditions

                                                                                                                        Advanced Notes

                                                                                                                        History

                                                                                                                        Calculator OS Version Description
                                                                                                                        TI-82 1.0 Added
                                                                                                                        Property Value
                                                                                                                        Hex Value $EF4F
                                                                                                                        Categories
                                                                                                                        Localizations
                                                                                                                        • FR: GRIS FON

                                                                                                                        DARKGRAY

                                                                                                                        Overview

                                                                                                                        Availability: Token available everywhere.

                                                                                                                        Syntax

                                                                                                                        DARKGRAY

                                                                                                                        Description

                                                                                                                        Examples

                                                                                                                        Explanation 1

                                                                                                                        code 1

                                                                                                                        Explanation 2

                                                                                                                        code 2

                                                                                                                        Error Conditions

                                                                                                                        Advanced Notes

                                                                                                                        History

                                                                                                                        Calculator OS Version Description
                                                                                                                        TI-84+CSE 4.0 Added
                                                                                                                        Property Value
                                                                                                                        Hex Value $EF3C
                                                                                                                        Categories
                                                                                                                          Localizations
                                                                                                                          • FR: DEC

                                                                                                                          DEC

                                                                                                                          Overview

                                                                                                                          Displays answers as integers or decimal numbers.

                                                                                                                          Availability: Token available everywhere.

                                                                                                                          Syntax

                                                                                                                          DEC

                                                                                                                          Location

                                                                                                                          mode, Answers: DEC

                                                                                                                          Description

                                                                                                                          Examples

                                                                                                                          Explanation 1

                                                                                                                          code 1

                                                                                                                          Explanation 2

                                                                                                                          code 2

                                                                                                                          Error Conditions

                                                                                                                          Advanced Notes

                                                                                                                          History

                                                                                                                          Calculator OS Version Description
                                                                                                                          TI-84+ 2.53 Added
                                                                                                                          Property Value
                                                                                                                          Hex Value $DB
                                                                                                                          Categories
                                                                                                                          Localizations
                                                                                                                          • FR: DS<(

                                                                                                                          DS<(

                                                                                                                          Overview

                                                                                                                          Decrements variable by 1; skips commandA if variable< value.

                                                                                                                          Availability: Token only available from within the Basic editor.

                                                                                                                          Syntax

                                                                                                                          DS<(variable,value):commandA:commands

                                                                                                                          Arguments

                                                                                                                          NameTypeOptional
                                                                                                                          variable
                                                                                                                          value
                                                                                                                          commandA
                                                                                                                          commands

                                                                                                                          Location

                                                                                                                          prgm, CTL, B:DS<(

                                                                                                                          Description

                                                                                                                          The decrement and skip if less than command — DS<( — is a specialized conditional command. It is equivalent to an If conditional, except the next command will be skipped when the condition is true and it has a variable update built-in. However, it is not used very often (if anything, it is often misused as a looping command) because of its obscure name and somewhat limited application.

                                                                                                                          The DS<( command takes two arguments:

                                                                                                                          • A variable, which is limited only to one of the real variables (A-Z or θ).
                                                                                                                          • A value, which can be any expression which evaluates to a real number.

                                                                                                                          When DS<( is executed it subtracts one from the variable (decrements it by one), and compares it to the value. The next command will be skipped if the variable is less than the value, while the next command will be executed if the variable is greater than or equal to the value.

                                                                                                                          The command DS<(A,B is equivalent to the following code:

                                                                                                                          :A-1→A
:If A≥B

                                                                                                                          Here are the two main cases where the DS<( command is used:

                                                                                                                          :5→A
:DS<(A,6
:Disp "Skipped
                                                                                                                          • Initializes A to 5 and then compares to the value
                                                                                                                          • 5<6 is true so the display message won't be displayed
                                                                                                                          :3→B
:DS<(B,2
:Disp "Not Skipped
                                                                                                                          • Initializes B to 3 and then compares to the value
                                                                                                                          • 3<2 is false so the display message will be displayed

                                                                                                                          Note: In addition to both of these cases, there is also the case where the variable and the value are equal to each other. This case is shown below under the 'Advanced Uses' section because it has some added background that goes with it.

                                                                                                                          Advanced Uses

                                                                                                                          When you want the skipping feature of the DS<( command to always occur, you just have to use the same variable for both the variable and value arguments of the command:

                                                                                                                          :DS<(B,B

                                                                                                                          An undefined error will occur if the variable and/or value doesn't exist before the DS<( command is used, which happens when the DelVar command is used. Consequently, you should not use DelVar with DS<(.

                                                                                                                          A similar code can be used as a substitute for B-1→B if you don't want to change Ans:

                                                                                                                          :DS<(B,B:

                                                                                                                          Note that due to the colon after the line, there will be no statement skipped, so you don't have to worry about that.

                                                                                                                          Optimization

                                                                                                                          If a program needs to decrement a positive variable, DS<( is one byte smaller than than decrementing a variable normally.

                                                                                                                          :A-1→A
can be
:DS<(A,0

                                                                                                                          The one caution about this is that if the variable is less than the value (in this case, '0'), the next command will be skipped. If you don't want the skipping functionality, then it is necessary to make sure that the value is never greater than the variable. Also, DS<( is slower than its more often used counterpart.

                                                                                                                          Related to the example code given, DS<( should always have a command following after it (i.e. it's not the last command in a program) because it will return an error otherwise. If you have no particular code choice, an empty line will suffice.

                                                                                                                          code that will run
:DS<(A,0
:
more code that will run

                                                                                                                          Command Timings

                                                                                                                          Using DS<( to decrement a variable is approximately 25% slower than using code like X-1→X. However, it is faster to use DS<( than to construct an If statement to do the same thing.

                                                                                                                          Note, however, that a quirk in the For( command (see its Optimization section) will slow down the DS<( command significantly if a closing parenthesis is not used for the For( statement.

                                                                                                                          Error Conditions

                                                                                                                          • ERR:INVALID occurs if this statement is used outside a program.
                                                                                                                          • ERR:SYNTAX is thrown if there is no next line to skip.
                                                                                                                          • ERR:UNDEFINED is thrown if the variable to be decremented is not defined.

                                                                                                                          Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583, Marcsine.

                                                                                                                          History

                                                                                                                          Calculator OS Version Description
                                                                                                                          TI-82 1.0 Added
                                                                                                                          Property Value
                                                                                                                          Hex Value $65
                                                                                                                          Categories
                                                                                                                          Localizations
                                                                                                                          • FR: Degré

                                                                                                                          Degree

                                                                                                                          Overview

                                                                                                                          Sets degree angle mode.

                                                                                                                          Availability: Token only available from within the Basic editor.

                                                                                                                          Syntax

                                                                                                                          Degree

                                                                                                                          Location

                                                                                                                          mode, Degree

                                                                                                                          Description

                                                                                                                          The Degree command puts the calculator into Degree mode, where the inputs and/or outputs to trig functions are assumed to be degree angles.

                                                                                                                          Angles measured in degrees range from 0 to 360, with 0 being an empty angle, 90 being a right angle, 180 being a straight angle, and 360 being a full angle all the way around a circle.

                                                                                                                          To convert from a radian angle to a degree angle, multiply by 180/π. To go the other way, and get a radian angle from a degree angle, multiply by π/180.

                                                                                                                          The following commands are affected by whether the calculator is in Radian or Degree mode:

                                                                                                                          The input is differently interpreted:

                                                                                                                          The output is differently expressed:

                                                                                                                          However, some commands are notably unaffected by angle mode, even though they involve angles, and this may cause confusion. This happens with the SinReg command, which assumes that the calculator is in Radian mode even when it's not. As a result, the regression model it generates will graph incorrectly in Degree mode.

                                                                                                                          Also, complex numbers in polar form are an endless source of confusion. The angle( command, as well as the polar display format, are affected by angle mode. However, complex exponentials (see the e^( command), defined as \(e^{i\theta}=\cos\theta+i\sin\theta\), are evaluated as though in Radian mode, regardless of the angle mode. This gives mysterious results like the following:

                                                                                                                          Degree:r𝑒^θ𝑖
        Done
𝑒^(πi)
        1𝑒^(180i)
Ans=𝑒^(180𝑖)
        0 (false)

                                                                                                                          Overall, it's better to put your calculator in Radian mode when dealing with polar form of complex numbers, especially since no mathematician would ever use degrees for the purpose anyway.

                                                                                                                          Optimization

                                                                                                                          It's sometimes beneficial to use the ° symbol instead of switching to Degree mode. The ° symbol will make sure a number is interpreted as a degree angle, even in Radian mode, so that, for example:

                                                                                                                          Radian
        Done
sin(90)
        -.8011526357
sin(90°)
        1

                                                                                                                          This is smaller when only one trig calculation needs to be done. Also, it doesn't change the user's settings, which are good to preserve whenever possible.

                                                                                                                          Source: parts of this page were written by the following TI|BD contributors: Adriweb, burr, DarkerLine, GoVegan, kg583, pandather.

                                                                                                                          History

                                                                                                                          Calculator OS Version Description
                                                                                                                          TI-82 1.0 Added
                                                                                                                          Property Value
                                                                                                                          Hex Value $BB54
                                                                                                                          Categories
                                                                                                                          Localizations
                                                                                                                          • FR: EffVar

                                                                                                                          DelVar

                                                                                                                          Overview

                                                                                                                          Deletes from memory the contents of variable.

                                                                                                                          Availability: Token only available from within the Basic editor.

                                                                                                                          Syntax

                                                                                                                          DelVar variable

                                                                                                                          Arguments

                                                                                                                          NameTypeOptional
                                                                                                                          variable

                                                                                                                          Location

                                                                                                                          prgm, CTL, G:DelVar

                                                                                                                          Description

                                                                                                                          The DelVar command deletes the contents of a variable (and thus the variable itself) from memory. You can use the DelVar command with any variable: reals, lists, matrices, strings, pictures, etc. However, you cannot use DelVar on specific elements of a matrix or string; it will actually throw a ERR:SYNTAX error. (It also does not work on programs, unfortunately.)

                                                                                                                          If the DelVar command is used with a real variable, the variable is not only deleted from memory but automatically set to zero the next time it is used. This is equivalent to using store (→) to manually set the variable yourself. Because the DelVar command is two bytes instead of one, there is no size difference between the two.

                                                                                                                          :0→A
same as
:DelVar A

                                                                                                                          While there is no size difference between the two, DelVar does have some problems that go along with using it. If used in a For loop to delete the counter variable or used to delete the variable and/or value in the IS>( or DS<( commands before using them, it will cause an ERR:UNDEFINED error.

                                                                                                                          This is a result of the way that the interpreter in TI-Basic is designed, so there is nothing you can do about it. You just need to be cognizant of it when using DelVar in a For( loop or together with IS>( or DS<(.

                                                                                                                          Advanced Uses

                                                                                                                          When you are done using variables, you should delete them at the end of the program with the DelVar command to cleanup. Each variable takes up a set amount of space (for example, a real variable is 15 bytes), and the more variables you can delete the more free memory is available. Free memory helps your programs run faster and allows you to pack more things on your calculator.

                                                                                                                          Because the DelVar command doesn't update the Ans variable, you can use DelVar and the current value in Ans will still be preserved for later use.

                                                                                                                          Optimizations

                                                                                                                          The DelVar command does not need a line break or colon (which indicates a new line of code) following the variable name. This allows you to make chains of variables (organized in whatever order you want), and it saves a byte for each line break or colon removed.

                                                                                                                          :DelVar A
:DelVar B
can be
:DelVar ADelVar B

                                                                                                                          Besides making chains of variables, the DelVar command also allows you to take the command from the next line and put it immediately after the DelVar command.

                                                                                                                          :DelVar A
:Disp "Hello
can be
:DelVar ADisp "Hello

                                                                                                                          There are, however, two cases in which the following statement will be ignored, so you should add a newline:

                                                                                                                          DelVar also does not count as a line with respect to IS>(, DS<(, and single-line If statements.

                                                                                                                          :If B
:Then
:DelVar A
:Disp "Hello
:End
can be
:If B
:DelVar ADisp "Hello

                                                                                                                          Command Timings

                                                                                                                          The speed of the DelVar command depends on the circumstance where it is used. When the variable already exists, DelVar is slower because it has to deallocate the variable from the RAM. DelVar is also significantly slower for zeroing real variables when compared to using → to set the variable to 0. The speed difference becomes apparent when the value is reset many times but is not a major factor if only used sparingly.

                                                                                                                          Error Conditions

                                                                                                                          • ERR:SYNTAX is thrown when trying to delete a system variable (e.g. DelVar Xmin) or a program, even though this is syntactically correct.
                                                                                                                          • ERR:UNDEFINED is thrown if you delete the loop variable while inside the loop, or delete the variable used in IS>( or DS<(.
                                                                                                                          • ERR:ARCHIVED is thrown if you use DelVar on an archived variable.

                                                                                                                          See Also

                                                                                                                          Source: parts of this page were written by the following TI|BD contributors: AntKou, basickevin, burr, DarkerLine, GoVegan, jonbush, kg583, Myles_Zadok.

                                                                                                                          History

                                                                                                                          Calculator OS Version Description
                                                                                                                          TI-83 1.010 Renamed DelVar to DelVar
                                                                                                                          Property Value
                                                                                                                          Hex Value $BBA2
                                                                                                                          Categories
                                                                                                                          Localizations
                                                                                                                          • FR: Δ

                                                                                                                          Δ

                                                                                                                          Overview

                                                                                                                          Availability: Token available everywhere.

                                                                                                                          Syntax

                                                                                                                          Δ

                                                                                                                          Description

                                                                                                                          Examples

                                                                                                                          Explanation 1

                                                                                                                          code 1

                                                                                                                          Explanation 2

                                                                                                                          code 2

                                                                                                                          Error Conditions

                                                                                                                          Advanced Notes

                                                                                                                          History

                                                                                                                          Calculator OS Version Description
                                                                                                                          TI-83+ 1.03 Added
                                                                                                                          Property Value
                                                                                                                          Hex Value $BB2C
                                                                                                                          Categories
                                                                                                                            Localizations
                                                                                                                            • FR: Δliste(

                                                                                                                            ΔList(

                                                                                                                            Overview

                                                                                                                            Returns a list containing the differences between consecutive elements in list.

                                                                                                                            Availability: Token available everywhere.

                                                                                                                            Syntax

                                                                                                                            ΔList(list)

                                                                                                                            Arguments

                                                                                                                            NameTypeOptional
                                                                                                                            Δ
                                                                                                                            listlist

                                                                                                                            Location

                                                                                                                            2nd, list, OPS, 7:List(

                                                                                                                            Description

                                                                                                                            ΔList( calculates the differences between consecutive terms of a list, and returns them in a new list.

                                                                                                                            ΔList({0,1,4,9,16,25,36})
    {1 3 5 7 9 11}

                                                                                                                            Advanced Uses

                                                                                                                            The ΔList( command is very nearly the inverse of the cumSum( command, which calculates the cumulative sums of a list. For any list, ΔList(cumSum(list)) will return the same list, but without its first element:

                                                                                                                            ΔList(cumSum({1,2,3,4,5,6,7}))
    {2 3 4 5 6 7}

                                                                                                                            Removing the first element would otherwise be a difficult procedure involving the seq( command, so this is a useful trick to know.

                                                                                                                            If a list is sorted in ascending order, min(ΔList(list)) will return 0 (false) if there are repeating values in the list, and a value corresponding to true if they are all distinct. The number of repeating elements can be determined similarly via 1+sum(0≠ΔList(list)) (again, so long as the list is sorted).

                                                                                                                            Error Conditions

                                                                                                                            Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, kg583, Timothy Foster.

                                                                                                                            History

                                                                                                                            Calculator OS Version Description
                                                                                                                            TI-83 0.01013 Added
                                                                                                                            Property Value
                                                                                                                            Hex Value $6321
                                                                                                                            Categories
                                                                                                                            Localizations
                                                                                                                            • FR: ∆Tbl

                                                                                                                            ∆Tbl

                                                                                                                            Overview

                                                                                                                            Availability: Token available everywhere.

                                                                                                                            Syntax

                                                                                                                            ∆Tbl

                                                                                                                            Description

                                                                                                                            Examples

                                                                                                                            Explanation 1

                                                                                                                            code 1

                                                                                                                            Explanation 2

                                                                                                                            code 2

                                                                                                                            Error Conditions

                                                                                                                            Advanced Notes

                                                                                                                            History

                                                                                                                            Calculator OS Version Description
                                                                                                                            TI-82 1.0 Added
                                                                                                                            Property Value
                                                                                                                            Hex Value $6326
                                                                                                                            Categories
                                                                                                                            Localizations
                                                                                                                            • FR: ∆X

                                                                                                                            ∆X

                                                                                                                            Overview

                                                                                                                            Availability: Token available everywhere.

                                                                                                                            Syntax

                                                                                                                            ∆X

                                                                                                                            Description

                                                                                                                            Examples

                                                                                                                            Explanation 1

                                                                                                                            code 1

                                                                                                                            Explanation 2

                                                                                                                            code 2

                                                                                                                            Error Conditions

                                                                                                                            Advanced Notes

                                                                                                                            History

                                                                                                                            Calculator OS Version Description
                                                                                                                            TI-82 1.0 Added
                                                                                                                            Property Value
                                                                                                                            Hex Value $6327
                                                                                                                            Categories
                                                                                                                            Localizations
                                                                                                                            • FR: ∆Y

                                                                                                                            ∆Y

                                                                                                                            Overview

                                                                                                                            Availability: Token available everywhere.

                                                                                                                            Syntax

                                                                                                                            ∆Y

                                                                                                                            Description

                                                                                                                            Examples

                                                                                                                            Explanation 1

                                                                                                                            code 1

                                                                                                                            Explanation 2

                                                                                                                            code 2

                                                                                                                            Error Conditions

                                                                                                                            Advanced Notes

                                                                                                                            History

                                                                                                                            Calculator OS Version Description
                                                                                                                            TI-82 1.0 Added
                                                                                                                            Property Value
                                                                                                                            Hex Value $7D
                                                                                                                            Categories
                                                                                                                            Localizations
                                                                                                                            • FR: CalculsDem

                                                                                                                            DependAsk

                                                                                                                            Overview

                                                                                                                            Sets table to ask for dependent-variable values.

                                                                                                                            Availability: Token only available from within the Basic editor.

                                                                                                                            Syntax

                                                                                                                            DependAsk

                                                                                                                            Location

                                                                                                                            2nd, tblset, Depend: Ask

                                                                                                                            Description

                                                                                                                            When the DependAsk setting (opposed to the DependAuto setting) is turned on, values in the table are not automatically calculated. To calculate the value of an equation, you have to select the column corresponding to that equation in the row corresponding to the value at which to calculate it, and press ENTER. For example, to calculate Y1 at X=0, select the X=0 column, scroll right to Y1, and press ENTER.

                                                                                                                            The DependAsk setting might be useful when dealing with a difficult-to-calculate function, for which you wouldn't want to have to calculate values that aren't really necessary.

                                                                                                                            Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Myles_Zadok.

                                                                                                                            History

                                                                                                                            Calculator OS Version Description
                                                                                                                            TI-82 1.0 Added
                                                                                                                            Property Value
                                                                                                                            Hex Value $7C
                                                                                                                            Categories
                                                                                                                            Localizations
                                                                                                                            • FR: CalculsAuto

                                                                                                                            DependAuto

                                                                                                                            Overview

                                                                                                                            Sets table to generate dependent-variable values automatically.

                                                                                                                            Availability: Token only available from within the Basic editor.

                                                                                                                            Syntax

                                                                                                                            DependAuto

                                                                                                                            Location

                                                                                                                            2nd, tblset, Depend: Auto

                                                                                                                            Description

                                                                                                                            When the DependAuto setting (opposed to the DependAsk setting) is turned on, values in the table are automatically calculated. With IndpntAuto, that means the table is automatically filled out completely; with IndpntAsk, that means that as soon as you enter a value for the independent variable, all the values of the dependent variables are calculated. This is usually the setting you want to use.

                                                                                                                            Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Myles_Zadok.

                                                                                                                            History

                                                                                                                            Calculator OS Version Description
                                                                                                                            TI-82 1.0 Added
                                                                                                                            Property Value
                                                                                                                            Hex Value $EF6B
                                                                                                                            Categories
                                                                                                                              Localizations
                                                                                                                              • FR: DétectAsymDés

                                                                                                                              DetectAsymOff

                                                                                                                              Overview

                                                                                                                              Turns off checks for rational function asymptotes when graphing. Impacts graph speed. Does not perform extra calculations to detect asymptotes pixel to pixel while graphing. Pixels will connect across the screen even across an asymptote.

                                                                                                                              Availability: Token only available from within the Basic editor.

                                                                                                                              Syntax

                                                                                                                              DetectAsymOff

                                                                                                                              Location

                                                                                                                              2nd, format, DetectAsymOff

                                                                                                                              Description

                                                                                                                              When DetectAsymOff is selected, the calculator will not detect asymptotes, adjusting the graph accordingly. This method of graphing is much faster than with asymptotes turned on. However, the graph can be erroneous when dealing with rational functions, as it will often draw extra lines to connect points near undefined values.

                                                                                                                              An asymptote is, by definition, "a line that continually approaches a given curve but does not meet it at any finite distance." Basically, an asymptote is the line where a function does not have any values on a certain axis.

                                                                                                                              Source: parts of this page were written by the following TI|BD contributors: kg583, Michael2_3B, Myles_Zadok.

                                                                                                                              History

                                                                                                                              Calculator OS Version Description
                                                                                                                              TI-84+CSE 4.0 Added
                                                                                                                              Property Value
                                                                                                                              Hex Value $EF6A
                                                                                                                              Categories
                                                                                                                                Localizations
                                                                                                                                • FR: DétectAsymAct

                                                                                                                                DetectAsymOn

                                                                                                                                Overview

                                                                                                                                Turns on checks for rational function asymptotes when graphing. Impacts graph speed. Performs more calculations and will not connect pixels across an asymptote on a graph.

                                                                                                                                Availability: Token only available from within the Basic editor.

                                                                                                                                Syntax

                                                                                                                                DetectAsymOn

                                                                                                                                Location

                                                                                                                                2nd, format

                                                                                                                                Description

                                                                                                                                When DetectAsymOn is selected, the calculator will detect asymptotes, adjusting the graph accordingly. This method of graphing is the most accurate but is also much slower than graphing with asymptotes turned off.

                                                                                                                                An asymptote is, by definition, "a line that continually approaches a given curve but does not meet it at any finite distance." Basically, an asymptote is the line where a function does not have any values on a certain axis.

                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: kg583, Michael2_3B, Myles_Zadok.

                                                                                                                                History

                                                                                                                                Calculator OS Version Description
                                                                                                                                TI-84+CSE 4.0 Added
                                                                                                                                Property Value
                                                                                                                                Hex Value $BB67
                                                                                                                                Categories
                                                                                                                                Localizations
                                                                                                                                • FR: CorrelNAff

                                                                                                                                DiagnosticOff

                                                                                                                                Overview

                                                                                                                                Sets diagnostics-off mode; r, r², and R² are not displayed as regression model results.

                                                                                                                                Availability: Token available everywhere.

                                                                                                                                Syntax

                                                                                                                                DiagnosticOff

                                                                                                                                Location

                                                                                                                                2nd, catalog, DiagnosticOff

                                                                                                                                Description

                                                                                                                                After the DiagnosticOff command is executed, all regression commands found in the STAT>CALC menu, as well as LinRegTTest, will not display the correlation statistics r and r2 (or just R2 in some cases). This is already turned off by default, although there is no disadvantage whatsoever to turning it on. To reverse this command, execute the DiagnosticOn command.

                                                                                                                                The statistic r, known as the correlation coefficient, measures the strength and direction of any linear relationship in the data (therefore if your regression model isn't linear, it may not exist, unless the calculator performed a transformation on the data). If r is close to 1, then the relationship is strong and positive (that is, the variables increase and decrease together). If r is close to -1, then the relationship is strong and negative (that is, as one variable increases, the other decreases). If r is close to 0, there is no linear relationship.

                                                                                                                                The statistic r2 or R2 is equal to the square of the above value (when it exists) and is also a measure of the strength of a relationship. Specifically, it represents the proportion of variance in the dependent variable that is accounted for by the regression model. If this value is close to 1, there is a strong relationship; if it's close to 0, there is either no relationship or the regression model doesn't fit the data.

                                                                                                                                Advanced

                                                                                                                                Although these statistics are a good indication of whether a regression curve is good or not, they are not infallible. For example, the initial portion of data that actually correlates exponentially may well appear linear and have a high correlation coefficient with a linear fit.

                                                                                                                                Another good way to check a regression curve is to look at the plot of the residuals vs. the x-values. If the regression curve is a good fit, then this plot should appear random in going from positive to negative. However, should you see a distinct pattern - say, if you tried a linear fit but the residual plot looks vaguely parabolic - you know you should try a different regression curve.

                                                                                                                                You should also consider what your regression line implies about the nature of the data and vice versa. For example, if you're comparing the height of release of a ball to the time it takes to fall, a natural assumption is that the regression curve should pass through (0,0), and a curve that doesn't do that may be incorrect. However, take this advice with a grain of salt: if your curve fits the data points you put in but not such natural-assumption points, that may simply mean that the curve works on a limited domain. Or, it may mean your assumptions are wrong.

                                                                                                                                Command Timings

                                                                                                                                Although the correlation statistics are not displayed with DiagnosticOff, they are calculated in either case. This means that DiagnosticOn and DiagnosticOff will not change how fast regressions are calculated.

                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Myles_Zadok.

                                                                                                                                History

                                                                                                                                Calculator OS Version Description
                                                                                                                                TI-83 1.010 Added
                                                                                                                                Property Value
                                                                                                                                Hex Value $BB66
                                                                                                                                Categories
                                                                                                                                Localizations
                                                                                                                                • FR: CorrelAff

                                                                                                                                DiagnosticOn

                                                                                                                                Overview

                                                                                                                                Sets diagnostics-on mode; r, r², and R² are displayed as regression model results.

                                                                                                                                Availability: Token available everywhere.

                                                                                                                                Syntax

                                                                                                                                DiagnosticOn

                                                                                                                                Location

                                                                                                                                2nd, catalog, DiagnosticOn

                                                                                                                                Description

                                                                                                                                After the DiagnosticOn command is executed, all regression commands found in the STAT>CALC menu, as well as LinRegTTest, will display the correlation statistics r and r² (or R2 for regressions that are not linear). This is turned off by default, but there is no disadvantage whatsoever to turning it on. To reverse this command, execute the DiagnosticOff command.

                                                                                                                                The statistic r, known as the Pearson correlation coefficient, measures the strength and direction of any linear relationship in the data. If r is close to 1, then the relationship is strong and positive (that is, the variables increase and decrease together). If r is close to -1, then the relationship is strong and negative (that is, as one variable increases, the other decreases). If r is close to 0, there is no linear relationship.

                                                                                                                                The statistic r² or R², known as the coefficient of determination, is equal to the square of the above value (when it exists) and is also a measure of the strength of a relationship. Specifically, it represents the proportion of variance in the dependent variable that is accounted for by the regression model. If this value is close to 1, there is a strong relationship; if it's close to 0, there is either no relationship or the regression model is not appropriate for the data.

                                                                                                                                Advanced

                                                                                                                                Although these statistics are a good indication of whether a regression curve is good or not, they are not infallible. For example, the initial portion of data that actually correlates exponentially may well appear linear and have a high correlation coefficient with a linear fit.

                                                                                                                                Another good way to check a regression curve is to look at the plot of the residuals vs. the x-values. If the regression curve is a good fit, then this plot should appear random in going from positive to negative. However, should you see a distinct pattern - say, if you tried a linear fit but the residual plot looks vaguely parabolic - you know you should try a different regression curve.

                                                                                                                                You should also consider what your regression line implies about the nature of the data and vice versa. For example, if you're comparing the height of release of a ball to the time it takes to fall, a natural assumption is that the regression curve should pass through (0,0), and a curve that doesn't do that may be incorrect. However, take this advice with a grain of salt: if your curve fits the data points you put in but not such natural-assumption points, that may simply mean that the curve works on a limited domain. Or, it may mean your assumptions are wrong.

                                                                                                                                Command Timings

                                                                                                                                Although the correlation statistics are displayed with DiagnosticOn, they are calculated in either case. This means that DiagnosticOn and DiagnosticOff will not change how fast regressions are calculated.

                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Myles_Zadok, thornahawk.

                                                                                                                                History

                                                                                                                                Calculator OS Version Description
                                                                                                                                TI-83 1.010 Added
                                                                                                                                Property Value
                                                                                                                                Hex Value $DE
                                                                                                                                Categories
                                                                                                                                Localizations
                                                                                                                                • FR: Disp

                                                                                                                                Disp

                                                                                                                                Overview

                                                                                                                                Displays the home screen.

                                                                                                                                Availability: Token only available from within the Basic editor.

                                                                                                                                Syntax

                                                                                                                                Disp

                                                                                                                                Location

                                                                                                                                prgm, I/O, 3:Disp

                                                                                                                                Overview

                                                                                                                                Displays each value.

                                                                                                                                Availability: Token only available from within the Basic editor.

                                                                                                                                Syntax

                                                                                                                                Disp [valueA,valueB,valueC,...,value n]

                                                                                                                                Arguments

                                                                                                                                NameTypeOptional
                                                                                                                                valueAYes
                                                                                                                                valueBYes
                                                                                                                                valueCYes
                                                                                                                                ...Yes
                                                                                                                                value nYes

                                                                                                                                Location

                                                                                                                                prgm, I/O, 3:Disp

                                                                                                                                Description

                                                                                                                                The first, and easiest, way to display text is using the Disp command. You can display whatever combination of text and values that you want. Text is displayed on the left side of the screen, while numbers, variables and expressions are displayed on the right side. Text can be moved over to the right by padding it with spaces, but there is no equivalent for numbers, variables, and expressions.

                                                                                                                                When displaying a matrix or a list, and the matrix or list is too large to display in its entirety, an ellipsis (…) is displayed at the boundaries of the screen. The matrix or list, unfortunately, cannot be scrolled so the rest of it can be seen (use the Pause command instead).

                                                                                                                                With the small screen size, you have to keep formatting in mind when displaying text. Because the text does not wrap to the next line if it is longer than sixteen characters, the text gets cut off and an ellipsis is displayed at the end of the line. When the text you want to display is longer than sixteen characters, you should break the text up and display each part with its own Disp command.

                                                                                                                                :Disp "Just Saying Hello
Break the text up
:Disp "Just Saying
:Disp "Hello

                                                                                                                                The Disp command displays text line by line, giving each argument its own blank line. If the screen is clear, the arguments are displayed beginning at the first line. But if there is text on the first line, the arguments are displayed beginning at the first available blank line. When all the lines have text on them including the last, the screen will automatically scroll up until every line is blank.

                                                                                                                                This means that, while a Disp command can technically display an unlimited amount of lines of text, you should not display more than seven consecutive lines of text at any one time (because of the screen height). If there are too many arguments, the arguments that were displayed will be pushed up out of sight, to allow the other arguments to be displayed. This is usually not desired, but it can be used to create some cool scrolling effects by messing with the text that you display.

                                                                                                                                The result is that you can never display text on the last line of the screen using the Disp command; you need to use the Output( command. (Using Output( does not have any affect on Disp and its text.) Also, if you have more than seven lines of text to display, you will need to place the Pause command after every seven lines to prevent the screen from scrolling. These two scenarios come up fairly often, so it is good to know how to deal with them.

                                                                                                                                PROGRAM:DISP
:ClrHome
:Disp A,B,C,D,E,F,G
:Pause
:Disp A,B,C,D,E,F,G
:Output(8,16,H

                                                                                                                                Like other text display commands, you can display each function and command as text. However, this is not without problems as each function and command is counted as one character. The two characters that you can't display are quotation marks (") and the store command (→). However, you can mimic these respectively by using two apostrophes (''), and two subtract signs and a greater than sign (—>).

                                                                                                                                Advanced Uses

                                                                                                                                You can use the Disp command by itself, which simply displays the home screen.

                                                                                                                                :Disp

                                                                                                                                When you use an empty string with no text (i.e., two quotes side by side — ""), a blank line is displayed.

                                                                                                                                :Disp ""

                                                                                                                                Optimization

                                                                                                                                When you have a list of Disp commands (and each one has its own argument), you can just use the first Disp command and combine the rest of the other Disp commands with it. You remove the Disp commands and combine the arguments, separating each argument with a comma. The arguments can be composed of whatever combination of text, numbers, variables, or expressions is desired.

                                                                                                                                The advantages of combining Disp commands are that it makes scrolling through code faster, and it is smaller when just displaying numbers, variables, or expressions. The disadvantages are that it can hinder readability (make the code harder to read) when you have lots of varied arguments, and it is easier to accidentally erase a Disp command with multiple arguments.

                                                                                                                                :Disp A
:Disp B
Combine the Disp commands
:Disp A,B

                                                                                                                                If you have a string of numbers that you are displaying, you do not need to put quotes around the numbers. This causes the numbers to be displayed on the right side of the screen, and they cease being a string. You may want to keep the numbers in a string, though, if they have any leading zeros. Because the numbers are no longer in a string, the leading zeros are truncated (taken off).

                                                                                                                                :Disp "2345
Remove the Quotes
:Disp 2345

                                                                                                                                Error Conditions

                                                                                                                                • ERR:INVALID occurs if this statement is used outside a program.

                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: burr, CloudVariable, DarkerLine, GoVegan, Myles_Zadok, Trenly.

                                                                                                                                History

                                                                                                                                Calculator OS Version Description
                                                                                                                                TI-82 1.0 Added
                                                                                                                                Property Value
                                                                                                                                Hex Value $DF
                                                                                                                                Categories
                                                                                                                                Localizations
                                                                                                                                • FR: AffGraph

                                                                                                                                DispGraph

                                                                                                                                Overview

                                                                                                                                Displays the graph.

                                                                                                                                Availability: Token only available from within the Basic editor.

                                                                                                                                Syntax

                                                                                                                                DispGraph

                                                                                                                                Location

                                                                                                                                prgm, I/O, 4:DispGraph

                                                                                                                                Description

                                                                                                                                The DispGraph command displays the graph screen, along with everything drawn or graphed on it.

                                                                                                                                In many cases, this doesn't need to be done explicitly: commands from the 2nd DRAW menu, as well as many other graph screen commands, will display the graph screen automatically when they are used. Mainly, it's used for displaying the graphs of equations or plots in a program — you would define the variable in question, then use DispGraph to graph it. For example:

                                                                                                                                :"sin(X)"→Y1
:DispGraph

                                                                                                                                Advanced Uses

                                                                                                                                DispGraph can also be used to update the graph screen, even if it's already being displayed. For example, changing the value of a plot or equation variable doesn't update the graph immediately. Consider this program:

                                                                                                                                :0→I
:"Isin(X)"→Y1
:DispGraph
:For(I,1,10)
:End

                                                                                                                                At first, it graphs the equation Y=Isin(X) with I=0. After this, I is cycled from 1 to 10. However, though the parameter I changes, the graph screen isn't updated, and only the initial graph of Y=0sin(X) and final graph of Y=10sin(X) are displayed. If, on the other hand, we change the program:

                                                                                                                                :0→I
:"Isin(X)"→Y1
:DispGraph
:For(I,1,10)
:DispGraph
:End

                                                                                                                                Now the DispGraph inside the loop ensures that the graph screen is updated every time, and the program will correctly display all eleven graphs.

                                                                                                                                Error Conditions

                                                                                                                                • ERR:INVALID occurs if this statement is used outside a program.

                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583.

                                                                                                                                History

                                                                                                                                Calculator OS Version Description
                                                                                                                                TI-82 1.0 Added
                                                                                                                                Property Value
                                                                                                                                Hex Value $E5
                                                                                                                                Categories
                                                                                                                                Localizations
                                                                                                                                • FR: AffTable

                                                                                                                                DispTable

                                                                                                                                Overview

                                                                                                                                Displays the table.

                                                                                                                                Availability: Token only available from within the Basic editor.

                                                                                                                                Syntax

                                                                                                                                DispTable

                                                                                                                                Location

                                                                                                                                prgm, I/O, 5:DispTable

                                                                                                                                Description

                                                                                                                                The DispTable comand displays the table screen you normally see by pressing 2nd TABLE, from a running program. The user will see the table screen with a "paused" run indicator, and will be able to use arrows to scroll through it. Pressing ENTER will exit the screen and continue the program.

                                                                                                                                Advanced Uses

                                                                                                                                The user can't select any cells in the table to be evaluated if they're not, already. So it's best to select the IndpntAuto and DependAuto options from the 2nd TBLSET menu before using this command. IndpntAsk can also work, however, as long as you store to TblInput first.

                                                                                                                                Error Conditions

                                                                                                                                • ERR:INVALID occurs if this statement is used outside a program.

                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, kg583.

                                                                                                                                History

                                                                                                                                Calculator OS Version Description
                                                                                                                                TI-82 1.0 Added
                                                                                                                                Property Value
                                                                                                                                Hex Value $7E07
                                                                                                                                Categories
                                                                                                                                  Localizations
                                                                                                                                  • FR: Dot-Thick

                                                                                                                                  Dot-Thick

                                                                                                                                  Overview

                                                                                                                                  Sets dot plotting mode; resets all Y=editor graph-style settings to Dot-Thick.

                                                                                                                                  Availability: Token only available from within the Basic editor.

                                                                                                                                  Syntax

                                                                                                                                  Dot-Thick

                                                                                                                                  Location

                                                                                                                                  mode, Dot-Thick

                                                                                                                                  Description

                                                                                                                                  The Dot-Thick command sets all lines in the current function type to be drawn using a series of thick points, about the size of a point drawn using Pt-On(, at each interval of the TraceStep. This command can be called on the homescreen or within a program.

                                                                                                                                  :AxesOff
:RectGC
:Dot-Thick

                                                                                                                                  Error Conditions

                                                                                                                                  • ERR:SYNTAX is thrown if any additional arguments are used with the command

                                                                                                                                  Source: parts of this page were written by the following TI|BD contributors: Battlesquid, kg583, MrWompWomp.

                                                                                                                                  History

                                                                                                                                  Calculator OS Version Description
                                                                                                                                  TI-82 1.0 Dot added
                                                                                                                                  TI-84+CSE 4.0 Renamed Dot to Dot-Thick
                                                                                                                                  Property Value
                                                                                                                                  Hex Value $EF75
                                                                                                                                  Categories
                                                                                                                                    Localizations
                                                                                                                                    • FR: Point fin

                                                                                                                                    Dot-Thin

                                                                                                                                    Overview

                                                                                                                                    Sets dot plotting mode; resets all Y=editor graph-style settings to Dot-Thin.

                                                                                                                                    Availability: Token only available from within the Basic editor.

                                                                                                                                    Syntax

                                                                                                                                    Dot-Thin

                                                                                                                                    Location

                                                                                                                                    mode, Dot-Thin

                                                                                                                                    Description

                                                                                                                                    The Dot-Thin command sets all lines in the current function type to be drawn using a series of individual pixels at each interval of TraceStep. The command can be called on the homescreen or within a program.

                                                                                                                                    :ClrDraw
:AxesOn
:Dot-Thin

                                                                                                                                    Error Conditions

                                                                                                                                    • ERR:SYNTAX is thrown if the command is executed with any additional arguments

                                                                                                                                    Source: parts of this page were written by the following TI|BD contributors: Battlesquid, kg583, MrWompWomp.

                                                                                                                                    History

                                                                                                                                    Calculator OS Version Description
                                                                                                                                    TI-84+CSE 4.0 Added
                                                                                                                                    Property Value
                                                                                                                                    Hex Value $A9
                                                                                                                                    Categories
                                                                                                                                    Localizations
                                                                                                                                    • FR: DessFonct

                                                                                                                                    DrawF

                                                                                                                                    Overview

                                                                                                                                    Draws expression (in terms of X) on the graph with specified
                                                                                                                                    Color#:10 - 24 or color name pasted from [vars] COLOR.

                                                                                                                                    Availability: Token available everywhere.

                                                                                                                                    Syntax

                                                                                                                                    DrawFexpression[,color#]

                                                                                                                                    Arguments

                                                                                                                                    NameTypeOptional
                                                                                                                                    expressionexpression
                                                                                                                                    color#colorNumYes

                                                                                                                                    Location

                                                                                                                                    2nd, draw, DRAW, 6:DrawF

                                                                                                                                    Description

                                                                                                                                    The DrawF commands draws a single expression on the graph screen in terms of X using Func graphing mode, regardless of what graphing mode the calculator is actually in. For example, DrawF X² will draw a parabola in the shape of a U on the screen. Of course, how it is displayed all depends on the window dimensions of the graph screen; you should use a friendly window to ensure it shows up as you intend.

                                                                                                                                    Advanced Uses

                                                                                                                                    DrawF will update X and Y for each coordinate drawn (like Tangent( and DrawInv), and exit with the last coordinate still stored.

                                                                                                                                    When evaluating the expression using DrawF, the calculator will ignore the following errors: ERR:DATA TYPE, ERR:DIVIDE BY 0, ERR:DOMAIN, ERR:INCREMENT, ERR:NONREAL ANS, ERR:OVERFLOW, and ERR:SINGULAR MAT. If one of these errors occurs, the data point will be omitted.

                                                                                                                                    For this reason, DrawF can sometimes behave in an unexpected fashion: for example, it doesn't throw an error for list or matrix expressions (it won't graph anything, either).

                                                                                                                                    You can use DrawF to draw an expression instead of having to store an expression to a Y# variable and then displaying it. At the same time, if you plan on manipulating the expression (either changing the value or changing the expression itself), it would be better to simply use the Y# variable.

                                                                                                                                    Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583.

                                                                                                                                    History

                                                                                                                                    Calculator OS Version Description
                                                                                                                                    TI-82 1.0 Added
                                                                                                                                    Property Value
                                                                                                                                    Hex Value $A8
                                                                                                                                    Categories
                                                                                                                                    Localizations
                                                                                                                                    • FR: DessRecip

                                                                                                                                    DrawInv

                                                                                                                                    Overview

                                                                                                                                    Draws the inverse of expression by plotting X values on the y-axis and Y values on the x-axis with specified
                                                                                                                                    Color#: 10 - 24 or color name pasted from [vars] COLOR.

                                                                                                                                    Availability: Token available everywhere.

                                                                                                                                    Syntax

                                                                                                                                    DrawInvexpression[,color#]

                                                                                                                                    Arguments

                                                                                                                                    NameTypeOptional
                                                                                                                                    expressionexpression
                                                                                                                                    color#colorNumYes

                                                                                                                                    Location

                                                                                                                                    2nd, draw, DRAW, 8:DrawInv

                                                                                                                                    Description

                                                                                                                                    The DrawInv command draws the inverse of a curve in terms of X. Its single argument is an expression in terms of X.

                                                                                                                                    For example, DrawInv X² will draw the inverse of the equation Y=X2. The inverse reverses the variables X and Y, so that the curve X=Y2 will be graphed. In this case, the inverse of the function has a simple form: Y=√(X) and Y=-√(X); most functions, however, do not have an inverse expressible as Y= equation, making this command particularly useful.

                                                                                                                                    You can also think of this as graphing the expression but with X representing the vertical direction, and Y representing the horizontal.

                                                                                                                                    DrawInv requires the calculator to be in Func mode, and is affected by the Connected/Dot setting.

                                                                                                                                    Advanced Uses

                                                                                                                                    DrawInv will update X and Y for each coordinate drawn (like Tangent( and DrawF), and exit with the last coordinate still stored.

                                                                                                                                    When evaluating the expression using DrawInv, the calculator will ignore the following errors: ERR:DATA TYPE, ERR:DIVIDE BY 0, ERR:DOMAIN, ERR:INCREMENT, ERR:NONREAL ANS, ERR:OVERFLOW, and ERR:SINGULAR MAT. If one of these errors occurs, the data point will be omitted.

                                                                                                                                    For this reason, DrawInv can sometimes behave in an unexpected fashion: for example, it doesn't throw an error for list or matrix expressions (it won't graph anything, either).

                                                                                                                                    Error Conditions

                                                                                                                                    • ERR:MODE is thrown if the calculator is not in Func mode when using DrawInv.

                                                                                                                                    Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, kg583.

                                                                                                                                    History

                                                                                                                                    Calculator OS Version Description
                                                                                                                                    TI-82 1.0 Added
                                                                                                                                    Property Value
                                                                                                                                    Hex Value $3B
                                                                                                                                    Categories
                                                                                                                                    Localizations
                                                                                                                                    • FR: ᴇ

                                                                                                                                    ᴇ

                                                                                                                                    Overview

                                                                                                                                    Returns value times 10 to the exponent.

                                                                                                                                    Availability: Token available everywhere.

                                                                                                                                    Syntax

                                                                                                                                    Exponent:valueᴇexponent

                                                                                                                                    Arguments

                                                                                                                                    NameTypeOptional
                                                                                                                                    Exponent:
                                                                                                                                    value
                                                                                                                                    ᴇ
                                                                                                                                    exponent

                                                                                                                                    Location

                                                                                                                                    2nd, ᴇᴇ

                                                                                                                                    Overview

                                                                                                                                    Returns list elements times 10 to the exponent.

                                                                                                                                    Availability: Token available everywhere.

                                                                                                                                    Syntax

                                                                                                                                    Exponent:listᴇexponent

                                                                                                                                    Arguments

                                                                                                                                    NameTypeOptional
                                                                                                                                    Exponent:
                                                                                                                                    listlist
                                                                                                                                    ᴇ
                                                                                                                                    exponent

                                                                                                                                    Location

                                                                                                                                    2nd, ᴇᴇ

                                                                                                                                    Overview

                                                                                                                                    Returns matrix elements times 10 to the exponent.

                                                                                                                                    Availability: Token available everywhere.

                                                                                                                                    Syntax

                                                                                                                                    Exponent:matrixᴇexponent

                                                                                                                                    Arguments

                                                                                                                                    NameTypeOptional
                                                                                                                                    Exponent:
                                                                                                                                    matrixmatrix
                                                                                                                                    ᴇ
                                                                                                                                    exponent

                                                                                                                                    Location

                                                                                                                                    2nd, ᴇᴇ

                                                                                                                                    Description

                                                                                                                                    Examples

                                                                                                                                    Explanation 1

                                                                                                                                    code 1

                                                                                                                                    Explanation 2

                                                                                                                                    code 2

                                                                                                                                    Error Conditions

                                                                                                                                    Advanced Notes

                                                                                                                                    History

                                                                                                                                    Calculator OS Version Description
                                                                                                                                    TI-82 1.0 Added
                                                                                                                                    Property Value
                                                                                                                                    Hex Value $D0
                                                                                                                                    Categories
                                                                                                                                    Localizations
                                                                                                                                    • FR: Else

                                                                                                                                    Else

                                                                                                                                    Overview

                                                                                                                                    SeeIf:Then:Else

                                                                                                                                    Availability: Token available everywhere.

                                                                                                                                    Syntax

                                                                                                                                    Else

                                                                                                                                    Location

                                                                                                                                    Else

                                                                                                                                    Description

                                                                                                                                    The If command is crucial to most programs. It allows you to execute code if and only if an expression is not equal to zero. Advanced uses of the If command allow you to execute a different block of code if the check turns out to be false. The simplest form of the command is quite easy to understand:

                                                                                                                                    :If (condition)
:statement

                                                                                                                                    When the calculator gets to that point in your program, it will check to see if the condition is nonzero. Most expressions you will use with If are called conditional expressions; that is, they return 1 if the condition is true and 0 if it is false. Examples include 2+2=4, A=5, and pxl-Test(R,C). Therefore, when the condition is true, the expression evaluates to 1 and the statement is run. When the condition is false, the expression evaluates to 0, and the statement is skipped.

                                                                                                                                    Using Then, Else, and End

                                                                                                                                    When you want more than one line of code to depend on the same condition, use an If-Then block.

                                                                                                                                    :If (condition)
:Then
code to execute if true
:End

                                                                                                                                    An If-Then block also has an optional Else clause, which is used to execute different code when the condition is false.

                                                                                                                                    :If (condition)
:Then
code to execute if true
:Else
code to execute if false
:End

                                                                                                                                    Advanced Uses

                                                                                                                                    If statements can execute and skip other If statements. This leads to odd yet effective constructs like these:

                                                                                                                                    :If A
:If B
//Executes if A is false or B is true

                                                                                                                                    If A:Then
//Executes if A is true
If B:Else
//Executes if A is false or B is false
End

                                                                                                                                    Memory Leaks

                                                                                                                                    Each time the program enters an If-Then block, the calculator uses 35+(size of the condition) bytes of memory to keep track of the block. This memory is given back to you as soon as the program reaches an End statement. This isn't really a problem unless you're low on RAM, or have a lot of nested If-Then statements. However, if you use Goto to jump out of such a statement, you lose those bytes for as long as the program is running — and if you keep doing this, you might easily run out of memory, resulting in ERR:MEMORY.

                                                                                                                                    Optimization

                                                                                                                                    As far as the TI-BASIC interpreter is concerned, a value of 0 is false, and any other value is true. We can use a numerical expression rather than a conditional one in the condition of the If statement in a case like the following:

                                                                                                                                    :If A≠0
:Disp "A IS NOT 0

can be
:If A
:Disp "A IS NOT 0

                                                                                                                                    When code in a single-line If statement simply changes a variable, it can often be replaced with an equivalent piecewise expression, which will be smaller and faster.

                                                                                                                                    :If A=B
:C+2→C

can be
:C+2(A=B→C

                                                                                                                                    Code Timings

                                                                                                                                    Single-line If statements are greatly slowed when they are the first line in For( loops without a closing parenthesis. For example,

                                                                                                                                    Very slow
:For(I,1,2000
:If 0:
:End

19 times faster (!)
:For(I,1,2000)
:If 0:
:End

                                                                                                                                    Error Conditions

                                                                                                                                    • ERR:DATA TYPE occurs if the parameter is complex, even if it's complex in a silly way like 0i.
                                                                                                                                    • ERR:INVALID occurs if this statement is used outside a program.
                                                                                                                                    • ERR:SYNTAX occurs if an If is the last statement in the program, or the last except for one empty line.

                                                                                                                                    Source: parts of this page were written by the following TI|BD contributors: burr, CloudVariable, DarkerLine, GoVegan, kg583, lirtosiast, Trenly.

                                                                                                                                    History

                                                                                                                                    Calculator OS Version Description
                                                                                                                                    TI-82 1.0 Added
                                                                                                                                    Property Value
                                                                                                                                    Hex Value $D4
                                                                                                                                    Categories
                                                                                                                                    Localizations
                                                                                                                                    • FR: End

                                                                                                                                    End

                                                                                                                                    Overview

                                                                                                                                    Identifies end ofFor(, If-Then-Else, Repeat, or While loop.

                                                                                                                                    Availability: Token only available from within the Basic editor.

                                                                                                                                    Syntax

                                                                                                                                    End

                                                                                                                                    Location

                                                                                                                                    prgm, CTL, 7:End

                                                                                                                                    Description

                                                                                                                                    The End command is used together with the different control structures, including the If conditional, While loop, Repeat loop, and For( loop, to indicate the end of the code block for the respective control structure. In the case of the If conditional, you also need to add a Then command, which is used to indicate the beginning of the control structure.

                                                                                                                                    Advanced Uses

                                                                                                                                    You can prematurely end a control structure by using a single If conditional and then having End be its executed command. Because the calculator stores the positions of the End commands, it will take this End command to be the End command of the control structure.

                                                                                                                                    :If <condition>
:End

                                                                                                                                    One of the most important features of the End command is putting multiple control structures inside of each other (known as nesting). While you typically nest If conditionals inside of loops, you can actually nest any control structure inside of any other control structure — this even works when using the same control structure, such as a While loop inside of another While loop.

                                                                                                                                    When nesting control structures, you need to remember to put the appropriate number of End commands to close the appropriate structure. The easiest way to keep track of lots of nested control structures is to code the first part, add an End immediately after the beginning, and then hit 2nd DEL on the line with the End, then hit ENTER a lot of times.

                                                                                                                                    Error Conditions

                                                                                                                                    • ERR:INVALID occurs if this statement is used outside a program.
                                                                                                                                    • ERR:SYNTAX occurs if this statement is used before a logic block has been initiated.

                                                                                                                                    Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, MufinMcFlufin, Myles_Zadok.

                                                                                                                                    History

                                                                                                                                    Calculator OS Version Description
                                                                                                                                    TI-82 1.0 Added
                                                                                                                                    Property Value
                                                                                                                                    Hex Value $68
                                                                                                                                    Categories
                                                                                                                                    Localizations
                                                                                                                                    • FR: Ing

                                                                                                                                    Eng

                                                                                                                                    Overview

                                                                                                                                    Sets engineering display mode.

                                                                                                                                    Availability: Token only available from within the Basic editor.

                                                                                                                                    Syntax

                                                                                                                                    Eng

                                                                                                                                    Location

                                                                                                                                    mode, Eng

                                                                                                                                    Description

                                                                                                                                    The Eng command puts the calculator in engineering notation mode. This is a variation on scientific notation in which the exponent is restricted to be a multiple of 3 (and the mantissa can range between 1 and 1000, not including 1000 itself)

                                                                                                                                    Eng
        Done
12345
        12.345e3
{1,2,3}
        {1e0 2e0 3e0}

                                                                                                                                    Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Myles_Zadok.

                                                                                                                                    History

                                                                                                                                    Calculator OS Version Description
                                                                                                                                    TI-82 1.0 Added
                                                                                                                                    Property Value
                                                                                                                                    Hex Value $BB55
                                                                                                                                    Categories
                                                                                                                                    Localizations
                                                                                                                                    • FR: Equ►Chaine(

                                                                                                                                    Equ►String(

                                                                                                                                    Overview

                                                                                                                                    Converts the contents of a Y= var to a string and stores it in Str``n

                                                                                                                                    Availability: Token available everywhere.

                                                                                                                                    Syntax

                                                                                                                                    Equ►String(Y= var,Strn)

                                                                                                                                    Arguments

                                                                                                                                    NameTypeOptional
                                                                                                                                    var
                                                                                                                                    n

                                                                                                                                    Location

                                                                                                                                    2nd, catalog, Equ►String(

                                                                                                                                    Description

                                                                                                                                    This command stores the contents of an equation variable (such as Y1 or X1T) to a string (one of Str0, Str1, … Str9). This can be used when you want to display the equation as text (either using the Text( command on the graph screen, or the Output( or Disp commands on the home screen). For example:

                                                                                                                                    :Equ►String(Y1,Str1
:Text(0,0,"Y1(X)=",Str1

                                                                                                                                    Apart from cases in which the user has already stored to the equation variable prior to running the program, about the only situation in which you would use Equ►String( is for the output of a regression.

                                                                                                                                    Advanced

                                                                                                                                    You can use Equ►String( (outside a program) to get the → or " symbols in a string:

                                                                                                                                    1. Type them on the home screen and press [ENTER]
                                                                                                                                    2. Select 2:Quit when the ERR:SYNTAX comes up.
                                                                                                                                    3. Press [Y=] to go to the equation editor.
                                                                                                                                    4. Press [2nd] [ENTRY] to recall the symbols to Y1
                                                                                                                                    5. Now, use Equ►String(Y1,Str1) to store the symbols to a string.

                                                                                                                                    See Also

                                                                                                                                    Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Myles_Zadok.

                                                                                                                                    History

                                                                                                                                    Calculator OS Version Description
                                                                                                                                    TI-83 0.01013 Added
                                                                                                                                    Property Value
                                                                                                                                    Hex Value $BB55
                                                                                                                                    Categories
                                                                                                                                    Localizations
                                                                                                                                    • FR: Equ►Chaine(

                                                                                                                                    Equ►String(

                                                                                                                                    Overview

                                                                                                                                    Converts the contents of a Y= var to a string and stores it in Str``n

                                                                                                                                    Availability: Token available everywhere.

                                                                                                                                    Syntax

                                                                                                                                    Equ►String(Y= var,Strn)

                                                                                                                                    Arguments

                                                                                                                                    NameTypeOptional
                                                                                                                                    var
                                                                                                                                    n

                                                                                                                                    Location

                                                                                                                                    2nd, catalog, Equ►String(

                                                                                                                                    Description

                                                                                                                                    This command stores the contents of an equation variable (such as Y1 or X1T) to a string (one of Str0, Str1, … Str9). This can be used when you want to display the equation as text (either using the Text( command on the graph screen, or the Output( or Disp commands on the home screen). For example:

                                                                                                                                    :Equ►String(Y1,Str1
:Text(0,0,"Y1(X)=",Str1

                                                                                                                                    Apart from cases in which the user has already stored to the equation variable prior to running the program, about the only situation in which you would use Equ►String( is for the output of a regression.

                                                                                                                                    Advanced

                                                                                                                                    You can use Equ►String( (outside a program) to get the → or " symbols in a string:

                                                                                                                                    1. Type them on the home screen and press [ENTER]
                                                                                                                                    2. Select 2:Quit when the ERR:SYNTAX comes up.
                                                                                                                                    3. Press [Y=] to go to the equation editor.
                                                                                                                                    4. Press [2nd] [ENTRY] to recall the symbols to Y1
                                                                                                                                    5. Now, use Equ►String(Y1,Str1) to store the symbols to a string.

                                                                                                                                    See Also

                                                                                                                                    Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Myles_Zadok.

                                                                                                                                    History

                                                                                                                                    Calculator OS Version Description
                                                                                                                                    TI-83 0.01013 Added
                                                                                                                                    Property Value
                                                                                                                                    Hex Value $EF12
                                                                                                                                    Categories
                                                                                                                                    Localizations
                                                                                                                                    • FR: ExécBiblio

                                                                                                                                    ExecLib

                                                                                                                                    Overview

                                                                                                                                    Extends TI-Basic (not available)

                                                                                                                                    Availability: Token only available from within the Basic editor.

                                                                                                                                    Syntax

                                                                                                                                    ExecLib

                                                                                                                                    Location

                                                                                                                                    prgm

                                                                                                                                    Description

                                                                                                                                    Together with OpenLib(, ExecLib is used on the TI-84 Plus and TI-84 Plus SE for running routines from a Flash App library. This only works, of course, with libraries that have been specifically written for this purpose. The only such library so far is usb8x, for advanced interfacing with the USB port.

                                                                                                                                    Since ExecLib doesn't have any arguments, it would normally be able to run only one library routine. To get around this, usb8x uses a list passed in Ans as arguments to the command. This is most likely how any future libraries will do it as well.

                                                                                                                                    The following program, which displays the version of usb8x, is an example of how to use OpenLib( and ExecLib:

                                                                                                                                    :OpenLib(USBDRV8X
:{6
:ExecLib
:Ans(2)+.01Ans(3

                                                                                                                                    Download usb8x here. You may also be interested in MSD8x which is a GUI for usb8x.

                                                                                                                                    Source: parts of this page were written by the following TI|BD contributors: Battlesquid, DarkerLine, GoVegan, Mapar007, Myles_Zadok, seb83.

                                                                                                                                    History

                                                                                                                                    Calculator OS Version Description
                                                                                                                                    TI-84+ 0.01 Added
                                                                                                                                    Property Value
                                                                                                                                    Hex Value $EF9E
                                                                                                                                    Categories
                                                                                                                                    Localizations
                                                                                                                                    • FR: Exécuter programme

                                                                                                                                    Execute Program

                                                                                                                                    Overview

                                                                                                                                    Comment:CE OS 5.3+

                                                                                                                                    Syntax

                                                                                                                                    Execute Program

                                                                                                                                    Description

                                                                                                                                    Examples

                                                                                                                                    Explanation 1

                                                                                                                                    code 1

                                                                                                                                    Explanation 2

                                                                                                                                    code 2

                                                                                                                                    Error Conditions

                                                                                                                                    Advanced Notes

                                                                                                                                    History

                                                                                                                                    Calculator OS Version Description
                                                                                                                                    TI-84+CE 5.3.0 Added
                                                                                                                                    Property Value
                                                                                                                                    Hex Value $F5
                                                                                                                                    Categories
                                                                                                                                    Localizations
                                                                                                                                    • FR: RegExp

                                                                                                                                    ExpReg

                                                                                                                                    Overview

                                                                                                                                    Fits an exponential regression model to Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ.

                                                                                                                                    Availability: Token available everywhere.

                                                                                                                                    Syntax

                                                                                                                                    ExpReg [Xlistname,Ylistname,freqlist,regequ]

                                                                                                                                    Arguments

                                                                                                                                    NameTypeOptional
                                                                                                                                    XlistnamelistYes
                                                                                                                                    YlistnamelistYes
                                                                                                                                    freqlistlistYes
                                                                                                                                    regequYes

                                                                                                                                    Location

                                                                                                                                    stat, CALC, 0:ExpReg

                                                                                                                                    Description

                                                                                                                                    ExpReg tries to fit an exponential curve (y=a*bx) through a set of points. To use it, you must first store the points to two lists: one of the x-coordinates and one of the y-coordinates ordered so that the Nth element of one list matches up with the Nth element of the other list. L₁ and L₂ are the default lists to use, and the List Editor (STAT > Edit…) is a useful window for entering the points.

                                                                                                                                    The calculator does this regression by taking the natural log ln( of the y-coordinates (this isn't stored anywhere) and then doing a linear regression. The result, ln(y)=ln(a)+x*ln(b), is transformed into y=eln(a)(eln(b))x, which is an exponential curve. This algorithm shows that if any y-coordinates are negative or 0, the calculator will instantly quit with ERR:DOMAIN.

                                                                                                                                    In its simplest form, ExpReg takes no arguments, and fits an exponential curve through the points in L₁ and L₂:

                                                                                                                                    :{9,13,21,30,31,31,34→L₁
:{260,320,420,530,560,550,590→L₂
:LnReg

                                                                                                                                    On the home screen, or as the last line of a program, this will display the equation of the curve: you'll be shown the format, y=a*b^x, and the values of a and b. It will also be stored in the RegEQ variable, but you won't be able to use this variable in a program - accessing it just pastes the equation wherever your cursor was. Finally, the statistical variables a, b, r, and r² will be set as well. These latter two variables will be displayed only if "Diagnostic Mode" is turned on (see DiagnosticOn and DiagnosticOff).

                                                                                                                                    You don't have to do the regression on L₁ and L₂, but if you don't you'll have to enter the names of the lists after the command. For example:

                                                                                                                                    :{9,13,21,30,31,31,34→FAT
:{260,320,420,530,560,550,590→CALS
:ExpReg ʟFAT,ʟCALS

                                                                                                                                    You can attach frequencies to points, for when a point occurs more than once, by supplying an additional argument - the frequency list. This list does not have to contain integer frequencies. If you add a frequency list, you must supply the names of the x-list and y-list as well, even when they're L₁ and L₂.

                                                                                                                                    Finally, you can enter an equation variable (such as Y₁) after the command, so that the curve's equation is stored in this variable automatically. This doesn't require you to supply the names of the lists, but if you do, the equation variable must come last. You can use polar, parametric, or sequential variables as well, but since the equation will be in terms of X anyway, this doesn't make much sense.

                                                                                                                                    An example of ExpReg with all the optional arguments:

                                                                                                                                    :{9,13,21,30,31,31,34→FAT
:{260,320,420,530,560,550,590→CALS
:{2,1,1,1,2,1,1→FREQ
:ExpReg ʟFAT,ʟCALS,ʟFREQ,Y1

                                                                                                                                    Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Myles_Zadok, thornahawk, Timothy Foster.

                                                                                                                                    History

                                                                                                                                    Calculator OS Version Description
                                                                                                                                    TI-82 1.0 Added
                                                                                                                                    Property Value
                                                                                                                                    Hex Value $BB51
                                                                                                                                    Categories
                                                                                                                                    Localizations
                                                                                                                                    • FR: ExpNAff

                                                                                                                                    ExprOff

                                                                                                                                    Overview

                                                                                                                                    Turns off the expression display during TRACE.

                                                                                                                                    Availability: Token only available from within the Basic editor.

                                                                                                                                    Syntax

                                                                                                                                    ExprOff

                                                                                                                                    Location

                                                                                                                                    2nd, format, ExprOff

                                                                                                                                    Description

                                                                                                                                    The ExprOff command enables a "short" form of displaying the equation or plot being traced. That is, only the number of the equation or plot will be displayed, in the top right corner of the screen. When tracing a plot, the number will be prefixed with a P to distinguish it from an equation.

                                                                                                                                    Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Myles_Zadok.

                                                                                                                                    History

                                                                                                                                    Calculator OS Version Description
                                                                                                                                    TI-83 0.01013 Added
                                                                                                                                    Property Value
                                                                                                                                    Hex Value $BB50
                                                                                                                                    Categories
                                                                                                                                    Localizations
                                                                                                                                    • FR: ExpAff

                                                                                                                                    ExprOn

                                                                                                                                    Overview

                                                                                                                                    Turns on the expression display during TRACE.

                                                                                                                                    Availability: Token only available from within the Basic editor.

                                                                                                                                    Syntax

                                                                                                                                    ExprOn

                                                                                                                                    Location

                                                                                                                                    2nd, format, ExprOn

                                                                                                                                    Description

                                                                                                                                    The ExprOn command enables a "long" form of displaying the equation or plot being traced.

                                                                                                                                    In this mode, when tracing an equation, the equation's name and its formula are written in small font at the top of the screen. For example, when tracing Y1 which is equal to 2X, "Y1=2X" will be displayed.

                                                                                                                                    When tracing a plot, the plot number is written, followed by the list or lists that it describes. For example, when tracing Plot1, which is a scatter plot of ʟX and ʟY, "P1:X,Y" will be displayed.

                                                                                                                                    Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Myles_Zadok.

                                                                                                                                    History

                                                                                                                                    Calculator OS Version Description
                                                                                                                                    TI-83 0.01013 Added
                                                                                                                                    Property Value
                                                                                                                                    Hex Value $46
                                                                                                                                    Categories
                                                                                                                                    Localizations
                                                                                                                                    • FR: F

                                                                                                                                    F

                                                                                                                                    Overview

                                                                                                                                    Availability: Token available everywhere.

                                                                                                                                    Syntax

                                                                                                                                    F

                                                                                                                                    Description

                                                                                                                                    Examples

                                                                                                                                    Explanation 1

                                                                                                                                    code 1

                                                                                                                                    Explanation 2

                                                                                                                                    code 2

                                                                                                                                    Error Conditions

                                                                                                                                    Advanced Notes

                                                                                                                                    History

                                                                                                                                    Calculator OS Version Description
                                                                                                                                    TI-82 1.0 Added
                                                                                                                                    Property Value
                                                                                                                                    Hex Value $EF3D
                                                                                                                                    Categories
                                                                                                                                    Localizations
                                                                                                                                    • FR: FRAC-APPROX

                                                                                                                                    FRAC-APPROX

                                                                                                                                    Overview

                                                                                                                                    Syntax

                                                                                                                                    FRAC-APPROX

                                                                                                                                    Description

                                                                                                                                    Examples

                                                                                                                                    Explanation 1

                                                                                                                                    code 1

                                                                                                                                    Explanation 2

                                                                                                                                    code 2

                                                                                                                                    Error Conditions

                                                                                                                                    Advanced Notes

                                                                                                                                    History

                                                                                                                                    Calculator OS Version Description
                                                                                                                                    TI-84+ 2.53 FRAC added
                                                                                                                                    TI-84+CSE 4.0 Renamed FRAC to FRAC-APPROX
                                                                                                                                    Property Value
                                                                                                                                    Hex Value $632F
                                                                                                                                    Categories
                                                                                                                                    Localizations
                                                                                                                                    • FR: VAC

                                                                                                                                    FV

                                                                                                                                    Overview

                                                                                                                                    Syntax

                                                                                                                                    FV

                                                                                                                                    Description

                                                                                                                                    Examples

                                                                                                                                    Explanation 1

                                                                                                                                    code 1

                                                                                                                                    Explanation 2

                                                                                                                                    code 2

                                                                                                                                    Error Conditions

                                                                                                                                    Advanced Notes

                                                                                                                                    History

                                                                                                                                    Calculator OS Version Description
                                                                                                                                    TI-83 0.01013 Added
                                                                                                                                    Property Value
                                                                                                                                    Hex Value $BBAF
                                                                                                                                    Categories
                                                                                                                                    Localizations
                                                                                                                                    • FR: 𝐅

                                                                                                                                    𝐅

                                                                                                                                    Overview

                                                                                                                                    Syntax

                                                                                                                                    𝐅

                                                                                                                                    Description

                                                                                                                                    Examples

                                                                                                                                    Explanation 1

                                                                                                                                    code 1

                                                                                                                                    Explanation 2

                                                                                                                                    code 2

                                                                                                                                    Error Conditions

                                                                                                                                    Advanced Notes

                                                                                                                                    History

                                                                                                                                    Calculator OS Version Description
                                                                                                                                    TI-83+ 1.03 Added
                                                                                                                                    Property Value
                                                                                                                                    Hex Value $6226
                                                                                                                                    Categories
                                                                                                                                    Localizations
                                                                                                                                    • FR: [|F]

                                                                                                                                    [|F]

                                                                                                                                    Overview

                                                                                                                                    Syntax

                                                                                                                                    [|F]

                                                                                                                                    Description

                                                                                                                                    Examples

                                                                                                                                    Explanation 1

                                                                                                                                    code 1

                                                                                                                                    Explanation 2

                                                                                                                                    code 2

                                                                                                                                    Error Conditions

                                                                                                                                    Advanced Notes

                                                                                                                                    History

                                                                                                                                    Calculator OS Version Description
                                                                                                                                    TI-82 1.0 Added
                                                                                                                                    Property Value
                                                                                                                                    Hex Value $BB14
                                                                                                                                    Categories
                                                                                                                                    Localizations
                                                                                                                                    • FR: 𝐅FRép(

                                                                                                                                    𝐅cdf(

                                                                                                                                    Overview

                                                                                                                                    Computes the 𝐅 distribution probability between lowerboundand upperbound for the specified numerator df (degrees of freedom) and denominator df.

                                                                                                                                    Availability: Token available everywhere.

                                                                                                                                    Syntax

                                                                                                                                    𝐅cdf(lowerbound,upperbound,numerator df,denominator df)

                                                                                                                                    Arguments

                                                                                                                                    NameTypeOptional
                                                                                                                                    𝐅
                                                                                                                                    lowerbound
                                                                                                                                    upperbound
                                                                                                                                    numerator df
                                                                                                                                    denominator df

                                                                                                                                    Location

                                                                                                                                    2nd, distr, DISTR, 0:cdf(

                                                                                                                                    Description

                                                                                                                                    Examples

                                                                                                                                    Explanation 1

                                                                                                                                    code 1

                                                                                                                                    Explanation 2

                                                                                                                                    code 2

                                                                                                                                    Error Conditions

                                                                                                                                    Advanced Notes

                                                                                                                                    History

                                                                                                                                    Calculator OS Version Description
                                                                                                                                    TI-83 0.01013 Added
                                                                                                                                    Property Value
                                                                                                                                    Hex Value $E2
                                                                                                                                    Categories
                                                                                                                                    Localizations
                                                                                                                                    • FR: Remplir(

                                                                                                                                    Fill(

                                                                                                                                    Overview

                                                                                                                                    Stores value to each element in matrixname.

                                                                                                                                    Availability: Token available everywhere.

                                                                                                                                    Syntax

                                                                                                                                    Fill(value,matrixname)

                                                                                                                                    Arguments

                                                                                                                                    NameTypeOptional
                                                                                                                                    value
                                                                                                                                    matrixnamematrix

                                                                                                                                    Location

                                                                                                                                    2nd, matrix, MATH, 4:Fill(

                                                                                                                                    Overview

                                                                                                                                    Stores value to each element in listname.

                                                                                                                                    Availability: Token available everywhere.

                                                                                                                                    Syntax

                                                                                                                                    Fill(value,listname)

                                                                                                                                    Arguments

                                                                                                                                    NameTypeOptional
                                                                                                                                    value
                                                                                                                                    listnamelist

                                                                                                                                    Location

                                                                                                                                    2nd, list, OPS, 4:Fill(

                                                                                                                                    Description

                                                                                                                                    The Fill( command takes an existing list or matrix variable and sets all its elements to a single number. It doesn't return anything and only works on already defined variables.

                                                                                                                                    {5}→dim(L1)
Fill(2,L1)
L1
    {2 2 2 2 2}

{3,4}→dim([A])
Fill(1,[A])
[A]
    [[1 1 1 1]
     [1 1 1 1]
     [1 1 1 1]]

                                                                                                                                    Fill( is very fast: on a twenty-element real list, it takes only about 3.5 ms, much less than any vectorized list operation.

                                                                                                                                    When Fill( is called on a list, the datatype of the list becomes the datatype of the number. That is, Fill(1,L₁) makes L₁ a real list, and Fill(i,L₁) makes L₁ a complex list.

                                                                                                                                    Optimization

                                                                                                                                    When creating a new list or matrix you want to fill with zeroes, it's better to delete it then create it with dim(, which will set all entries to 0, than to set its dimensions with dim( (which may not clear what was there before) then use Fill(.

                                                                                                                                    Errors

                                                                                                                                    On a TI-84+CSE, using Fill(List,List) will cause a RAM clear. For example: Fill({1,2,3},{1,2,3} will cause a RAM Clear. This does not apply on any other models, as they only give you argument and data type errors.

                                                                                                                                    Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, iPhoenixOnTIBD, kg583, lirtosiast, Silver Phantom.

                                                                                                                                    History

                                                                                                                                    Calculator OS Version Description
                                                                                                                                    TI-82 1.0 Added
                                                                                                                                    Property Value
                                                                                                                                    Hex Value $73
                                                                                                                                    Categories
                                                                                                                                    Localizations
                                                                                                                                    • FR: Fixe

                                                                                                                                    Fix

                                                                                                                                    Overview

                                                                                                                                    Sets fixed-decimal mode for # of decimal places.

                                                                                                                                    Availability: Token only available from within the Basic editor.

                                                                                                                                    Syntax

                                                                                                                                    Fix #

                                                                                                                                    Arguments

                                                                                                                                    NameTypeOptional
                                                                                                                                    #

                                                                                                                                    Location

                                                                                                                                    mode, 0123456789

                                                                                                                                    Description

                                                                                                                                    The Fix command puts the calculator in fixed-point display mode: all numbers will be displayed with a fixed number of digits (0-9) after the decimal, depending on the argument of Fix. This could be useful if you're trying to display potentially fractional numbers in a limited amount of space.

                                                                                                                                    A note on more technical aspects: first, if more digits are available than are displayed, the calculator will round off the displayed number (but not its stored value), so 3.97 will be displayed as 4 in Fix 1 mode. Second, the Fix command can't force more than 10 significant digits to be displayed, so something like 123456789.1 will only display one decimal digit even in Fix 9 mode.

                                                                                                                                    Finally, note that the Float and Fix commands only change the way numbers are displayed: they are saved in the same way in each case. Even if you're in Fix 0 mode, the calculations are not done using integers, and in general, the calculations are still done using floating-point numbers no matter the number mode. The one exception is with regressions: if you store a regression to an equation in Fix N mode, it will truncate the numbers involved before storing them to the equation, and as a result, the equation will be different.

                                                                                                                                    Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Myles_Zadok.

                                                                                                                                    History

                                                                                                                                    Calculator OS Version Description
                                                                                                                                    TI-82 1.0 Added
                                                                                                                                    Property Value
                                                                                                                                    Hex Value $69
                                                                                                                                    Categories
                                                                                                                                    Localizations
                                                                                                                                    • FR: Flottant

                                                                                                                                    Float

                                                                                                                                    Overview

                                                                                                                                    Sets floating decimal mode.

                                                                                                                                    Availability: Token only available from within the Basic editor.

                                                                                                                                    Syntax

                                                                                                                                    Float

                                                                                                                                    Location

                                                                                                                                    mode, Float

                                                                                                                                    Description

                                                                                                                                    The Float command makes the calculator display numbers with a "floating decimal point" — only as many digits after the decimal as needed are displayed (so whole numbers, for example, are shown without any decimal points). This is the default mode, and usually the most useful.

                                                                                                                                    A technicality of displaying real numbers on the calculator: A maximum of 14 significant digits are stored in a number, but only 10 of them are actually displayed (or used for comparisons) — the rest are used for additional precision. This means that if a number is displayed as a whole number, it isn't necessarily whole. For example, 1234567890.7 will be displayed as 1234567891 (rounded to 10 significant digits), and 1.0000000003 will be displayed as 1.

                                                                                                                                    This makes sense from many perspectives: if you get a result of 1.0000000003 after a calculation, odds are that this should be 1, and isn't just because of a precision error. Because the extra digits are there, though, even if they're not displayed, such a number will still be invalid for functions such as Pxl-On( or sub( that want integer arguments, and this sort of error is hard to track down.

                                                                                                                                    Finally, note that the Float and Fix commands only change the way numbers are displayed: they are saved in the same way in each case. Even if you're in Fix 0 mode, the calculations are not done using integers, and in general the calculations are still done using floating-point numbers no matter the number mode. The one exception is with regressions: if you store a regression to an equation in Fix N mode, it will truncate the numbers involved before storing them to the equation, and as a result, the equation will be different.

                                                                                                                                    Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583.

                                                                                                                                    History

                                                                                                                                    Calculator OS Version Description
                                                                                                                                    TI-82 1.0 Added
                                                                                                                                    Property Value
                                                                                                                                    Hex Value $97
                                                                                                                                    Categories
                                                                                                                                    Localizations
                                                                                                                                    • FR: FonctNAff

                                                                                                                                    FnOff

                                                                                                                                    Overview

                                                                                                                                    Deselects all Y= functions or specified Y= functions.

                                                                                                                                    Availability: Token available everywhere.

                                                                                                                                    Syntax

                                                                                                                                    FnOff [function#,function#,...,function n]

                                                                                                                                    Arguments

                                                                                                                                    NameTypeOptional
                                                                                                                                    function#Yes
                                                                                                                                    function#Yes
                                                                                                                                    function nYes

                                                                                                                                    Location

                                                                                                                                    vars, Y-VARS, 4:On/Off2:FnOff

                                                                                                                                    Description

                                                                                                                                    The FnOff command is used to turn off equations in the current graphing mode. When you turn off an equation, it's still defined, but isn't graphed; you can reverse this with the FnOn command. To turn functions on and off manually, put your cursor over the = symbol in the equation editor, and press enter.

                                                                                                                                    When FnOff is used by itself, it will turn off all defined equations in the current graphing mode. You can also specify which equations to turn off, by writing their numbers after FnOff: for example, FnOff 1 will turn off the first equation, and FnOff 2,3,4,5 will off turn the second, third, fourth, and fifth. The numbers you give FnOff have to be valid equation numbers in the graphing mode. When turning equations on and off in sequence mode, use 1 for u, 2 for v, and 3 for w.

                                                                                                                                    The most common use for FnOn and FnOff is to disable functions when running a program, so that they won't interfere with what you're doing on the graph screen, then enable them again when you're done.

                                                                                                                                    Error Conditions

                                                                                                                                    • ERR:DOMAIN is thrown if an equation number isn't valid in the current graphing mode, or at all.

                                                                                                                                    Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, kg583.

                                                                                                                                    History

                                                                                                                                    Calculator OS Version Description
                                                                                                                                    TI-82 1.0 Added
                                                                                                                                    Property Value
                                                                                                                                    Hex Value $96
                                                                                                                                    Categories
                                                                                                                                    Localizations
                                                                                                                                    • FR: FonctAff

                                                                                                                                    FnOn

                                                                                                                                    Overview

                                                                                                                                    Selects all Y= functions or specified Y= functions.

                                                                                                                                    Availability: Token available everywhere.

                                                                                                                                    Syntax

                                                                                                                                    FnOn [function#,function#,...,function n]

                                                                                                                                    Arguments

                                                                                                                                    NameTypeOptional
                                                                                                                                    function#Yes
                                                                                                                                    function#Yes
                                                                                                                                    function nYes

                                                                                                                                    Location

                                                                                                                                    vars, Y-VARS, 4:On/Off1:FnOn

                                                                                                                                    Description

                                                                                                                                    The FnOn command is used to turn on equations in the current graphing mode. When you define an equation, it's turned on by default, but the FnOff command can turn an equation off (in which case, it's still defined, but isn't graphed). To turn functions on and off manually, put your cursor over the = symbol in the equation editor, and press enter.

                                                                                                                                    When FnOn is used by itself, it will turn on all defined equations in the current graphing mode. You can also specify which equations to turn on, by writing their numbers after FnOn: for example, FnOn 1 will turn off the first equation, and FnOn 2,3,4,5 will turn the second, third, fourth, and fifth. The numbers you give FnOn have to be valid equation numbers in the graphing mode. When turning equations on and off in sequence mode, use 1 for u, 2 for v, and 3 for w.

                                                                                                                                    The most common use for FnOn and FnOff is to disable functions when running a program, so that they won't interfere with what you're doing on the graph screen, then enable them again when you're done.

                                                                                                                                    Error Conditions

                                                                                                                                    • ERR:DOMAIN is thrown if an equation number isn't valid in the current graphing mode, or at all.

                                                                                                                                    Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, kg583.

                                                                                                                                    History

                                                                                                                                    Calculator OS Version Description
                                                                                                                                    TI-82 1.0 Added
                                                                                                                                    Property Value
                                                                                                                                    Hex Value $D3
                                                                                                                                    Categories
                                                                                                                                    Localizations
                                                                                                                                    • FR: For(

                                                                                                                                    For(

                                                                                                                                    Overview

                                                                                                                                    Executes commands through End, incrementing variable from begin by increment until variable>end.

                                                                                                                                    Availability: Token only available from within the Basic editor.

                                                                                                                                    Syntax

                                                                                                                                    :For(variable,begin,end[,increment]):commands:End:commands

                                                                                                                                    Arguments

                                                                                                                                    NameTypeOptional
                                                                                                                                    variable
                                                                                                                                    begin
                                                                                                                                    end
                                                                                                                                    incrementYes
                                                                                                                                    commandsYes
                                                                                                                                    commandsYes

                                                                                                                                    Location

                                                                                                                                    prgm, CTL, 4:For(

                                                                                                                                    Description

                                                                                                                                    A For( loop is generally used to do something a specific number of times or to go through each one of a bunch of things (such as elements of a list, or the pixels of your screen). Of all the loops, it's the most complicated. The syntax:

                                                                                                                                    For(variable,start,end[,step]
statement(s)
End

                                                                                                                                    What the loop does:

                                                                                                                                    1. Stores start to variable.
                                                                                                                                    2. If variable is greater than end (or less than, if step is negative), then the For( loop ends immediately.
                                                                                                                                    3. Runs the statement(s).
                                                                                                                                    4. Adds step to variable and returns to Step 2.

                                                                                                                                    If no value for step is given, step is assumed to be 1.

                                                                                                                                    In other words: a For( loop repeats its contents once for every value of variable between start and end.

                                                                                                                                    This is perhaps best explained with an example. The following code will display the numbers 1 to 10, in order:

                                                                                                                                    :For(A,1,10)
:Disp A
:End

                                                                                                                                    Now, all of this could be done with a Repeat or While command and some manipulation, except that this is faster because it's a single command. Still, why have a separate command for something that seems so specific and arbitrary? Well, it's because For( has so many uses!

                                                                                                                                    • Do something to each element of a list, matrix, or string.
                                                                                                                                    • Draw several similar objects on the graph screen.
                                                                                                                                    • Create animations.
                                                                                                                                    • Easily add the possibility of levels to many games.
                                                                                                                                    • Any number of other things…

                                                                                                                                    An advanced note: each time the program enters a For( loop, the calculator uses 43 bytes of memory to keep track of this. This memory is given back to you as soon as the program reaches End. This isn't really a problem unless you're low on RAM, or have a lot of nested For( statements. However, if you use Goto to jump out of a For( loop, you lose those bytes for as long as the program is running—and if you keep doing this, you might easily run out of memory, resulting in ERR:MEMORY.

                                                                                                                                    Advanced Uses

                                                                                                                                    Sometimes you want to exit out of a For( loop when it hasn't finished. You can do this by storing the end value to the variable you used in the For( loop. For example:

                                                                                                                                    :For(A,1,100)
<some code>
:If <condition for exiting out>
:100→A
:End

                                                                                                                                    For( can also be used to create a delay:

                                                                                                                                    //delays for about 0.5 second (83+) or 0.2 second (83+SE/84+/SE/CSE)
:For(A,1,200)
:End

                                                                                                                                    If X is end, the delay will be about X/1000 seconds for the TI-83/83+, and X/400 for other calculators.

                                                                                                                                    Unlike delays that use rand, a For( loop delay can execute an animation or other code during the delay.

                                                                                                                                    For( loops can be nested to execute code once for every combination of values of several variables. For example:

                                                                                                                                    :For(A,1,50)
:For(B,1,50)
:(some code)
:End
:End

                                                                                                                                    This will run (some code) 2500 times—once for every combination of a value of A from 1 to 50 and a value of B from 1 to 50.

                                                                                                                                    There's a standard way to exclude repetitions if the order of the variables doesn't matter (for example, if A=30, B=40 is the same situation as A=40, B=30 in the example above). In this case, the beginning of the loop should be changed to:

                                                                                                                                    :For(A,1,50)
:For(B,1,A)

                                                                                                                                    On the CSE, a list index can be used as the variable in a For( loop. When this is done, the loop will operate and exit normally, but the list will not be affected. For instance, this program

                                                                                                                                    :{1,2,3→L₁
:For(L₁(1),2,5
:Disp "X
:End
:Disp L₁

                                                                                                                                    will output:

                                                                                                                                    X
X
X
X
  {1,2,3}

                                                                                                                                    For( loops can also be used to exceed the normal overflow limit of \(10^{100}\) for variables and computations. For example, utilizing the optional step argument,

                                                                                                                                    :For(A,9E99,9E99,9E99
:End

                                                                                                                                    the value of A will be 1.8E100, which is otherwise impossible to assign to a variable by normal means. One could then use A as the step value for a For( command,

                                                                                                                                    :For(A,A,A,A
:End

                                                                                                                                    which doubles the value of A (so 1.8E100 becomes 3.6E100). This process can be repeated until the "true" overflow limit is reached at \(10^{128}\) (since the calculator stores the exponent as a signed 8-bit integer, ranging from -128 to 127).

                                                                                                                                    Optimization

                                                                                                                                    The seq( command, or simple math, can often be used in place of the For( command when dealing with lists. For example:

                                                                                                                                    :For(A,1,dim(L1
:cos(A)→L1(A
:End
//can be
:seq(cos(A),A,1,dim(L1→L1

                                                                                                                                    and

                                                                                                                                    :For(A,1,dim(L1
:1+L1(A→L1(A
:End
//can be
:1+L1→L1

                                                                                                                                    One rather strange optimization when using For( loops is actually leaving on the ending parenthesis of the For( loop in certain cases. If you don't do this, the following cases will be processed much slower when they are the first line of code in the loop:

                                                                                                                                    • IS>( and DS<( (no matter if the following command is skipped or not).
                                                                                                                                    • A lone If without an accompanying Then, but only when the condition is false (If with a true condition is unchanged).

                                                                                                                                    If the condition of the If command can be false (as in most actual cases), you should add a closing parenthesis because the difference is so great.

                                                                                                                                    An example use of this optimization:

                                                                                                                                    :For(I,1,1200
:If 0
:1
:End

//should be
:For(I,1,1200)
:If 0
:1
:End

                                                                                                                                    Command Timings

                                                                                                                                    Using a For( loop when it fits your purpose is much faster than adapting a While or Repeat loop to do so. Conclusion: For( loops are good!

                                                                                                                                    Error Conditions

                                                                                                                                    • ERR:INCREMENT is thrown if the increment of the For( loop is 0.
                                                                                                                                    • ERR:INVALID occurs if this statement is used outside a program.
                                                                                                                                    • ERR:UNDEFINED is thrown if you DelVar the loop variable while inside the loop.

                                                                                                                                    Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, Edward H, Electromagnet8, GoVegan, kg583, lirtosiast, MI Wright, muffinzrock, Myles_Zadok, Weregoose.

                                                                                                                                    History

                                                                                                                                    Calculator OS Version Description
                                                                                                                                    TI-82 1.0 Added
                                                                                                                                    Property Value
                                                                                                                                    Hex Value $BB1E
                                                                                                                                    Categories
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                                                                                                                                    • FR: 𝐅fdp(

                                                                                                                                    𝐅pdf(

                                                                                                                                    Overview

                                                                                                                                    Computes the 𝐅 distribution probability between lowerboundand upperbound for the specified numerator df (degrees of freedom) and denominator df.

                                                                                                                                    Availability: Token available everywhere.

                                                                                                                                    Syntax

                                                                                                                                    𝐅pdf(x,numerator df,denominator df)

                                                                                                                                    Arguments

                                                                                                                                    NameTypeOptional
                                                                                                                                    𝐅
                                                                                                                                    x
                                                                                                                                    numerator df
                                                                                                                                    denominator df

                                                                                                                                    Location

                                                                                                                                    2nd, distr, DISTR, 9:pdf(

                                                                                                                                    Description

                                                                                                                                    Fpdf( is the F-distribution probability density function.

                                                                                                                                    Since the F-distribution is continuous, the value of Fpdf( doesn't represent an actual probability - in fact, one of the only uses for this command is to draw a graph of the distribution. You could also use it for various calculus purposes, such as finding inflection points.

                                                                                                                                    The command takes 3 arguments: x is the point at which to evaluate the function (when graphing, use X for this argument), numerator df and denominator df are the numerator degrees of freedom and denominator degrees of freedom respectively (these specify a single Fpdf( curve out of an infinite family).

                                                                                                                                    The F-distribution is used mainly in significance tests of variance.

                                                                                                                                    Formulas

                                                                                                                                    The value of the Fpdf( is given by

                                                                                                                                    (1) \(\begin{align} \texttt{Fpdf}(x,d_1,d_2) = \frac{\left( \frac{d_1x}{d_1x+d_2} \right)^{d_1/2} \left(1-\frac{d_1x}{d_1x+d_2}\right)^{d_2/2}}{x \texttt{B}(d_1/2,d_2/2)} \end{align}\)

                                                                                                                                    where B(x,y) is the Beta function.

                                                                                                                                    Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583.

                                                                                                                                    History

                                                                                                                                    Calculator OS Version Description
                                                                                                                                    TI-83 0.01013 Added
                                                                                                                                    Property Value
                                                                                                                                    Hex Value $75
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                                                                                                                                    • FR: PleinEcr

                                                                                                                                    Full

                                                                                                                                    Overview

                                                                                                                                    Sets full screen mode.

                                                                                                                                    Availability: Token only available from within the Basic editor.

                                                                                                                                    Syntax

                                                                                                                                    Full

                                                                                                                                    Location

                                                                                                                                    mode, Full

                                                                                                                                    Description

                                                                                                                                    The Full command cancels the effects of either Horiz or G-T.

                                                                                                                                    Full is usually used either at the beginning and/or ending of a program. It is used at the beginning to ensure that the screen mode is Full, the standard setting. It is used at the end if the screen mode was changed in the middle of the program (as clean up).

                                                                                                                                    :Full

                                                                                                                                    Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583, Timothy Foster, Xphoenix, ztrumpet.

                                                                                                                                    History

                                                                                                                                    Calculator OS Version Description
                                                                                                                                    TI-82 1.0 Added
                                                                                                                                    Property Value
                                                                                                                                    Hex Value $76
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                                                                                                                                    Localizations
                                                                                                                                    • FR: Fonct

                                                                                                                                    Func

                                                                                                                                    Overview

                                                                                                                                    Sets function graphing mode.

                                                                                                                                    Availability: Token only available from within the Basic editor.

                                                                                                                                    Syntax

                                                                                                                                    Func

                                                                                                                                    Location

                                                                                                                                    mode, Func

                                                                                                                                    Description

                                                                                                                                    The Func command enables the default function graphing mode. This command is usually unnecessary in a program, but if you want to graph a Y= equation, you'd want to make sure the calculator is in function mode first.

                                                                                                                                    In function mode, you can graph equations where y (the vertical coordinate) is a function of x (the horizontal coordinate). This mode is most commonly discussed in algebra and single-variable calculus courses. Many curves, such as a parabola, have simple expressions when written in the form y=f(x).

                                                                                                                                    However, in function mode, many expressions cannot be graphed at all. For example, a circle can't be easily graphed in function mode, since for some x-values, there are two y-values. Using two functions, you can achieve a circle, but it will still require a friendly graphing window to display perfectly.

                                                                                                                                    Many calculator features are specifically targeted at function mode graphing. For example, two graphing styles (see GraphStyle() can be only used with function mode. The DrawF and DrawInv commands draw functions as if in graphing mode.

                                                                                                                                    Advanced Uses

                                                                                                                                    The window variables that apply to function mode are:

                                                                                                                                    • Xmin — Determines the minimum X-value shown on the screen.
                                                                                                                                    • Xmax — Determines the maximum X-value shown on the screen.
                                                                                                                                    • Xscl — Determines the horizontal space between marks on the X-axis in AxesOn mode or dots in GridOn mode.
                                                                                                                                    • Ymin — Determines the minimum Y-value shown on the screen.
                                                                                                                                    • Ymax — Determines the maximum Y-value shown on the screen.
                                                                                                                                    • Yscl — Determines the vertical space between marks on the Y-axis in AxesOn mode or dots in GridOn mode.
                                                                                                                                    • Xres — Determines the pixel distance between points used for graphing. This is a value 1-8: 1 for best quality, 8 for best speed.

                                                                                                                                    Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583.

                                                                                                                                    History

                                                                                                                                    Calculator OS Version Description
                                                                                                                                    TI-82 1.0 Added
                                                                                                                                    Property Value
                                                                                                                                    Hex Value $BB64
                                                                                                                                    Categories
                                                                                                                                      Localizations
                                                                                                                                      • FR: G-T

                                                                                                                                      G-T

                                                                                                                                      Overview

                                                                                                                                      Sets graph-table vertical split-screen mode.

                                                                                                                                      Availability: Token only available from within the Basic editor.

                                                                                                                                      Syntax

                                                                                                                                      G-T

                                                                                                                                      Location

                                                                                                                                      mode, GRAPH-TABLE

                                                                                                                                      Description

                                                                                                                                      G-T puts the calculator into "Graph-Table" mode: this mode shows the home screen at full size, but the graph screen and table will be displayed together, each taking up half the screen (divided vertically).

                                                                                                                                      G-T is usually used at the beginning of a program to ensure that the screen mode is G-T , for programs such as math programs that want to demonstrate the thinking step-by-step.

                                                                                                                                      :G-T

                                                                                                                                      With OS version 2.30 (on the TI-84+ and TI-84+ SE calculators), G-T mode can be used with stat plots as well.

                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583, mattyjraps, Xphoenix.

                                                                                                                                      History

                                                                                                                                      Calculator OS Version Description
                                                                                                                                      TI-83 1.010 Added
                                                                                                                                      Property Value
                                                                                                                                      Hex Value $47
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                                                                                                                                      • FR: G

                                                                                                                                      G

                                                                                                                                      Overview

                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                      Syntax

                                                                                                                                      G

                                                                                                                                      Description

                                                                                                                                      Examples

                                                                                                                                      Explanation 1

                                                                                                                                      code 1

                                                                                                                                      Explanation 2

                                                                                                                                      code 2

                                                                                                                                      Error Conditions

                                                                                                                                      Advanced Notes

                                                                                                                                      History

                                                                                                                                      Calculator OS Version Description
                                                                                                                                      TI-82 1.0 Added
                                                                                                                                      Property Value
                                                                                                                                      Hex Value $6109
                                                                                                                                      Categories
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                                                                                                                                      • FR: BDG0

                                                                                                                                      GDB0

                                                                                                                                      Overview

                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                      Syntax

                                                                                                                                      GDB0

                                                                                                                                      Description

                                                                                                                                      Examples

                                                                                                                                      Explanation 1

                                                                                                                                      code 1

                                                                                                                                      Explanation 2

                                                                                                                                      code 2

                                                                                                                                      Error Conditions

                                                                                                                                      Advanced Notes

                                                                                                                                      History

                                                                                                                                      Calculator OS Version Description
                                                                                                                                      TI-83 0.01013 Added
                                                                                                                                      Property Value
                                                                                                                                      Hex Value $6100
                                                                                                                                      Categories
                                                                                                                                      Localizations
                                                                                                                                      • FR: BDG1

                                                                                                                                      GDB1

                                                                                                                                      Overview

                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                      Syntax

                                                                                                                                      GDB1

                                                                                                                                      Description

                                                                                                                                      Examples

                                                                                                                                      Explanation 1

                                                                                                                                      code 1

                                                                                                                                      Explanation 2

                                                                                                                                      code 2

                                                                                                                                      Error Conditions

                                                                                                                                      Advanced Notes

                                                                                                                                      History

                                                                                                                                      Calculator OS Version Description
                                                                                                                                      TI-82 1.0 Added
                                                                                                                                      Property Value
                                                                                                                                      Hex Value $6101
                                                                                                                                      Categories
                                                                                                                                      Localizations
                                                                                                                                      • FR: BDG2

                                                                                                                                      GDB2

                                                                                                                                      Overview

                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                      Syntax

                                                                                                                                      GDB2

                                                                                                                                      Description

                                                                                                                                      Examples

                                                                                                                                      Explanation 1

                                                                                                                                      code 1

                                                                                                                                      Explanation 2

                                                                                                                                      code 2

                                                                                                                                      Error Conditions

                                                                                                                                      Advanced Notes

                                                                                                                                      History

                                                                                                                                      Calculator OS Version Description
                                                                                                                                      TI-82 1.0 Added
                                                                                                                                      Property Value
                                                                                                                                      Hex Value $6102
                                                                                                                                      Categories
                                                                                                                                      Localizations
                                                                                                                                      • FR: BDG3

                                                                                                                                      GDB3

                                                                                                                                      Overview

                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                      Syntax

                                                                                                                                      GDB3

                                                                                                                                      Description

                                                                                                                                      Examples

                                                                                                                                      Explanation 1

                                                                                                                                      code 1

                                                                                                                                      Explanation 2

                                                                                                                                      code 2

                                                                                                                                      Error Conditions

                                                                                                                                      Advanced Notes

                                                                                                                                      History

                                                                                                                                      Calculator OS Version Description
                                                                                                                                      TI-82 1.0 Added
                                                                                                                                      Property Value
                                                                                                                                      Hex Value $6103
                                                                                                                                      Categories
                                                                                                                                      Localizations
                                                                                                                                      • FR: BDG4

                                                                                                                                      GDB4

                                                                                                                                      Overview

                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                      Syntax

                                                                                                                                      GDB4

                                                                                                                                      Description

                                                                                                                                      Examples

                                                                                                                                      Explanation 1

                                                                                                                                      code 1

                                                                                                                                      Explanation 2

                                                                                                                                      code 2

                                                                                                                                      Error Conditions

                                                                                                                                      Advanced Notes

                                                                                                                                      History

                                                                                                                                      Calculator OS Version Description
                                                                                                                                      TI-82 1.0 Added
                                                                                                                                      Property Value
                                                                                                                                      Hex Value $6104
                                                                                                                                      Categories
                                                                                                                                      Localizations
                                                                                                                                      • FR: BDG5

                                                                                                                                      GDB5

                                                                                                                                      Overview

                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                      Syntax

                                                                                                                                      GDB5

                                                                                                                                      Description

                                                                                                                                      Examples

                                                                                                                                      Explanation 1

                                                                                                                                      code 1

                                                                                                                                      Explanation 2

                                                                                                                                      code 2

                                                                                                                                      Error Conditions

                                                                                                                                      Advanced Notes

                                                                                                                                      History

                                                                                                                                      Calculator OS Version Description
                                                                                                                                      TI-82 1.0 Added
                                                                                                                                      Property Value
                                                                                                                                      Hex Value $6105
                                                                                                                                      Categories
                                                                                                                                      Localizations
                                                                                                                                      • FR: BDG6

                                                                                                                                      GDB6

                                                                                                                                      Overview

                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                      Syntax

                                                                                                                                      GDB6

                                                                                                                                      Description

                                                                                                                                      Examples

                                                                                                                                      Explanation 1

                                                                                                                                      code 1

                                                                                                                                      Explanation 2

                                                                                                                                      code 2

                                                                                                                                      Error Conditions

                                                                                                                                      Advanced Notes

                                                                                                                                      History

                                                                                                                                      Calculator OS Version Description
                                                                                                                                      TI-82 1.0 Added
                                                                                                                                      Property Value
                                                                                                                                      Hex Value $6106
                                                                                                                                      Categories
                                                                                                                                      Localizations
                                                                                                                                      • FR: BDG7

                                                                                                                                      GDB7

                                                                                                                                      Overview

                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                      Syntax

                                                                                                                                      GDB7

                                                                                                                                      Description

                                                                                                                                      Examples

                                                                                                                                      Explanation 1

                                                                                                                                      code 1

                                                                                                                                      Explanation 2

                                                                                                                                      code 2

                                                                                                                                      Error Conditions

                                                                                                                                      Advanced Notes

                                                                                                                                      History

                                                                                                                                      Calculator OS Version Description
                                                                                                                                      TI-83 0.01013 Added
                                                                                                                                      Property Value
                                                                                                                                      Hex Value $6107
                                                                                                                                      Categories
                                                                                                                                      Localizations
                                                                                                                                      • FR: BDG8

                                                                                                                                      GDB8

                                                                                                                                      Overview

                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                      Syntax

                                                                                                                                      GDB8

                                                                                                                                      Description

                                                                                                                                      Examples

                                                                                                                                      Explanation 1

                                                                                                                                      code 1

                                                                                                                                      Explanation 2

                                                                                                                                      code 2

                                                                                                                                      Error Conditions

                                                                                                                                      Advanced Notes

                                                                                                                                      History

                                                                                                                                      Calculator OS Version Description
                                                                                                                                      TI-83 0.01013 Added
                                                                                                                                      Property Value
                                                                                                                                      Hex Value $6108
                                                                                                                                      Categories
                                                                                                                                      Localizations
                                                                                                                                      • FR: BDG9

                                                                                                                                      GDB9

                                                                                                                                      Overview

                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                      Syntax

                                                                                                                                      GDB9

                                                                                                                                      Description

                                                                                                                                      Examples

                                                                                                                                      Explanation 1

                                                                                                                                      code 1

                                                                                                                                      Explanation 2

                                                                                                                                      code 2

                                                                                                                                      Error Conditions

                                                                                                                                      Advanced Notes

                                                                                                                                      History

                                                                                                                                      Calculator OS Version Description
                                                                                                                                      TI-83 0.01013 Added
                                                                                                                                      Property Value
                                                                                                                                      Hex Value $EF4E
                                                                                                                                      Categories
                                                                                                                                      Localizations
                                                                                                                                      • FR: GRIS

                                                                                                                                      GRAY

                                                                                                                                      Overview

                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                      Syntax

                                                                                                                                      GRAY

                                                                                                                                      Description

                                                                                                                                      Examples

                                                                                                                                      Explanation 1

                                                                                                                                      code 1

                                                                                                                                      Explanation 2

                                                                                                                                      code 2

                                                                                                                                      Error Conditions

                                                                                                                                      Advanced Notes

                                                                                                                                      History

                                                                                                                                      Calculator OS Version Description
                                                                                                                                      TI-84+CSE 4.0 Added
                                                                                                                                      Property Value
                                                                                                                                      Hex Value $EF45
                                                                                                                                      Categories
                                                                                                                                      Localizations
                                                                                                                                      • FR: VERT

                                                                                                                                      GREEN

                                                                                                                                      Overview

                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                      Syntax

                                                                                                                                      GREEN

                                                                                                                                      Description

                                                                                                                                      Examples

                                                                                                                                      Explanation 1

                                                                                                                                      code 1

                                                                                                                                      Explanation 2

                                                                                                                                      code 2

                                                                                                                                      Error Conditions

                                                                                                                                      Advanced Notes

                                                                                                                                      History

                                                                                                                                      Calculator OS Version Description
                                                                                                                                      TI-84+CSE 4.0 Added
                                                                                                                                      Property Value
                                                                                                                                      Hex Value $BBCE
                                                                                                                                      Categories
                                                                                                                                      Localizations
                                                                                                                                      • FR: RéorganiserMém

                                                                                                                                      GarbageCollect

                                                                                                                                      Overview

                                                                                                                                      Displays the garbage collection menu to allow cleanup of unused archive memory.

                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                      Syntax

                                                                                                                                      GarbageCollect

                                                                                                                                      Location

                                                                                                                                      2nd, catalog, GarbageCollect

                                                                                                                                      Description

                                                                                                                                      A bit of a preamble: unlike RAM, which is the easy-to-access memory, Flash ROM (the archive), used for long-term storage on the 83+ and higher, can't be written to easily. Skipping over technicalities, what's written in the archive once is semi-permanent, and can't be written to again unless an entire 64KB sector of memory is erased.

                                                                                                                                      As a result, when you delete a variable from archive, the calculator doesn't delete it immediately (there may be other, good variables in the same block that would get erased as well), it just marks it as deleted. Similarly, when you unarchive a variable, its data is copied to RAM and the original is marked as deleted.

                                                                                                                                      Naturally, this can't be done forever: sooner or later you'll run out of space in the archive because all of it is taken up by these "garbage variables". At this point, the calculator does something known as "garbage collecting". It copies the actually-used variables in each sector to a backup sector (set aside just for this purpose), then erases it; the process is repeated for the other sectors. Additionally, the variables are rearranged so that they aren't spread out all over the place; this makes it more likely that a spot will be found for large variables.

                                                                                                                                      While "garbage collecting" will be done automatically when it's absolutely necessary, this may be a time-consuming process at that stage. Instead, you can call the GarbageCollect command yourself periodically (how often depends on your calculator habits, but generally once a month or so could work) to keep the Flash ROM in a semi-neat state, and then it will be a fairly quick process.

                                                                                                                                      During garbage collection, a menu will appear that asks you "Garbage Collect?", giving you the options No and Yes. If you didn't select the GarbageCollect command yourself, it's highly recommended to select Yes. If you did select it, you probably want to garbage collect, so you should also select Yes. At that point, the message "Garbage collecting…" will be displayed for some time, and then the process will end.

                                                                                                                                      Advanced Uses

                                                                                                                                      To avoid garbage collecting often, reduce the amount of times you archive and unarchive variables. There's also the consideration that too many writes to the Flash ROM (which are directly related to the number of GarbageCollects you do) can, in theory, wear it out. This probably would take much longer than anyone's used a TI-83+ calculator so far, though, and in all probability you don't really have to worry about this.

                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: burr, CloudVariable, DarkerLine, GoVegan, kg583, Trenly.

                                                                                                                                      History

                                                                                                                                      Calculator OS Version Description
                                                                                                                                      TI-83+ 1.03 Added
                                                                                                                                      Property Value
                                                                                                                                      Hex Value $E8
                                                                                                                                      Categories
                                                                                                                                      Localizations
                                                                                                                                      • FR: Capt(

                                                                                                                                      Get(

                                                                                                                                      Overview

                                                                                                                                      Retrieves a value from a connected TI-Innovator™ Hub and stores the data to a variable on the receiving CE calculator.
                                                                                                                                      Note: See also Send( and eval(

                                                                                                                                      Availability: Token only available from within the Basic editor.

                                                                                                                                      Syntax

                                                                                                                                      Get(variable)

                                                                                                                                      Arguments

                                                                                                                                      NameTypeOptional
                                                                                                                                      variable

                                                                                                                                      Location

                                                                                                                                      prgm, I/O, A:Get(

                                                                                                                                      Overview

                                                                                                                                      Retrieves a value from a connected TI-Innovator™ Hub and stores the data to a variable on the receiving CE calculator.
                                                                                                                                      Note: See also Send( and eval(

                                                                                                                                      Availability: Token only available from within the Basic editor.

                                                                                                                                      Syntax

                                                                                                                                      Get(variable

                                                                                                                                      Arguments

                                                                                                                                      NameTypeOptional
                                                                                                                                      variable

                                                                                                                                      Location

                                                                                                                                      prgm, HUB, 5:Get

                                                                                                                                      Special Category

                                                                                                                                      Ti-Innovator™ Hub

                                                                                                                                      Description

                                                                                                                                      The Get( command is meant for use with the CBL (Calculator Based Laboratory) device, or other compatible devices. When the calculator is connected by a link cable to such a device, Get(variable) will read data from the device and store it to variable. Usually, this data is a list, and so you want to Get(L₁) or some other list variable.

                                                                                                                                      Advanced Uses

                                                                                                                                      In fact, the Get( command can also be used for linking two calculators, in which case it functions precisely like GetCalc(. This is probably for compatibility with the TI-82, which used Get( rather than GetCalc( for linking two calculators. However, since this isn't a documented feature (in fact, your TI-83+ manual will insist that Get( cannot be used in this way), it isn't guaranteed to work with future calculator versions.

                                                                                                                                      Optimization

                                                                                                                                      Nevertheless, using Get( instead of GetCalc( will make your program smaller, and probably preserve functionality.

                                                                                                                                      Norland Robot

                                                                                                                                      The Get( command is usually used after a Send command to confirm its transmission like this: Get(var). The variable in the parentheses is where the time of the robot's movement is stored. You can display the time moved with a Disp command.

                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: burr, CloudVariable, DarkerLine, GoVegan, jonbush, kg583, princetonlion, Timtech, Trenly.

                                                                                                                                      History

                                                                                                                                      Calculator OS Version Description
                                                                                                                                      TI-82 1.0 Added
                                                                                                                                      Property Value
                                                                                                                                      Hex Value $BB53
                                                                                                                                      Categories
                                                                                                                                      Localizations
                                                                                                                                      • FR: GetCalc(

                                                                                                                                      GetCalc(

                                                                                                                                      Overview

                                                                                                                                      Gets contents of variable on another TI-84 Plus CE and stores it to variable on the receiving TI-84 Plus CE. By default, the TI-84 Plus CE uses the USB port if it is connected. If the USB cable is not connected, it uses the I/O port.portflag=0 use USB port if connected;portflag=1 use USB port;portflag=2 use I/O port.(Ignored when program runs on the TI-84 Plus CE.)

                                                                                                                                      Availability: Token only available from within the Basic editor.

                                                                                                                                      Syntax

                                                                                                                                      GetCalc(variable[,portflag])

                                                                                                                                      Arguments

                                                                                                                                      NameTypeOptional
                                                                                                                                      variable
                                                                                                                                      portflagYes

                                                                                                                                      Location

                                                                                                                                      prgm, I/O, 0:GetCalc(

                                                                                                                                      Description

                                                                                                                                      The GetCalc( command allows you to make multiplayer games, where two calculators communicate with each other across a link cable that is connected between them. The GetCalc( command can only receive one variable from another calculator, and the variable can be any variable (a real, list, matrix, string, etc.). The calculator doesn't exchange variable values when the variable is received, but instead replace the variable of the same name on the receiving calculator.

                                                                                                                                      For the GetCalc( command to work correctly, the sending calculator must be in a preemptible state and it cannot be executing an assembly program. (The sending calculator is the one which is not executing the GetCalc( command.) The two main commands that you should use to ensure this are Pause and Menu(; however, any command that is waiting for user input will also work perfectly fine (such as Prompt and Input).

                                                                                                                                      The GetCalc( command behaves a little differently in the older TI-83 models. If the sending calculator is idle with the Pause or Menu( command, it will automatically "press enter" when the receiving calculator executes GetCalc(. This can be frustrating when in a menu, because it prevents the user's opportunity to make a selection.

                                                                                                                                      However, this can make real-time gaming more possible if used in conjunction with the Pause command. When the receiving calculator receives the variable, it could then execute the Pause command, while the sending calculator automatically exits the power-saving state and could then perform the GetCalc( command. All models after the TI-83 do not automatically exit their power-saving states.

                                                                                                                                      Advanced Uses

                                                                                                                                      The TI-84+ and TI-84+SE will use the USB port if it is connected to a USB cable, otherwise they will use the I/O port. However, you can specify which port you want to use by putting a number after the variable as GetCalc('s second argument: zero to use the USB port if connected to a USB cable, one to use the USB port without checking to see if it's connected, and two to use the I/O port.

                                                                                                                                      See Also

                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, jonbush, kg583, Myles_Zadok, Timtech.

                                                                                                                                      History

                                                                                                                                      Calculator OS Version Description
                                                                                                                                      TI-83 0.01013 Added
                                                                                                                                      Property Value
                                                                                                                                      Hex Value $D7
                                                                                                                                      Categories
                                                                                                                                      Localizations
                                                                                                                                      • FR: Goto

                                                                                                                                      Goto

                                                                                                                                      Overview

                                                                                                                                      Transfers control to label.

                                                                                                                                      Availability: Token only available from within the Basic editor.

                                                                                                                                      Syntax

                                                                                                                                      Gotolabel

                                                                                                                                      Arguments

                                                                                                                                      NameTypeOptional
                                                                                                                                      label

                                                                                                                                      Location

                                                                                                                                      prgm, CTL, 0:Goto

                                                                                                                                      Description

                                                                                                                                      The Goto command is used together with the Lbl command to jump (or branch) to another place in a program. When the calculator executes a Goto command, it stores the label name in memory, and then searches from the beginning of the program for the Lbl command with the supplied name. If it finds it, it continues running the program from that point; otherwise, if the label does not exist, it throws an ERR: LABEL error.

                                                                                                                                      Label names can be either one or two characters long, and the only characters you're allowed to use are letters (including θ) and numbers 0 to 9; this means 37+37*37=1406 possible combinations. Of course, you should use all of the single character names first, before using the two character names. While you can technically have the same label name multiple times in a program, it is rather pointless since the calculator always goes to the first occurrence of the label.

                                                                                                                                      You can position a Lbl command one or more lines before a Goto command to create a kind of loop structure. However, you have to provide the break-out code, since it isn't built-in. An If conditional is easiest, but if there is no code that ends the branching, then program execution will continue indefinitely, until you manually exit it (by pressing the ON key).

                                                                                                                                      :Lbl A
:...
:If <exit condition>
:Goto A  // this line is skipped

                                                                                                                                      Although the Goto command may seem like a good alternative to loops, it should be avoided whenever possible, which is especially important when you are first planning a program. This is because it has several serious drawbacks associated with it:

                                                                                                                                      • It is quite slow, and gets slower the further the Lbl is in your program.
                                                                                                                                      • It makes reading code (your own, or someone else's) much more confusing.
                                                                                                                                      • In most cases, If, For(, While, or Repeat can be used instead, saving space and improving speed.
                                                                                                                                      • Using a Goto to exit any block of code requiring an End command causes a memory leak, which will not be usable until the program finishes running or executes a Return command, and which will slow down your program down. See below for ways to fix this.

                                                                                                                                      The Goto command isn't all bad, however, and is actually useful when a loop isn't practical and when something only happens once or twice (see below for examples). Just remember that you should never use Goto to repeat a block of code several times. Use For(, Repeat, or While instead.

                                                                                                                                      Fixing Memory Leaks

                                                                                                                                      One of the simplest memory leaks that occurs is using branching to exit out of a loop when a certain condition of an If conditional is true. If the loop is an infinite loop (i.e., Repeat 0 or While 1), you should take the condition from the If conditional and place it as the condition of the loop. This allows you to remove the branching, since it is now unnecessary.

                                                                                                                                      :Repeat 0
:getKey→B
:If B:Goto A
:End:Lbl A
Make Loop Condition
:Repeat B
:getKey→B
:End

                                                                                                                                      Of course, the only reason that this memory leak fix is possible is because of the If conditional (since the If conditional doesn't need a closing End command). When dealing with a complex If conditional, you will have to rework the conditionals so the branching has its own If conditional. Depending on how many commands there are in the conditionals, you might be able to just use an If conditional or you might need to use an If-Then conditional.

                                                                                                                                      :If B:Then
:Disp "Hello
:Goto A
:End
Separate Into Conditionals
:If B:Disp "Hello
:If B:Goto A

                                                                                                                                      This memory leak fix will work most of the time, but it isn't applicable when one of the values of the variables in the condition is changed by one of the commands inside the condition. The way to get around this is by using another variable for the If conditional that the branching uses. You initialize the variable to zero, assign the variable whatever value you want in the conditional, and then check to see if the variable is equal to that value in the branching conditional.

                                                                                                                                      :If A=1:Then
:3→A:4→B
:Goto A
:End
Use Another Variable
:Delvar CIf A=1:Then
:3→A:4→B:π→C
:End
:If C=π
:Goto A

                                                                                                                                      Advanced Uses

                                                                                                                                      If your program requires cleanup after it finishes, but it can exit from several different places, use Goto and place a Lbl at that point. This saves memory over repeating the cleanup code every time you exit. The usual considerations about Goto don't apply here: since you're exiting the program, all memory leaks will be gone anyway, and speed isn't much of an issue for something that only gets done once.

                                                                                                                                      The code looks something like this:

                                                                                                                                      :If K=45:Goto Q  //user pressed CLEAR
:...
:If L:Goto Q  // game over
:...
:Lbl Q
:DelVar L1ClrHome

                                                                                                                                      A common situation in programs is when a decision has to be made about where the program execution should go next. The obvious approach would be to use the value of a variable as the label name (i.e., something like Goto A, with A being a variable), but that doesn't work because the calculator doesn't interpret the label as a variable. So, the next best approach is to use If conditionals with the different values of the variable:

                                                                                                                                      :If not(A:Goto 0
:If A=1:Goto 1
:If A=2:Goto 2

                                                                                                                                      Another possible use for Goto is in program protection to break a program with an error without letting the user see where it happened. If the label that you want to Goto doesn't exist, you'll get a ERR: LABEL error, which doesn't provide a 2:Goto option. So, all you have to do is Goto a label that you know doesn't exist.
                                                                                                                                      An alternative method would be to lock the program from being able to be edited. (which you currently cannot do on-calc without a shell) This gives you the possibility to throw whatever error you want! For example, if the user entered something invalid, you can add a blank line with a closing parenthesis, and a syntax error will be thrown, without the 2:Goto option! If you do go this route, be sure to only lock it when you are done editing. It is also good practice to include a text file with the source, as well.

                                                                                                                                      Error Conditions

                                                                                                                                      • ERR:INVALID occurs if this statement is used outside a program.
                                                                                                                                      • ERR:LABEL is thrown if the corresponding label doesn't exist.

                                                                                                                                      See Also

                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: alexrudd, burr, DarkerLine, GoVegan, iPhoenixOnTIBD, Myles_Zadok.

                                                                                                                                      History

                                                                                                                                      Calculator OS Version Description
                                                                                                                                      TI-82 1.0 Added
                                                                                                                                      Property Value
                                                                                                                                      Hex Value $7E
                                                                                                                                      Categories
                                                                                                                                      Localizations
                                                                                                                                      • FR: Graph Format

                                                                                                                                      Graph Format

                                                                                                                                      Overview

                                                                                                                                      Syntax

                                                                                                                                      Graph Format

                                                                                                                                      Description

                                                                                                                                      Examples

                                                                                                                                      Explanation 1

                                                                                                                                      code 1

                                                                                                                                      Explanation 2

                                                                                                                                      code 2

                                                                                                                                      Error Conditions

                                                                                                                                      Advanced Notes

                                                                                                                                      History

                                                                                                                                      Calculator OS Version Description
                                                                                                                                      Property Value
                                                                                                                                      Hex Value $EF65
                                                                                                                                      Categories
                                                                                                                                        Localizations
                                                                                                                                        • FR: CouleurGraph(

                                                                                                                                        GraphColor(

                                                                                                                                        Overview

                                                                                                                                        Sets the color for function#.
                                                                                                                                        Color#: 10 - 24 or color name pasted from [vars] COLOR.

                                                                                                                                        Availability: Token only available from within the Basic editor.

                                                                                                                                        Syntax

                                                                                                                                        GraphColor(function#,color#)

                                                                                                                                        Arguments

                                                                                                                                        NameTypeOptional
                                                                                                                                        function#
                                                                                                                                        color#colorNum

                                                                                                                                        Location

                                                                                                                                        prgm, CTL, H:GraphColor(

                                                                                                                                        Description

                                                                                                                                        The GraphColor( command will change the color of any function from Y0 to Y9. So, for example, to change the color of Y3 to NAVY, do:

                                                                                                                                        GraphColor(3,NAVY

                                                                                                                                        Notice, you must use the number of the function, rather than the entire function name, which would be Y3.

                                                                                                                                        As you may know, you can also use the value of the color, which can be any integer between 10 and 24. So, our last command could also be:

                                                                                                                                        GraphColor(3,17

                                                                                                                                        Source: parts of this page were written by the following TI|BD contributors: kg583, Michael2_3B.

                                                                                                                                        History

                                                                                                                                        Calculator OS Version Description
                                                                                                                                        TI-84+CSE 4.0 Added
                                                                                                                                        Property Value
                                                                                                                                        Hex Value $BB45
                                                                                                                                        Categories
                                                                                                                                        Localizations
                                                                                                                                        • FR: GraphStyle(

                                                                                                                                        GraphStyle(

                                                                                                                                        Overview

                                                                                                                                        Sets a graphstyle for function#.

                                                                                                                                        Availability: Token only available from within the Basic editor.

                                                                                                                                        Syntax

                                                                                                                                        GraphStyle(function#,graphstyle#)

                                                                                                                                        Arguments

                                                                                                                                        NameTypeOptional
                                                                                                                                        function#
                                                                                                                                        graphstyle#

                                                                                                                                        Location

                                                                                                                                        prgm, CTL, H:GraphStyle(

                                                                                                                                        Description

                                                                                                                                        The GraphStyle( command allows you to set the graphing style of an equation (line, thick line, dotted line, etc.) from within a program.

                                                                                                                                        Its first argument, equation #, is the number of the equation whose graphing style you want to change - this depends on the mode you're in. For example, if you wanted to change the graphing style of Y1, you would need to be in function mode and use the value 1 for this argument. If you wanted to change the graphing style of r4, you would need to be in polar mode and use the value 4.

                                                                                                                                        The second argument is a number from 1 to 7, which translates to a graphing style as follows:

                                                                                                                                        • 1 - a normal line, usually the default graph style.
                                                                                                                                        • 2 - a thick line (three pixels wide).
                                                                                                                                        • 3 - a line, with everything above it shaded (only valid in function mode).
                                                                                                                                        • 4 - a line, with everything below it shaded (only valid in function mode).
                                                                                                                                        • 5 - a path: a line, with a ball moving along it as it is graphed (not valid in sequential mode).
                                                                                                                                        • 6 - animated: a ball moving along the graph (not valid in sequential mode).
                                                                                                                                        • 7 - a dotted line.

                                                                                                                                        Compare this to the effect of Connected or Dot mode. When either of these modes is set, all equations, from all graphing modes, are reverted to line style or dotted line style respectively; furthermore, it becomes the default graph style and clearing an equation will revert it to this graph style. The GraphStyle( command simply overrides these modes temporarily.

                                                                                                                                        Advanced

                                                                                                                                        In shading modes (3 and 4), the shading style cycles as follows:

                                                                                                                                        • The first function graphed shades using vertical lines one pixel apart
                                                                                                                                        • The second function shades using horizontal lines one pixel apart
                                                                                                                                        • The third function shades using negatively sloping diagonal lines, two pixels apart.
                                                                                                                                        • The fourth function shades using positively sloping diagonal lines, two pixels apart.
                                                                                                                                        • After that, functions will cycle through these four styles in that order.

                                                                                                                                        Error Conditions

                                                                                                                                        • ERR:DOMAIN if the equation # is not a valid equation number in this mode, or if style # is not an integer 1-7.
                                                                                                                                        • ERR:INVALID if the graphing style chosen is not valid for the current graphing mode.

                                                                                                                                        Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, kg583.

                                                                                                                                        History

                                                                                                                                        Calculator OS Version Description
                                                                                                                                        TI-83 0.01013 Added
                                                                                                                                        Property Value
                                                                                                                                        Hex Value $7E0A
                                                                                                                                        Categories
                                                                                                                                          Localizations
                                                                                                                                          • FR: GridDot

                                                                                                                                          GridDot

                                                                                                                                          Overview

                                                                                                                                          Turns on grid dots in the graph area in the specified color.
                                                                                                                                          Color#: 10 - 24 or color name pasted from [vars] COLOR.

                                                                                                                                          Availability: Token only available from within the Basic editor.

                                                                                                                                          Syntax

                                                                                                                                          GridDot [color#]

                                                                                                                                          Arguments

                                                                                                                                          NameTypeOptional
                                                                                                                                          color#colorNumYes

                                                                                                                                          Location

                                                                                                                                          2nd, format, GridDot

                                                                                                                                          Description

                                                                                                                                          Examples

                                                                                                                                          Explanation 1

                                                                                                                                          code 1

                                                                                                                                          Explanation 2

                                                                                                                                          code 2

                                                                                                                                          Error Conditions

                                                                                                                                          Advanced Notes

                                                                                                                                          History

                                                                                                                                          Calculator OS Version Description
                                                                                                                                          TI-82 1.0 GridOn added
                                                                                                                                          TI-84+CSE 4.0 Renamed GridOn to GridDot
                                                                                                                                          Property Value
                                                                                                                                          Hex Value $EF5A
                                                                                                                                          Categories
                                                                                                                                            Localizations
                                                                                                                                            • FR: LigneAff

                                                                                                                                            GridLine

                                                                                                                                            Overview

                                                                                                                                            Turns on grid lines in the graph area in the specified color.
                                                                                                                                            Color#: 10 - 24 or color name pasted from [vars] COLOR.

                                                                                                                                            Availability: Token only available from within the Basic editor.

                                                                                                                                            Syntax

                                                                                                                                            GridLine [color#]

                                                                                                                                            Arguments

                                                                                                                                            NameTypeOptional
                                                                                                                                            color#colorNumYes

                                                                                                                                            Location

                                                                                                                                            2nd, format, GridLine

                                                                                                                                            Description

                                                                                                                                            Examples

                                                                                                                                            Explanation 1

                                                                                                                                            code 1

                                                                                                                                            Explanation 2

                                                                                                                                            code 2

                                                                                                                                            Error Conditions

                                                                                                                                            Advanced Notes

                                                                                                                                            History

                                                                                                                                            Calculator OS Version Description
                                                                                                                                            TI-84+CSE 4.0 Added
                                                                                                                                            Property Value
                                                                                                                                            Hex Value $7E0B
                                                                                                                                            Categories
                                                                                                                                            Localizations
                                                                                                                                            • FR: QuadNAff

                                                                                                                                            GridOff

                                                                                                                                            Overview

                                                                                                                                            Turns off grid format.

                                                                                                                                            Availability: Token only available from within the Basic editor.

                                                                                                                                            Syntax

                                                                                                                                            GridOff

                                                                                                                                            Location

                                                                                                                                            2nd, format, GridOff

                                                                                                                                            Description

                                                                                                                                            The GridOff command disables the grid on the graph screen. This is the default setting. Use GridOn to enable the grid.

                                                                                                                                            Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, kg583.

                                                                                                                                            History

                                                                                                                                            Calculator OS Version Description
                                                                                                                                            TI-82 1.0 Added
                                                                                                                                            Property Value
                                                                                                                                            Hex Value $48
                                                                                                                                            Categories
                                                                                                                                            Localizations
                                                                                                                                            • FR: H
                                                                                                                                            H

                                                                                                                                            Overview

                                                                                                                                            Availability: Token available everywhere.

                                                                                                                                            Syntax

                                                                                                                                            H

                                                                                                                                            Description

                                                                                                                                            Examples

                                                                                                                                            Explanation 1

                                                                                                                                            code 1

                                                                                                                                            Explanation 2

                                                                                                                                            code 2

                                                                                                                                            Error Conditions

                                                                                                                                            Advanced Notes

                                                                                                                                            History

                                                                                                                                            Calculator OS Version Description
                                                                                                                                            TI-82 1.0 Added
                                                                                                                                            Property Value
                                                                                                                                            Hex Value $FC
                                                                                                                                            Categories
                                                                                                                                            Localizations
                                                                                                                                            • FR: Histogramme

                                                                                                                                            Histogram

                                                                                                                                            Overview

                                                                                                                                            Used as the "type" argument in the command
                                                                                                                                            Where # gives Plot1, Plot2 or Plot3.

                                                                                                                                            Availability: Token only available from within the Basic editor.

                                                                                                                                            Syntax

                                                                                                                                            Plot#(type,Xlist[,freqlist,color#])

                                                                                                                                            Arguments

                                                                                                                                            NameTypeOptional
                                                                                                                                            typeHistogram token
                                                                                                                                            Xlistlist
                                                                                                                                            freqlistlist
                                                                                                                                            color#colorNum

                                                                                                                                            Location

                                                                                                                                            2nd, stat plot, TYPE

                                                                                                                                            Description

                                                                                                                                            The commands Plot1(, Plot2(, and Plot3(, which are identical except for which stat plot (1, 2, or 3) they affect, define their corresponding stat plot. When the stat plot is defined, it is also turned on so no PlotsOn command is necessary.

                                                                                                                                            The first argument of the commands is always the type of plot, and is one of Scatter, xyLine, Histogram, Boxplot, ModBoxplot, and NormProbPlot - these types are found in the TYPE submenu of the stat plot menu. The other arguments vary. For all but Histogram and Boxplot, there is a mark argument - this is a dot, a cross, or a box, symbols that can be found in the MARK submenu of the stat plot menu. On color calculators, there is an optional final argument to specify the color of the plot.

                                                                                                                                            Scatter plot

                                                                                                                                            Plot#(Scatter, x-list, y-list, mark) defines a scatter plot. The points defined by x-list and y-list are plotted using mark on the graph screen.

                                                                                                                                            x-list and y-list must be the same length.

                                                                                                                                            xyLine plot

                                                                                                                                            Plot#(xyLine, x-list, y-list, mark) defines an xyLine plot. Similarly to a scatter plot, the points defined by x-list and y-list are plotted using mark on the graph screen, but with an xyLine plot they are also connected by a line, in the order that they occur in the lists.

                                                                                                                                            x-list and y-list must be the same length.

                                                                                                                                            Histogram plot

                                                                                                                                            Plot#(Histogram, x-list, freq list) defines a Histogram plot. The x-axis is divided into intervals that are Xscl wide. A bar is drawn in in each interval whose height corresponds to the number of points in the interval. Points that are not between Xmin and Xmax are not tallied.

                                                                                                                                            Xscl must not be too small - it can divide the screen into no more than 47 different bars.

                                                                                                                                            Box plot

                                                                                                                                            Plot#(Boxplot, x-list, freq list) defines a box plot. A rectangular box is drawn whose left edge is Q1 (the first quartile) of the data, and whose right edge is Q3 (the third quartile). A vertical segment is drawn within the box at the median, and 'whiskers' are drawn from the box to the minimum and maximum data points.

                                                                                                                                            The box plot ignores the Ymax and Ymin dimensions of the screen, and any plots that aren't box plots or modified box plots. Each box plot takes approximately 1/3 of the screen in height, and if more than one are plotted, they will take up different areas of the screen.

                                                                                                                                            Modified box plot

                                                                                                                                            Plot#(ModBoxplot, x-list, freq list, mark) defines a modified box plot. This is almost entirely like the normal box plot, except that it also draws outliers. Whiskers are only drawn to the furthers point within 1.5 times the interquartile range (Q3-Q1) of the box. Beyond this point, data points are drawn individually, using mark.

                                                                                                                                            The box plot ignores the Ymax and Ymin dimensions of the screen, and any plots that aren't box plots or modified box plots. Each box plot takes approximately 1/3 of the screen in height, and if more than one are plotted, they will take up different areas of the screen.

                                                                                                                                            Normal probability plot

                                                                                                                                            Plot#(NormProbPlot, data list, data axis, mark) defines a normal probability plot. The mean and standard deviation of the data are calculated. Then for each point, the number of standard deviations it is from the mean is calculated, and the point is plotted against this number using mark. data axis can be either X or Y: it determines whether the value of a point determines it's x-coordinate or y-coordinate.

                                                                                                                                            The point behind this rather convoluted process is to test the extent to which the data is normally distributed. If it follows the normal distribution closely, then the result will be close to a straight line - otherwise it will be curved.

                                                                                                                                            Advanced Uses

                                                                                                                                            After doing a regression, a scatter plot of ʟRESID against the x-list is a useful measure of the effectiveness of the regression. If the plot appears random, this is a good sign; if there is a pattern to the plot, this means it's likely that a better regression model exists.

                                                                                                                                            Optimization

                                                                                                                                            The ʟ symbol at the beginning of list names can be omitted everywhere in this command.

                                                                                                                                            In addition, every element except the plot type and the data list or data lists are optional, and take on the following default values:

                                                                                                                                            • freq list is 1 by default, meaning that all frequencies are 1.
                                                                                                                                            • mark is the box by default.
                                                                                                                                            • data axis is X by default.

                                                                                                                                            Error Conditions

                                                                                                                                            • ERR:DIM MISMATCH is thrown if the x and y lists, or the data and frequency lists, have different dimensions.
                                                                                                                                            • ERR:STAT is thrown if Xscl is too small in the case of a Histogram.

                                                                                                                                            All errors are thrown when plotting the stat plot, as opposed to when the command is executed, and do not provide a 2:Goto option.

                                                                                                                                            Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Myles_Zadok.

                                                                                                                                            History

                                                                                                                                            Calculator OS Version Description
                                                                                                                                            TI-82 1.0 Added
                                                                                                                                            Property Value
                                                                                                                                            Hex Value $74
                                                                                                                                            Categories
                                                                                                                                            Localizations
                                                                                                                                            • FR: Horiz

                                                                                                                                            Horiz

                                                                                                                                            Overview

                                                                                                                                            Sets horizontal split-screen mode.

                                                                                                                                            Availability: Token only available from within the Basic editor.

                                                                                                                                            Syntax

                                                                                                                                            Horiz

                                                                                                                                            Location

                                                                                                                                            mode, Horiz

                                                                                                                                            Description

                                                                                                                                            Horiz is usually at the beginning of a program. It is used at the beginning to ensure that the screen mode is Horiz, for programs such as Hangman that want to use Input but also have the graph screen shown. Note that if you use pixels, the y-coordinate can be no larger than 30, since that is the maximum pixel's range.

                                                                                                                                            :Horiz

                                                                                                                                            Source: parts of this page were written by the following TI|BD contributors: alexrudd, Battlesquid, burr, DarkerLine, GoVegan, kg583, Xphoenix.

                                                                                                                                            History

                                                                                                                                            Calculator OS Version Description
                                                                                                                                            TI-82 1.0 Added
                                                                                                                                            Property Value
                                                                                                                                            Hex Value $A6
                                                                                                                                            Categories
                                                                                                                                            Localizations
                                                                                                                                            • FR: Horizontale

                                                                                                                                            Horizontal

                                                                                                                                            Overview

                                                                                                                                            Draws a horizontal line at y in a specified
                                                                                                                                            Color#: 10 - 24 or color name pasted from [vars] COLOR.
                                                                                                                                            line style #: 1-4.

                                                                                                                                            Availability: Token available everywhere.

                                                                                                                                            Syntax

                                                                                                                                            Horizontal y[,color#,linestyle#]

                                                                                                                                            Arguments

                                                                                                                                            NameTypeOptional
                                                                                                                                            y
                                                                                                                                            color#colorNumYes
                                                                                                                                            linestyle#integerYes

                                                                                                                                            Location

                                                                                                                                            2nd, draw, DRAW, 3:Horizontal

                                                                                                                                            Description

                                                                                                                                            Horizontal Y draws a vertical line from the left of the graph screen to the right at Y. Horizontal is usually only used to replace a line that stretches the entire length of the graph screen, along with its counterpart Vertical.

                                                                                                                                            Horizontal is affected by the window settings, unlike the Pxl- commands.

                                                                                                                                            :Horizontal 5

                                                                                                                                            Advanced Uses

                                                                                                                                            One of the fastest ways to make the entire screen black is by drawing horizontal lines from the bottom of the screen to the top.

                                                                                                                                            :For(A,Ymin,Ymax,ΔY
:Horizontal A
:End

                                                                                                                                            If working with TI 84+C version calculators, the Horizontal command takes an additional color argument, as shown below:

                                                                                                                                            Horizontal 5,GRAY

                                                                                                                                            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583, Xphoenix.

                                                                                                                                            History

                                                                                                                                            Calculator OS Version Description
                                                                                                                                            TI-82 1.0 Added
                                                                                                                                            Property Value
                                                                                                                                            Hex Value $632C
                                                                                                                                            Categories
                                                                                                                                            Localizations
                                                                                                                                            • FR: I%

                                                                                                                                            I%

                                                                                                                                            Overview

                                                                                                                                            Syntax

                                                                                                                                            I%

                                                                                                                                            Description

                                                                                                                                            Examples

                                                                                                                                            Explanation 1

                                                                                                                                            code 1

                                                                                                                                            Explanation 2

                                                                                                                                            code 2

                                                                                                                                            Error Conditions

                                                                                                                                            Advanced Notes

                                                                                                                                            History

                                                                                                                                            Calculator OS Version Description
                                                                                                                                            TI-83 0.01013 Added
                                                                                                                                            Property Value
                                                                                                                                            Hex Value $49
                                                                                                                                            Categories
                                                                                                                                            Localizations
                                                                                                                                            • FR: I

                                                                                                                                            I

                                                                                                                                            Overview

                                                                                                                                            Availability: Token available everywhere.

                                                                                                                                            Syntax

                                                                                                                                            I

                                                                                                                                            Description

                                                                                                                                            Examples

                                                                                                                                            Explanation 1

                                                                                                                                            code 1

                                                                                                                                            Explanation 2

                                                                                                                                            code 2

                                                                                                                                            Error Conditions

                                                                                                                                            Advanced Notes

                                                                                                                                            History

                                                                                                                                            Calculator OS Version Description
                                                                                                                                            TI-82 1.0 Added
                                                                                                                                            Property Value
                                                                                                                                            Hex Value $DA
                                                                                                                                            Categories
                                                                                                                                            Localizations
                                                                                                                                            • FR: IS>(

                                                                                                                                            IS>(

                                                                                                                                            Overview

                                                                                                                                            Increments variable by 1; skips commandA if variable>value.

                                                                                                                                            Comment::commandA,:commands

                                                                                                                                            Availability: Token only available from within the Basic editor.

                                                                                                                                            Syntax

                                                                                                                                            :IS>(variable,value) :commandA:commands

                                                                                                                                            Arguments

                                                                                                                                            NameTypeOptional
                                                                                                                                            variable
                                                                                                                                            value
                                                                                                                                            commandA
                                                                                                                                            commands

                                                                                                                                            Location

                                                                                                                                            prgm, CTL, A:IS>(

                                                                                                                                            Description

                                                                                                                                            The increment and skip if greater than command — IS>( — is a specialized conditional command. It is equivalent to an If conditional, except the next command will be skipped when the condition is true and it has a variable update built-in. However, it is not used very often (if anything, it is often misused as a looping command) because of its obscure name and somewhat limited application.

                                                                                                                                            The IS>( command takes two arguments:

                                                                                                                                            • A variable, which is limited only to one of the real variables (A-Z or θ).
                                                                                                                                            • A value, which can be any expression which evaluates to a real number.

                                                                                                                                            When IS>( is executed it adds one to the variable (increments it by one), and compares it to the value. The next command will be skipped if the variable is greater than the value, while the next command will be executed if the variable is less than or equal to the value.

                                                                                                                                            The command IS>(A,B is equivalent to the following code:

                                                                                                                                            :A+1→A
:If A≤B

                                                                                                                                            Here are the two main cases where the IS>( command is used:

                                                                                                                                            :7→A
:IS>(A,6
:Disp "Skipped
                                                                                                                                            • Initializes A to 7 and then compares to the value
                                                                                                                                            • 7>6 is true so the display message won't be displayed
                                                                                                                                            :1→B
:IS>(B,2
:Disp "Not Skipped
                                                                                                                                            • Initializes B to 1 and then compares to the value
                                                                                                                                            • 1>2 is false so the display message will be displayed

                                                                                                                                            Note: In addition to both of these cases, there is also the case where the variable and the value are equal to each other. This case is shown below under the 'Advanced Uses' section because it has some added background that goes with it.

                                                                                                                                            Advanced Uses

                                                                                                                                            When you want the skipping feature of the IS>( command to always occur, you just have to use the same variable for both the variable and value arguments of the command:

                                                                                                                                            :IS>(B,B

                                                                                                                                            An undefined error will occur if the variable and/or value doesn't exist before the IS>( command is used, which happens when the DelVar command is used. Consequently, you should not use DelVar with IS>(.

                                                                                                                                            Similar code can be used as a substitute for B+1→B if you don't want to change Ans:

                                                                                                                                            :IS>(B,B:

                                                                                                                                            Note that due to the colon after the line, there will be no statement skipped, so you don't have to worry about that.

                                                                                                                                            Optimization

                                                                                                                                            Because the IS>( command has the variable update built-in, it is smaller than manually incrementing a variable by one along with using an If conditional.

                                                                                                                                            :A+1→A
can be
:IS>(A,0

                                                                                                                                            The one caution about this is that if the variable is greater than the value (in this case, '0'), the next command will be skipped. If you don't want the skipping functionality, then you need to make sure that the value is never less than the variable. This is not always possible to do. Also, IS>( is slightly slower than its more normal counterpart.

                                                                                                                                            Related to the example code given, IS>( should always have a command following after it (i.e., it's not the last command in a program) because it will return an error otherwise. If you have no particular code choice, just put an empty line or something meaningless.

                                                                                                                                            Command Timings

                                                                                                                                            Using IS>( to increment a variable is approximately 25% slower than using code like X+1→X. However, it is faster to use IS>( than to construct an If statement to do the same thing.

                                                                                                                                            Note, however, that a quirk in the For( command (see its Optimizations section) will slow down the IS>( command significantly if a closing parenthesis is not used for the For( statement.

                                                                                                                                            Error Conditions

                                                                                                                                            • ERR:INVALID occurs if this statement is used outside a program.
                                                                                                                                            • ERR:UNDEFINED is thrown if the variable to be incremented is not defined.
                                                                                                                                            • ERR:SYNTAX is thrown if there is no next line to skip, or if there is only one next line and it is empty.

                                                                                                                                            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583.

                                                                                                                                            History

                                                                                                                                            Calculator OS Version Description
                                                                                                                                            TI-82 1.0 Added
                                                                                                                                            Property Value
                                                                                                                                            Hex Value $CE
                                                                                                                                            Categories
                                                                                                                                            Localizations
                                                                                                                                            • FR: If

                                                                                                                                            If

                                                                                                                                            Overview

                                                                                                                                            If condition = 0 (false), skips commandA.

                                                                                                                                            Availability: Token only available from within the Basic editor.

                                                                                                                                            Syntax

                                                                                                                                            If condition:commandA:commands

                                                                                                                                            Arguments

                                                                                                                                            NameTypeOptional
                                                                                                                                            condition
                                                                                                                                            commandA
                                                                                                                                            commands

                                                                                                                                            Location

                                                                                                                                            prgm, CTL, 1:If

                                                                                                                                            If Then End

                                                                                                                                            Overview

                                                                                                                                            Executes commands from Then to End if condition = 1 (true).

                                                                                                                                            Availability: Token only available from within the Basic editor.

                                                                                                                                            Syntax

                                                                                                                                            If:conditionThen:commandsEnd:commands

                                                                                                                                            Arguments

                                                                                                                                            NameTypeOptional
                                                                                                                                            :
                                                                                                                                            condition
                                                                                                                                            commands
                                                                                                                                            commands

                                                                                                                                            Location

                                                                                                                                            prgm, CTL, 2:Then

                                                                                                                                            If Then Else End

                                                                                                                                            Overview

                                                                                                                                            Executes commands from Then to Else if condition = 1 (true); from Else to End if condition = 0 (false).

                                                                                                                                            Availability: Token only available from within the Basic editor.

                                                                                                                                            Syntax

                                                                                                                                            If:conditionThen:commandsElse:commandsEnd:commands

                                                                                                                                            Arguments

                                                                                                                                            NameTypeOptional
                                                                                                                                            condition
                                                                                                                                            commands
                                                                                                                                            commands
                                                                                                                                            commands

                                                                                                                                            Location

                                                                                                                                            prgm, CTL, 3:Else

                                                                                                                                            Description

                                                                                                                                            The If command is crucial to most programs. It allows you to execute code if and only if an expression is not equal to zero. Advanced uses of the If command allow you to execute a different block of code if the check turns out to be false. The simplest form of the command is quite easy to understand:

                                                                                                                                            :If (condition)
:statement

                                                                                                                                            When the calculator gets to that point in your program, it will check to see if the condition is nonzero. Most expressions you will use with If are called conditional expressions; that is, they return 1 if the condition is true and 0 if it is false. Examples include 2+2=4, A=5, and pxl-Test(R,C). Therefore, when the condition is true, the expression evaluates to 1 and the statement is run. When the condition is false, the expression evaluates to 0, and the statement is skipped.

                                                                                                                                            Using Then, Else, and End

                                                                                                                                            When you want more than one line of code to depend on the same condition, use an If-Then block.

                                                                                                                                            :If (condition)
:Then
code to execute if true
:End

                                                                                                                                            An If-Then block also has an optional Else clause, which is used to execute different code when the condition is false.

                                                                                                                                            :If (condition)
:Then
code to execute if true
:Else
code to execute if false
:End

                                                                                                                                            Advanced Uses

                                                                                                                                            If statements can execute and skip other If statements. This leads to odd yet effective constructs like these:

                                                                                                                                            :If A
:If B
//Executes if A is false or B is true

                                                                                                                                            If A:Then
//Executes if A is true
If B:Else
//Executes if A is false or B is false
End

                                                                                                                                            Memory Leaks

                                                                                                                                            Each time the program enters an If-Then block, the calculator uses 35+(size of the condition) bytes of memory to keep track of the block. This memory is given back to you as soon as the program reaches an End statement. This isn't really a problem unless you're low on RAM, or have a lot of nested If-Then statements. However, if you use Goto to jump out of such a statement, you lose those bytes for as long as the program is running — and if you keep doing this, you might easily run out of memory, resulting in ERR:MEMORY.

                                                                                                                                            Optimization

                                                                                                                                            As far as the TI-BASIC interpreter is concerned, a value of 0 is false, and any other value is true. We can use a numerical expression rather than a conditional one in the condition of the If statement in a case like the following:

                                                                                                                                            :If A≠0
:Disp "A IS NOT 0

can be
:If A
:Disp "A IS NOT 0

                                                                                                                                            When code in a single-line If statement simply changes a variable, it can often be replaced with an equivalent piecewise expression, which will be smaller and faster.

                                                                                                                                            :If A=B
:C+2→C

can be
:C+2(A=B→C

                                                                                                                                            Code Timings

                                                                                                                                            Single-line If statements are greatly slowed when they are the first line in For( loops without a closing parenthesis. For example,

                                                                                                                                            Very slow
:For(I,1,2000
:If 0:
:End

19 times faster (!)
:For(I,1,2000)
:If 0:
:End

                                                                                                                                            Error Conditions

                                                                                                                                            • ERR:DATA TYPE occurs if the parameter is complex, even if it's complex in a silly way like 0i.
                                                                                                                                            • ERR:INVALID occurs if this statement is used outside a program.
                                                                                                                                            • ERR:SYNTAX occurs if an If is the last statement in the program, or the last except for one empty line.

                                                                                                                                            Source: parts of this page were written by the following TI|BD contributors: burr, CloudVariable, DarkerLine, GoVegan, kg583, lirtosiast, Trenly.

                                                                                                                                            History

                                                                                                                                            Calculator OS Version Description
                                                                                                                                            TI-82 1.0 Added
                                                                                                                                            Property Value
                                                                                                                                            Hex Value $EF59
                                                                                                                                            Categories
                                                                                                                                            Localizations
                                                                                                                                            • FR: Image0

                                                                                                                                            Image0

                                                                                                                                            Overview

                                                                                                                                            Availability: Token available everywhere.

                                                                                                                                            Syntax

                                                                                                                                            Image0

                                                                                                                                            Description

                                                                                                                                            Examples

                                                                                                                                            Explanation 1

                                                                                                                                            code 1

                                                                                                                                            Explanation 2

                                                                                                                                            code 2

                                                                                                                                            Error Conditions

                                                                                                                                            Advanced Notes

                                                                                                                                            History

                                                                                                                                            Calculator OS Version Description
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                                                                                                                                            Hex Value $EF50
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                                                                                                                                            • FR: Image1

                                                                                                                                            Image1

                                                                                                                                            Overview

                                                                                                                                            Availability: Token available everywhere.

                                                                                                                                            Syntax

                                                                                                                                            Image1

                                                                                                                                            Description

                                                                                                                                            Examples

                                                                                                                                            Explanation 1

                                                                                                                                            code 1

                                                                                                                                            Explanation 2

                                                                                                                                            code 2

                                                                                                                                            Error Conditions

                                                                                                                                            Advanced Notes

                                                                                                                                            History

                                                                                                                                            Calculator OS Version Description
                                                                                                                                            TI-84+CSE 4.0 Added
                                                                                                                                            Property Value
                                                                                                                                            Hex Value $EF51
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                                                                                                                                            • FR: Image2

                                                                                                                                            Image2

                                                                                                                                            Overview

                                                                                                                                            Availability: Token available everywhere.

                                                                                                                                            Syntax

                                                                                                                                            Image2

                                                                                                                                            Description

                                                                                                                                            Examples

                                                                                                                                            Explanation 1

                                                                                                                                            code 1

                                                                                                                                            Explanation 2

                                                                                                                                            code 2

                                                                                                                                            Error Conditions

                                                                                                                                            Advanced Notes

                                                                                                                                            History

                                                                                                                                            Calculator OS Version Description
                                                                                                                                            TI-84+CSE 4.0 Added
                                                                                                                                            Property Value
                                                                                                                                            Hex Value $EF52
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                                                                                                                                            • FR: Image3

                                                                                                                                            Image3

                                                                                                                                            Overview

                                                                                                                                            Availability: Token available everywhere.

                                                                                                                                            Syntax

                                                                                                                                            Image3

                                                                                                                                            Description

                                                                                                                                            Examples

                                                                                                                                            Explanation 1

                                                                                                                                            code 1

                                                                                                                                            Explanation 2

                                                                                                                                            code 2

                                                                                                                                            Error Conditions

                                                                                                                                            Advanced Notes

                                                                                                                                            History

                                                                                                                                            Calculator OS Version Description
                                                                                                                                            TI-84+CSE 4.0 Added
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                                                                                                                                            Hex Value $EF53
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                                                                                                                                            • FR: Image4

                                                                                                                                            Image4

                                                                                                                                            Overview

                                                                                                                                            Availability: Token available everywhere.

                                                                                                                                            Syntax

                                                                                                                                            Image4

                                                                                                                                            Description

                                                                                                                                            Examples

                                                                                                                                            Explanation 1

                                                                                                                                            code 1

                                                                                                                                            Explanation 2

                                                                                                                                            code 2

                                                                                                                                            Error Conditions

                                                                                                                                            Advanced Notes

                                                                                                                                            History

                                                                                                                                            Calculator OS Version Description
                                                                                                                                            TI-84+CSE 4.0 Added
                                                                                                                                            Property Value
                                                                                                                                            Hex Value $EF54
                                                                                                                                            Categories
                                                                                                                                            Localizations
                                                                                                                                            • FR: Image5

                                                                                                                                            Image5

                                                                                                                                            Overview

                                                                                                                                            Availability: Token available everywhere.

                                                                                                                                            Syntax

                                                                                                                                            Image5

                                                                                                                                            Description

                                                                                                                                            Examples

                                                                                                                                            Explanation 1

                                                                                                                                            code 1

                                                                                                                                            Explanation 2

                                                                                                                                            code 2

                                                                                                                                            Error Conditions

                                                                                                                                            Advanced Notes

                                                                                                                                            History

                                                                                                                                            Calculator OS Version Description
                                                                                                                                            TI-84+CSE 4.0 Added
                                                                                                                                            Property Value
                                                                                                                                            Hex Value $EF55
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                                                                                                                                            • FR: Image6

                                                                                                                                            Image6

                                                                                                                                            Overview

                                                                                                                                            Availability: Token available everywhere.

                                                                                                                                            Syntax

                                                                                                                                            Image6

                                                                                                                                            Description

                                                                                                                                            Examples

                                                                                                                                            Explanation 1

                                                                                                                                            code 1

                                                                                                                                            Explanation 2

                                                                                                                                            code 2

                                                                                                                                            Error Conditions

                                                                                                                                            Advanced Notes

                                                                                                                                            History

                                                                                                                                            Calculator OS Version Description
                                                                                                                                            TI-84+CSE 4.0 Added
                                                                                                                                            Property Value
                                                                                                                                            Hex Value $EF56
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                                                                                                                                            • FR: Image7

                                                                                                                                            Image7

                                                                                                                                            Overview

                                                                                                                                            Availability: Token available everywhere.

                                                                                                                                            Syntax

                                                                                                                                            Image7

                                                                                                                                            Description

                                                                                                                                            Examples

                                                                                                                                            Explanation 1

                                                                                                                                            code 1

                                                                                                                                            Explanation 2

                                                                                                                                            code 2

                                                                                                                                            Error Conditions

                                                                                                                                            Advanced Notes

                                                                                                                                            History

                                                                                                                                            Calculator OS Version Description
                                                                                                                                            TI-84+CSE 4.0 Added
                                                                                                                                            Property Value
                                                                                                                                            Hex Value $EF57
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                                                                                                                                            • FR: Image8

                                                                                                                                            Image8

                                                                                                                                            Overview

                                                                                                                                            Availability: Token available everywhere.

                                                                                                                                            Syntax

                                                                                                                                            Image8

                                                                                                                                            Description

                                                                                                                                            Examples

                                                                                                                                            Explanation 1

                                                                                                                                            code 1

                                                                                                                                            Explanation 2

                                                                                                                                            code 2

                                                                                                                                            Error Conditions

                                                                                                                                            Advanced Notes

                                                                                                                                            History

                                                                                                                                            Calculator OS Version Description
                                                                                                                                            TI-84+CSE 4.0 Added
                                                                                                                                            Property Value
                                                                                                                                            Hex Value $EF58
                                                                                                                                            Categories
                                                                                                                                            Localizations
                                                                                                                                            • FR: Image9

                                                                                                                                            Image9

                                                                                                                                            Overview

                                                                                                                                            Availability: Token available everywhere.

                                                                                                                                            Syntax

                                                                                                                                            Image9

                                                                                                                                            Description

                                                                                                                                            Examples

                                                                                                                                            Explanation 1

                                                                                                                                            code 1

                                                                                                                                            Explanation 2

                                                                                                                                            code 2

                                                                                                                                            Error Conditions

                                                                                                                                            Advanced Notes

                                                                                                                                            History

                                                                                                                                            Calculator OS Version Description
                                                                                                                                            TI-84+CSE 4.0 Added
                                                                                                                                            Property Value
                                                                                                                                            Hex Value $7B
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                                                                                                                                            • FR: ValeursDem

                                                                                                                                            IndpntAsk

                                                                                                                                            Overview

                                                                                                                                            Sets table to ask for independent-variable values.

                                                                                                                                            Availability: Token only available from within the Basic editor.

                                                                                                                                            Syntax

                                                                                                                                            IndpntAsk

                                                                                                                                            Location

                                                                                                                                            2nd, tblset, Indpnt: Ask

                                                                                                                                            Description

                                                                                                                                            With the IndpntAsk setting, the independent variable (X, T, θ, or n depending on graphing mode) will not be calculated automatically in the table. Instead, when looking at the table, you must select an entry in the independent variable column, press ENTER, and enter a value. The values entered will also be stored to the TblInput list.

                                                                                                                                            (To access the table, press [2ND][TABLE], or use the DispTable command in a program)

                                                                                                                                            The alternative, IndpntAuto, fills in several values starting at TblStart and increasing by ΔTbl, and makes the table scrollable (up and down).

                                                                                                                                            Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, kg583.

                                                                                                                                            History

                                                                                                                                            Calculator OS Version Description
                                                                                                                                            TI-82 1.0 Added
                                                                                                                                            Property Value
                                                                                                                                            Hex Value $7A
                                                                                                                                            Categories
                                                                                                                                            Localizations
                                                                                                                                            • FR: ValeursAuto

                                                                                                                                            IndpntAuto

                                                                                                                                            Overview

                                                                                                                                            Sets table to generate independent-variable values automatically.

                                                                                                                                            Availability: Token only available from within the Basic editor.

                                                                                                                                            Syntax

                                                                                                                                            IndpntAuto

                                                                                                                                            Location

                                                                                                                                            2nd, tblset, Indpnt: Auto

                                                                                                                                            Description

                                                                                                                                            The IndpntAuto setting sets the independent variable (X, T, θ, or n depending on graphing mode) to be filled in automatically in the table (which is accessible by pressing 2nd TABLE, or from a program with the DispTable command).

                                                                                                                                            The values which will be filled in start at the value TblStart and increment by ΔTbl(which can be negative, but not 0). They will also be stored in the list TblInput. All these variables can be accessed through the VARS|6:Table… menu; TblStart and ΔTbl can also be edited in the [2ND][TBLSET] menu.

                                                                                                                                            The other possibility for this setting is IndpntAsk - if that setting is turned on, you must scroll to the corresponding row in the independent variable column, and enter a value.

                                                                                                                                            Error Conditions

                                                                                                                                            Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, kg583.

                                                                                                                                            History

                                                                                                                                            Calculator OS Version Description
                                                                                                                                            TI-82 1.0 Added
                                                                                                                                            Property Value
                                                                                                                                            Hex Value $DC
                                                                                                                                            Categories
                                                                                                                                            Localizations
                                                                                                                                            • FR: Input

                                                                                                                                            Input

                                                                                                                                            Overview

                                                                                                                                            Displays graph.

                                                                                                                                            Availability: Token only available from within the Basic editor.

                                                                                                                                            Syntax

                                                                                                                                            Input

                                                                                                                                            Location

                                                                                                                                            prgm, I/O, 2:Input

                                                                                                                                            Overview

                                                                                                                                            Prompts for value to store to variable.

                                                                                                                                            Availability: Token only available from within the Basic editor.

                                                                                                                                            Syntax

                                                                                                                                            Input [variable]

                                                                                                                                            Arguments

                                                                                                                                            NameTypeOptional
                                                                                                                                            variableYes

                                                                                                                                            Location

                                                                                                                                            prgm, I/O, 2:Input

                                                                                                                                            Overview

                                                                                                                                            Prompts for value to store to variable.

                                                                                                                                            Availability: Token only available from within the Basic editor.

                                                                                                                                            Syntax

                                                                                                                                            Input ["text",variable]

                                                                                                                                            Arguments

                                                                                                                                            NameTypeOptional
                                                                                                                                            textstringYes
                                                                                                                                            variableYes

                                                                                                                                            Location

                                                                                                                                            prgm, I/O, 2:Input

                                                                                                                                            Overview

                                                                                                                                            Displays Strn and stores entered value to variable.

                                                                                                                                            Availability: Token only available from within the Basic editor.

                                                                                                                                            Syntax

                                                                                                                                            Input [Strn,variable]

                                                                                                                                            Arguments

                                                                                                                                            NameTypeOptional
                                                                                                                                            nYes
                                                                                                                                            variableYes

                                                                                                                                            Location

                                                                                                                                            prgm, I/O, 2:Input

                                                                                                                                            Description

                                                                                                                                            The Input command is the other way of getting user input on the home screen (getting user input on the graph screen is only possible with the getKey command). The Input command asks the user to enter a value for a variable (only one variable can be inputted at a time), waiting until the user enters a value and then presses ENTER. It does not display what variable the user is being asked for, but instead just displays a question mark (?).

                                                                                                                                            Because just displaying a question mark on the screen does not really tell the user what to enter for input or what the input will be used for, the Input command has an optional text message that can be either text or a string variable that will be displayed alongside the input.

                                                                                                                                            Only the first sixteen characters of the text message will be shown on the screen (because of the screen dimensions), so the text message should be kept as short as possible (a good goal is twelve characters or less). This is so the value the user inputs can fit on the same line as the text. In the case that the value is too long, it will wrap around to the next line.

                                                                                                                                            PROGRAM:INPUT
:"Fruit
:Input "Best "+Ans,Str1
:Input "Worst "+Ans,Str2
:Disp "That's "+Ans+"astic!

                                                                                                                                            Input can be used to display every variable just before it requests user input, but some of the variables have to be entered in a certain way. If the variable is a string or a Y= function, the user must put quotes ("") around the value or expression. The user must also put curly braces ({}) around lists with the list elements separated by commas, and square brackets ([]) around matrices with the matrix elements separated by commas and each row individually wrapped with square brackets.

                                                                                                                                            Advanced Uses

                                                                                                                                            When you just use the Input command by itself (without any arguments), the graph screen will be shown and the user can move the cursor around. Program execution will then pause until the user presses ENTER, at which time the coordinates of the cursor will be stored to the respective variables (R and θ for PolarGC format, otherwise X and Y).

                                                                                                                                            If a text message is longer than twelve characters or you want to give the user plenty of space to enter a value, you can put a Disp command before the Input command. You break the text message up and display it in parts. The Input command will be displayed one line lower, though, because the Disp command automatically creates a new line.

                                                                                                                                            :Disp "What is your"
:Input "Name",Str0

                                                                                                                                            Normally you can't get a quote character into a string (because quotes are used to identify the beginning and end of the string), but the Input command actually allows the user to enter a quote character (") as part of a string. This works without problems, and the quote can even be accessed by the user afterwards.

                                                                                                                                            Because a user-defined list variable doesn't need the ʟ prefixed character before it when referring to the list, you may be only asking the user to input a simple real variable but a list would also be allowed. There is nothing you can really do about this problem, except including the ʟ prefixed character when wanting a list inputted and trying to limit your use of Input and Prompt.

                                                                                                                                            :Input A
should be
:Input ʟA

                                                                                                                                            Optimizations

                                                                                                                                            When you are just using the text message to tell the user what the variable being stored to is, you should use the Prompt command instead. And, if there is a list of Input commands following the same pattern, you can reduce them to just one Prompt command.

                                                                                                                                            :Input "A",A
:Input "B",B
Replace with Prompt
:Prompt A,B

                                                                                                                                            Error Conditions

                                                                                                                                            • ERR:INVALID occurs if this statement is used outside a program.

                                                                                                                                            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583.

                                                                                                                                            History

                                                                                                                                            Calculator OS Version Description
                                                                                                                                            TI-82 1.0 Added
                                                                                                                                            Property Value
                                                                                                                                            Hex Value $EFA4
                                                                                                                                            Categories
                                                                                                                                            Localizations
                                                                                                                                            • FR: Insérer commentaire ↑

                                                                                                                                            Insert Comment Above

                                                                                                                                            Overview

                                                                                                                                            Comment:CE OS 5.3+

                                                                                                                                            Syntax

                                                                                                                                            Insert Comment Above

                                                                                                                                            Description

                                                                                                                                            Examples

                                                                                                                                            Explanation 1

                                                                                                                                            code 1

                                                                                                                                            Explanation 2

                                                                                                                                            code 2

                                                                                                                                            Error Conditions

                                                                                                                                            Advanced Notes

                                                                                                                                            History

                                                                                                                                            Calculator OS Version Description
                                                                                                                                            TI-84+CE 5.3.0 Added
                                                                                                                                            Property Value
                                                                                                                                            Hex Value $EFA0
                                                                                                                                            Categories
                                                                                                                                            Localizations
                                                                                                                                            • FR: Insérer ligne ↑

                                                                                                                                            Insert Line Above

                                                                                                                                            Overview

                                                                                                                                            Comment:CE OS 5.3+

                                                                                                                                            Syntax

                                                                                                                                            Insert Line Above

                                                                                                                                            Description

                                                                                                                                            Examples

                                                                                                                                            Explanation 1

                                                                                                                                            code 1

                                                                                                                                            Explanation 2

                                                                                                                                            code 2

                                                                                                                                            Error Conditions

                                                                                                                                            Advanced Notes

                                                                                                                                            History

                                                                                                                                            Calculator OS Version Description
                                                                                                                                            TI-84+CE 5.3.0 Added
                                                                                                                                            Property Value
                                                                                                                                            Hex Value $4A
                                                                                                                                            Categories
                                                                                                                                            Localizations
                                                                                                                                            • FR: J

                                                                                                                                            J

                                                                                                                                            Overview

                                                                                                                                            Availability: Token available everywhere.

                                                                                                                                            Syntax

                                                                                                                                            J

                                                                                                                                            Description

                                                                                                                                            Examples

                                                                                                                                            Explanation 1

                                                                                                                                            code 1

                                                                                                                                            Explanation 2

                                                                                                                                            code 2

                                                                                                                                            Error Conditions

                                                                                                                                            Advanced Notes

                                                                                                                                            History

                                                                                                                                            Calculator OS Version Description
                                                                                                                                            TI-82 1.0 Added
                                                                                                                                            Property Value
                                                                                                                                            Hex Value $4B
                                                                                                                                            Categories
                                                                                                                                            Localizations
                                                                                                                                            • FR: K

                                                                                                                                            K

                                                                                                                                            Overview

                                                                                                                                            Availability: Token available everywhere.

                                                                                                                                            Syntax

                                                                                                                                            K

                                                                                                                                            Description

                                                                                                                                            Examples

                                                                                                                                            Explanation 1

                                                                                                                                            code 1

                                                                                                                                            Explanation 2

                                                                                                                                            code 2

                                                                                                                                            Error Conditions

                                                                                                                                            Advanced Notes

                                                                                                                                            History

                                                                                                                                            Calculator OS Version Description
                                                                                                                                            TI-82 1.0 Added
                                                                                                                                            Property Value
                                                                                                                                            Hex Value $4C
                                                                                                                                            Categories
                                                                                                                                            Localizations
                                                                                                                                            • FR: L

                                                                                                                                            L

                                                                                                                                            Overview

                                                                                                                                            Availability: Token available everywhere.

                                                                                                                                            Syntax

                                                                                                                                            L

                                                                                                                                            Description

                                                                                                                                            Examples

                                                                                                                                            Explanation 1

                                                                                                                                            code 1

                                                                                                                                            Explanation 2

                                                                                                                                            code 2

                                                                                                                                            Error Conditions

                                                                                                                                            Advanced Notes

                                                                                                                                            History

                                                                                                                                            Calculator OS Version Description
                                                                                                                                            TI-82 1.0 Added
                                                                                                                                            Property Value
                                                                                                                                            Hex Value $5D00
                                                                                                                                            Categories
                                                                                                                                            Localizations
                                                                                                                                            • FR: L₁

                                                                                                                                            L₁

                                                                                                                                            Overview

                                                                                                                                            Availability: Token available everywhere.

                                                                                                                                            Syntax

                                                                                                                                            L₁

                                                                                                                                            Description

                                                                                                                                            Examples

                                                                                                                                            Explanation 1

                                                                                                                                            code 1

                                                                                                                                            Explanation 2

                                                                                                                                            code 2

                                                                                                                                            Error Conditions

                                                                                                                                            Advanced Notes

                                                                                                                                            History

                                                                                                                                            Calculator OS Version Description
                                                                                                                                            TI-82 1.0 Added
                                                                                                                                            Property Value
                                                                                                                                            Hex Value $5D01
                                                                                                                                            Categories
                                                                                                                                            Localizations
                                                                                                                                            • FR: L₂

                                                                                                                                            L₂

                                                                                                                                            Overview

                                                                                                                                            Availability: Token available everywhere.

                                                                                                                                            Syntax

                                                                                                                                            L₂

                                                                                                                                            Description

                                                                                                                                            Examples

                                                                                                                                            Explanation 1

                                                                                                                                            code 1

                                                                                                                                            Explanation 2

                                                                                                                                            code 2

                                                                                                                                            Error Conditions

                                                                                                                                            Advanced Notes

                                                                                                                                            History

                                                                                                                                            Calculator OS Version Description
                                                                                                                                            TI-82 1.0 Added
                                                                                                                                            Property Value
                                                                                                                                            Hex Value $5D02
                                                                                                                                            Categories
                                                                                                                                            Localizations
                                                                                                                                            • FR: L₃

                                                                                                                                            L₃

                                                                                                                                            Overview

                                                                                                                                            Availability: Token available everywhere.

                                                                                                                                            Syntax

                                                                                                                                            L₃

                                                                                                                                            Description

                                                                                                                                            Examples

                                                                                                                                            Explanation 1

                                                                                                                                            code 1

                                                                                                                                            Explanation 2

                                                                                                                                            code 2

                                                                                                                                            Error Conditions

                                                                                                                                            Advanced Notes

                                                                                                                                            History

                                                                                                                                            Calculator OS Version Description
                                                                                                                                            TI-82 1.0 Added
                                                                                                                                            Property Value
                                                                                                                                            Hex Value $5D03
                                                                                                                                            Categories
                                                                                                                                            Localizations
                                                                                                                                            • FR: L₄

                                                                                                                                            L₄

                                                                                                                                            Overview

                                                                                                                                            Availability: Token available everywhere.

                                                                                                                                            Syntax

                                                                                                                                            L₄

                                                                                                                                            Description

                                                                                                                                            Examples

                                                                                                                                            Explanation 1

                                                                                                                                            code 1

                                                                                                                                            Explanation 2

                                                                                                                                            code 2

                                                                                                                                            Error Conditions

                                                                                                                                            Advanced Notes

                                                                                                                                            History

                                                                                                                                            Calculator OS Version Description
                                                                                                                                            TI-82 1.0 Added
                                                                                                                                            Property Value
                                                                                                                                            Hex Value $5D04
                                                                                                                                            Categories
                                                                                                                                            Localizations
                                                                                                                                            • FR: L₅

                                                                                                                                            L₅

                                                                                                                                            Overview

                                                                                                                                            Availability: Token available everywhere.

                                                                                                                                            Syntax

                                                                                                                                            L₅

                                                                                                                                            Description

                                                                                                                                            Examples

                                                                                                                                            Explanation 1

                                                                                                                                            code 1

                                                                                                                                            Explanation 2

                                                                                                                                            code 2

                                                                                                                                            Error Conditions

                                                                                                                                            Advanced Notes

                                                                                                                                            History

                                                                                                                                            Calculator OS Version Description
                                                                                                                                            TI-82 1.0 Added
                                                                                                                                            Property Value
                                                                                                                                            Hex Value $5D05
                                                                                                                                            Categories
                                                                                                                                            Localizations
                                                                                                                                            • FR: L₆

                                                                                                                                            L₆

                                                                                                                                            Overview

                                                                                                                                            Availability: Token available everywhere.

                                                                                                                                            Syntax

                                                                                                                                            L₆

                                                                                                                                            Description

                                                                                                                                            Examples

                                                                                                                                            Explanation 1

                                                                                                                                            code 1

                                                                                                                                            Explanation 2

                                                                                                                                            code 2

                                                                                                                                            Error Conditions

                                                                                                                                            Advanced Notes

                                                                                                                                            History

                                                                                                                                            Calculator OS Version Description
                                                                                                                                            TI-82 1.0 Added
                                                                                                                                            Property Value
                                                                                                                                            Hex Value $EF92
                                                                                                                                            Categories
                                                                                                                                              Localizations
                                                                                                                                              • FR: GAUCHE

                                                                                                                                              LEFT

                                                                                                                                              Overview

                                                                                                                                              LEFT is a tail argument for the invNorm( command where the optional argument tail can be LEFT (-∞,-a), CENTER [-a,a] or RIGHT (a, ∞) for Real a.
                                                                                                                                              See also invNorm(.

                                                                                                                                              Comment:CE OS 5.2+

                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                              Syntax

                                                                                                                                              LEFT

                                                                                                                                              Location

                                                                                                                                              2nd, catalog

                                                                                                                                              Description

                                                                                                                                              Examples

                                                                                                                                              Explanation 1

                                                                                                                                              code 1

                                                                                                                                              Explanation 2

                                                                                                                                              code 2

                                                                                                                                              Error Conditions

                                                                                                                                              Advanced Notes

                                                                                                                                              History

                                                                                                                                              Calculator OS Version Description
                                                                                                                                              TI-84+CE 5.2.0 Added
                                                                                                                                              Property Value
                                                                                                                                              Hex Value $EF49
                                                                                                                                              Categories
                                                                                                                                              Localizations
                                                                                                                                              • FR: BLEU CLR

                                                                                                                                              LTBLUE

                                                                                                                                              Overview

                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                              Syntax

                                                                                                                                              LTBLUE

                                                                                                                                              Description

                                                                                                                                              Examples

                                                                                                                                              Explanation 1

                                                                                                                                              code 1

                                                                                                                                              Explanation 2

                                                                                                                                              code 2

                                                                                                                                              Error Conditions

                                                                                                                                              Advanced Notes

                                                                                                                                              History

                                                                                                                                              Calculator OS Version Description
                                                                                                                                              TI-84+CSE 4.0 Added
                                                                                                                                              Property Value
                                                                                                                                              Hex Value $EF4C
                                                                                                                                              Categories
                                                                                                                                              Localizations
                                                                                                                                              • FR: GRIS CLR

                                                                                                                                              LTGRAY

                                                                                                                                              Overview

                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                              Syntax

                                                                                                                                              LTGRAY

                                                                                                                                              Description

                                                                                                                                              Examples

                                                                                                                                              Explanation 1

                                                                                                                                              code 1

                                                                                                                                              Explanation 2

                                                                                                                                              code 2

                                                                                                                                              Error Conditions

                                                                                                                                              Advanced Notes

                                                                                                                                              History

                                                                                                                                              Calculator OS Version Description
                                                                                                                                              TI-84+CSE 4.0 Added
                                                                                                                                              Property Value
                                                                                                                                              Hex Value $EB
                                                                                                                                              Categories
                                                                                                                                                Localizations
                                                                                                                                                • FR: ʟ

                                                                                                                                                ʟ

                                                                                                                                                Overview

                                                                                                                                                Identifies the next one to five characters as a user-created list name.

                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                Syntax

                                                                                                                                                ʟlistname

                                                                                                                                                Arguments

                                                                                                                                                NameTypeOptional
                                                                                                                                                listnamelist

                                                                                                                                                Location

                                                                                                                                                2nd, list, OPS, B:

                                                                                                                                                Description

                                                                                                                                                The ʟ character is used at the start of the name of any custom list you create, for example:

                                                                                                                                                {1,2,3}→ʟHELLO
{4,5,6}→ʟWORLD

                                                                                                                                                In most cases you need to include this when accessing or manipulating a custom list (although there's a few exceptions, see the Optimization section below). You do not need this character when accessing the the default lists L₁…L₆).

                                                                                                                                                The maximum length of the list name (not including the ʟ) is five letters. ʟABCDE works, but ʟABCDEF does not. List names must start with a letter A-Z but can also include numbers so ʟLIST1 and ʟLIST2 are valid list names, but ʟ123 is not.

                                                                                                                                                There are two ways to insert this character:

                                                                                                                                                1. Press 2nd, LIST, press right arrow to access the OPS menu, scroll to the bottom, and press ENTER to insert the ʟ character. You can then type the rest of the name of your list.
                                                                                                                                                2. If your custom list already exists, you can press 2nd, LIST, select the name of your list, and press ENTER. The whole name including the ʟ character will be inserted.

                                                                                                                                                Optimization

                                                                                                                                                You don't actually need to include the ʟ command when storing (→) to a list.

                                                                                                                                                {1,2,3}→HELLO
{4,5,6}→WORLD
{7,8,9}→X

                                                                                                                                                Although the name X as used above also matches the name of a regular real variable, since the data being stored is a list, it will be saved to ʟX.

                                                                                                                                                When storing to a specific list item, you MUST still include the ʟ character:

                                                                                                                                                1→ʟHELLO(1)
2→ʟWORLD(2)
3→ʟX(3)

                                                                                                                                                Some of the list commands also allow for leaving off the ʟ character, such as SetUpEditor. However, be careful when doing so with Input and Prompt because you might only be asking the user to input a list, but if a real value is entered, it would be saved to a real variable instead.

                                                                                                                                                Error Conditions

                                                                                                                                                • ERR:SYNTAX is thrown if you try to reference/create a list with more than 5 characters in its name.
                                                                                                                                                • ERR:UNDEFINED is thrown if you try to use ʟ on an undefined list.

                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583, Timtech.

                                                                                                                                                History

                                                                                                                                                Calculator OS Version Description
                                                                                                                                                TI-83 0.01013 Added
                                                                                                                                                Property Value
                                                                                                                                                Hex Value $7E0D
                                                                                                                                                Categories
                                                                                                                                                Localizations
                                                                                                                                                • FR: EtiqNAff

                                                                                                                                                LabelOff

                                                                                                                                                Overview

                                                                                                                                                Turns off axes labels.

                                                                                                                                                Availability: Token only available from within the Basic editor.

                                                                                                                                                Syntax

                                                                                                                                                LabelOff

                                                                                                                                                Location

                                                                                                                                                2nd, format, LabelOff

                                                                                                                                                Description

                                                                                                                                                The LabelOff setting disables labels on the X and Y coordinate axes. This is unnecessary if you've disabled the axes themselves, since the labels are only displayed when the axes are. To enable the labels, use the reverse setting LabelOn.

                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan.

                                                                                                                                                History

                                                                                                                                                Calculator OS Version Description
                                                                                                                                                TI-82 1.0 Added
                                                                                                                                                Property Value
                                                                                                                                                Hex Value $7E0C
                                                                                                                                                Categories
                                                                                                                                                Localizations
                                                                                                                                                • FR: EtiqAff

                                                                                                                                                LabelOn

                                                                                                                                                Overview

                                                                                                                                                Turns on axes labels.

                                                                                                                                                Availability: Token only available from within the Basic editor.

                                                                                                                                                Syntax

                                                                                                                                                LabelOn

                                                                                                                                                Location

                                                                                                                                                2nd, format, LabelOn

                                                                                                                                                Description

                                                                                                                                                The LabelOn setting enables labels on the X and Y coordinate axes. If both LabelOnand AxesOn are set, the axes will be displayed with an X next to the X (horizontal) axis, and a Y next to the Y (vertical) axis. To disable these labels, use the LabelOff setting.

                                                                                                                                                LabelOn and LabelOff have no effect if the coordinate axes aren't displayed; there's nothing to label.

                                                                                                                                                A somewhat quirky behavior of the X and Y labels is that they aren't saved by StorePic. If you save a picture of the graph screen, it records every detail of the way it looks, including equations, drawn elements, axes, grid, everything — but not the labels.

                                                                                                                                                One final comment: okay, so by the way the command works we know it was once intended to label the axes. However, the command doesn't actually check where the axes are. It puts an "x" slightly above the bottom right corner, and a "y" slightly below the top left. Most of the time, including the default graphing window, that doesn't help you to distinguish the axes in the slightest. And in split-screen mode, as shown in the screenshot, they both seem to label the x-axis. Weird.

                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: Battlesquid, burr, DarkerLine, GoVegan, kg583, Myles_Zadok.

                                                                                                                                                History

                                                                                                                                                Calculator OS Version Description
                                                                                                                                                TI-82 1.0 Added
                                                                                                                                                Property Value
                                                                                                                                                Hex Value $D6
                                                                                                                                                Categories
                                                                                                                                                Localizations
                                                                                                                                                • FR: Lbl

                                                                                                                                                Lbl

                                                                                                                                                Overview

                                                                                                                                                Creates a label of one or two characters.

                                                                                                                                                Availability: Token only available from within the Basic editor.

                                                                                                                                                Syntax

                                                                                                                                                Lbl label

                                                                                                                                                Arguments

                                                                                                                                                NameTypeOptional
                                                                                                                                                label

                                                                                                                                                Location

                                                                                                                                                prgm, CTL, 9:Lbl

                                                                                                                                                Description

                                                                                                                                                The Lbl command is used together with the Goto command to jump (or branch) to another place in a program. When the calculator executes a Goto command, it stores the label name in memory, and then searches from the beginning of the program for the Lbl command with the supplied name. If it finds it, it continues running the program from that point; otherwise, if the label does not exist, it throws a ERR: LABEL error.

                                                                                                                                                Label names can be either one or two characters long, and the only characters you're allowed to use are letters (including θ) and numbers 0 to 9; this means 37+37*37=1406 possible combinations. Of course, you should use all of the single character names first, before using the two character names. While you can technically have the same label name multiple times in a program, it is rather pointless since the calculator always goes to the first occurrence of the label.

                                                                                                                                                You can position a Lbl command one or more lines before a Goto command to create a kind of loop structure. However, you have to provide the break-out code, since it isn't built-in. An If conditional is easiest, but if there is no code that ends the branching, then program execution will continue indefinitely, until you manually exit it (by pressing the ON key).

                                                                                                                                                :Lbl A
:...
:If <exit condition>
:Goto A  // this line is skipped

                                                                                                                                                Although the Lbl/Goto loop structure may seem like a good alternative to loops, it should be avoided whenever possible, which is especially important when you are first planning a program. This is because it has several serious drawbacks associated with it:

                                                                                                                                                • It is quite slow, and gets slower the further the Lbl is in your program.
                                                                                                                                                • It makes reading code (your own, or someone else's) much more confusing.
                                                                                                                                                • In most cases, If, For(, While, or Repeat can be used instead, saving space and improving speed.
                                                                                                                                                • Using a Goto to exit any block of code requiring an End command causes a memory leak — around 40 bytes of memory will be rendered useless each time you do it until the program finishes running, which will also slow down your program down.

                                                                                                                                                They aren't all bad, however, and are actually useful when a loop isn't practical and when something only happens once or twice. Just remember that you should never use Goto to repeat a block of code several times. Use For(, Repeat, or While instead.

                                                                                                                                                Labels are also used with the Menu( command. The same considerations apply as with Goto, except that (unless you write a custom menu routine) there's no simple alternative to using labels with Menu(.

                                                                                                                                                Error Conditions

                                                                                                                                                • ERR:INVALID is thrown if this statement is used outside a program.
                                                                                                                                                • ERR:LABEL is thrown if the corresponding label doesn't exist.

                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

                                                                                                                                                History

                                                                                                                                                Calculator OS Version Description
                                                                                                                                                TI-82 1.0 Added
                                                                                                                                                Property Value
                                                                                                                                                Hex Value $F4
                                                                                                                                                Categories
                                                                                                                                                Localizations
                                                                                                                                                • FR: RegLin(a+bx)

                                                                                                                                                LinReg(a+bx)

                                                                                                                                                Overview

                                                                                                                                                Fits a linear regression model toXlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ.

                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                Syntax

                                                                                                                                                LinReg(a+bx) [Xlistname,Ylistname,freqlist,regequ]

                                                                                                                                                Arguments

                                                                                                                                                NameTypeOptional
                                                                                                                                                XlistnamelistYes
                                                                                                                                                YlistnamelistYes
                                                                                                                                                freqlistlistYes
                                                                                                                                                regequYes

                                                                                                                                                Location

                                                                                                                                                stat, CALC, 8:LinReg(a+bx)

                                                                                                                                                Description

                                                                                                                                                The LinReg(a+bx) command is one of several that can calculate the line of best fit through a set of points (it differs from LinReg(ax+b) only in the format of its output). To use it, you must first store the points to two lists: one of the x-coordinates and one of the y-coordinates, ordered so that the nth element of one list matches up with the nth element of the other list. L₁ and L₂ are the default lists to use, and the List Editor (STAT > Edit…) is a useful window for entering the points.

                                                                                                                                                In its simplest form, LinReg(a+bx) takes no arguments, and calculates a best fit line through the points in L₁ and L₂:

                                                                                                                                                :{9,13,21,30,31,31,34→L₁
:{260,320,420,530,560,550,590→L₂
:LinReg(a+bx)

                                                                                                                                                On the home screen, or as the last line of a program, this will display the equation of the line of best fit: you'll be shown the format, y=a+bx, and the values of a and b. It will also be stored in the RegEQ variable, but you won't be able to use this variable in a program - accessing it just pastes the equation wherever your cursor was. Finally, the statistical variables a, b, r, and r² will be set as well. These latter two variables will be displayed only if "Diagnostic Mode" is turned on (see DiagnosticOn and DiagnosticOff).

                                                                                                                                                You don't have to do the regression on L₁ and L₂, but if you don't you'll have to enter the names of the lists after the command. For example:

                                                                                                                                                :{9,13,21,30,31,31,34→FAT
:{260,320,420,530,560,550,590→CALS
:LinReg(a+bx) ʟFAT,ʟCALS

                                                                                                                                                You can attach frequencies to points, for when a point occurs more than once, by supplying an additional argument - the frequency list. This list does not have to contain integer frequencies. If you add a frequency list, you must supply the names of the x-list and y-list as well, even when they're L₁ and L₂.

                                                                                                                                                Finally, you can enter an equation variable (such as Y₁) after the command, so that the line of best fit is stored to this equation automatically. This doesn't require you to supply the names of the lists, but if you do, the equation variable must come last. You can use polar, parametric, or sequential variables as well, but since the line of best fit will be in terms of X anyway, this doesn't make much sense.

                                                                                                                                                An example of LinReg(a+bx) with all the optional arguments:

                                                                                                                                                :{9,13,21,30,31,31,34→FAT
:{260,320,420,530,560,550,590→CALS
:{2,1,1,1,2,1,1→FREQ
:LinReg(a+bx) ʟFAT,ʟCALS,ʟFREQ,Y₁

                                                                                                                                                Advanced Uses (for programmers)

                                                                                                                                                LinReg(a+bx), along with LinReg(ax+b), can be used to convert a number to a string.

                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, jojo40605, thornahawk, Timothy Foster.

                                                                                                                                                History

                                                                                                                                                Calculator OS Version Description
                                                                                                                                                TI-82 1.0 Added
                                                                                                                                                Property Value
                                                                                                                                                Hex Value $FF
                                                                                                                                                Categories
                                                                                                                                                Localizations
                                                                                                                                                • FR: RegLin(ax+b)

                                                                                                                                                LinReg(ax+b)

                                                                                                                                                Overview

                                                                                                                                                Fits a linear regression model toXlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ.

                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                Syntax

                                                                                                                                                LinReg(ax+b) [Xlistname,Ylistname,freqlist,regequ]

                                                                                                                                                Arguments

                                                                                                                                                NameTypeOptional
                                                                                                                                                XlistnamelistYes
                                                                                                                                                YlistnamelistYes
                                                                                                                                                freqlistlistYes
                                                                                                                                                regequYes

                                                                                                                                                Location

                                                                                                                                                stat, CALC, 4:LinReg(ax+b)

                                                                                                                                                Description

                                                                                                                                                The LinReg(ax+b) is one of several commands that can calculate the line of best fit through a set of points. To use it, you must first store the points to two lists: one of the x-coordinates and one of the y-coordinates, ordered so that the nth element of one list matches up with the nth element of the other list. L₁ and L₂ are the default lists to use, and the List Editor (STAT > Edit…) is a useful window for entering the points.

                                                                                                                                                In its simplest form, LinReg(ax+b) takes no arguments, and calculates a best fit line through the points in L₁ and L₂:

                                                                                                                                                :{9,13,21,30,31,31,34→L₁
:{260,320,420,530,560,550,590→L₂
:LinReg(ax+b)

                                                                                                                                                On the home screen, or as the last line of a program, this will display the equation of the line of best fit: you'll be shown the format, y=ax+b, and the values of a and b. It will also be stored in the RegEQ variable, but you won't be able to use this variable in a program - accessing it just pastes the equation wherever your cursor was. Finally, the statistical variables a, b, r, and r² will be set as well. These latter two variables will be displayed only if "Diagnostic Mode" is turned on (see DiagnosticOn and DiagnosticOff).

                                                                                                                                                You don't have to do the regression on L₁ and L₂, but if you don't you'll have to enter the names of the lists after the command. For example:

                                                                                                                                                :{9,13,21,30,31,31,34→FAT
:{260,320,420,530,560,550,590→CALS
:LinReg(ax+b) ʟFAT,ʟCALS

                                                                                                                                                You can attach frequencies to points, for when a point occurs more than once, by supplying an additional argument - the frequency list. This list does not have to contain integer frequencies. If you add a frequency list, you must supply the names of the x-list and y-list as well, even when they're L₁ and L₂.

                                                                                                                                                Finally, you can enter an equation variable (such as Y₁) after the command, so that the line of best fit is stored to this equation automatically. This doesn't require you to supply the names of the lists, but if you do, the equation variable must come last. You can use polar, parametric, or sequential variables as well, but since the line of best fit will be in terms of X anyway, this doesn't make much sense.

                                                                                                                                                An example of LinReg(ax+b) with all the optional arguments:

                                                                                                                                                :{9,13,21,30,31,31,34→FAT
:{260,320,420,530,560,550,590→CALS
:{2,1,1,1,2,1,1→FREQ
:LinReg(ax+b) ʟFAT,ʟCALS,ʟFREQ,Y₁

                                                                                                                                                Advanced Uses (for programmers)

                                                                                                                                                LinReg(ax+b), along with LinReg(a+bx) and Med-Med, can be used to convert a number to a string.

                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: Apersoma, burr, DarkerLine, GoVegan, thornahawk, Timothy Foster.

                                                                                                                                                History

                                                                                                                                                Calculator OS Version Description
                                                                                                                                                TI-82 1.0 Added
                                                                                                                                                Property Value
                                                                                                                                                Hex Value $EF15
                                                                                                                                                Categories
                                                                                                                                                  Localizations
                                                                                                                                                  • FR: LinRegTInt

                                                                                                                                                  LinRegTInt

                                                                                                                                                  Overview

                                                                                                                                                  Performs a linear regression and computes the t confidence interval for the slope coefficient b.

                                                                                                                                                  Availability: Token only available from within the Basic editor.

                                                                                                                                                  Syntax

                                                                                                                                                  LinRegTInt [Xlistname,Ylistname,freqlist,confidence level, regequ]

                                                                                                                                                  Arguments

                                                                                                                                                  NameTypeOptional
                                                                                                                                                  XlistnamelistYes
                                                                                                                                                  YlistnamelistYes
                                                                                                                                                  freqlistlistYes
                                                                                                                                                  confidence levelYes
                                                                                                                                                  regequYes

                                                                                                                                                  Location

                                                                                                                                                  stat, TESTS, G:LinRegTInt

                                                                                                                                                  Description

                                                                                                                                                  Like LinReg(ax+b) and similar commands, LinRegTInt finds the best fit line through a set of points. However, LinRegTInt adds another method of checking the quality of the fit, by calculating a t confidence interval for the slope b. If the confidence interval calculated contains zero, the data supplied is insufficient to conclude a linear relation between the variables.

                                                                                                                                                  To use LinRegTInt, you must first store the points to two lists: one of the x-coordinates and one of the y-coordinates, ordered so that the nth element of one list matches up with the nth element of the other list. L₁ and L₂ are the default lists to use, and the List Editor (STAT > Edit…) is a useful window for entering the points. You do not have to do the regression on L₁ and L₂, but if you don't you'll have to enter the names of the lists after the command.

                                                                                                                                                  You can attach frequencies to points, for when a point occurs more than once, by supplying an additional argument - the frequency list. This list does not have to contain integer frequencies. If you add a frequency list, you must supply the names of the x-list and y-list as well, even when they are L₁ and L₂.

                                                                                                                                                  You can supply a confidence level probability as the fourth argument. It should be a real number between zero and one. If not supplied, the default value is .95. (95% confidence level) If you need to specify a different confidence level, you must enter the names of the lists as well, even if they're L₁ and L₂.

                                                                                                                                                  Finally, you can enter an equation variable (such as Y₁) after the command, so that the line of best fit is stored to this equation automatically. This doesn't require you to supply the names of the lists, but if you do, the equation variable must come last.

                                                                                                                                                  For example, both

                                                                                                                                                  :{4,5,6,7,8→L₁
:{1,2,3,3.5,4.5→L₂
:LinRegTInt

                                                                                                                                                  and

                                                                                                                                                  :{4,5,6,7,8→X
:{1,2,3,3.5,4.5→Y
:{1,1,1,1,1→FREQ
:LinRegTTest ʟX,ʟY,ʟFREQ,.95,Y₁

                                                                                                                                                  will give the following output:

                                                                                                                                                  LinRegTInt
    y=a+bx
    (.69088,1.0091)
    b=.85
    df=3
    s=.158113883
    a=-2.3
    r²=.9897260274
    r=.9948497512

                                                                                                                                                  (the last two lines will only appear if diagnostics have been turned on - see DiagnosticOn)

                                                                                                                                                  • The first line shows the confidence interval containing the slope of the fitted line; as mentioned above, if the interval contains 0, it cannot be concluded that the two variables have a linear relationship. Also, the smaller the difference between the two numbers, the more precision that can be attributed to the calculated slope.
                                                                                                                                                  • df is the degrees of freedom, equal to the number of points minus two.
                                                                                                                                                  • a and b are the parameters of the equation y=a+bx, the regression line we've calculated
                                                                                                                                                  • s is the standard error about the line, a measure of the typical size of a residual (the numbers stored in ʟRESID). It is the square root of the sum of squares of the residuals divided by the degrees of freedom. Smaller values indicate that the points tend to be close to the fitted line, while large values indicate scattering.
                                                                                                                                                  • r² and r are respectively the coefficients of determination and correlation: a value near 1 or -1 for the former, and near 1 for the latter, indicates a good fit.

                                                                                                                                                  Source: parts of this page were written by the following TI|BD contributors: Mapar007, thornahawk, Timothy Foster.

                                                                                                                                                  History

                                                                                                                                                  Calculator OS Version Description
                                                                                                                                                  TI-84+ 2.30 Added
                                                                                                                                                  Property Value
                                                                                                                                                  Hex Value $BB34
                                                                                                                                                  Categories
                                                                                                                                                  Localizations
                                                                                                                                                  • FR: RegLinTTest

                                                                                                                                                  LinRegTTest

                                                                                                                                                  Overview

                                                                                                                                                  Performs a linear regression and a t-test. alternative=-1 is <; alternative=0 is ≠; alternative=1 is >.

                                                                                                                                                  Availability: Token only available from within the Basic editor.

                                                                                                                                                  Syntax

                                                                                                                                                  LinRegTTest [Xlistname,Ylistname,freqlist,alternative,regequ]

                                                                                                                                                  Arguments

                                                                                                                                                  NameTypeOptional
                                                                                                                                                  XlistnamelistYes
                                                                                                                                                  YlistnamelistYes
                                                                                                                                                  freqlistlistYes
                                                                                                                                                  alternativeYes
                                                                                                                                                  regequYes

                                                                                                                                                  Location

                                                                                                                                                  stat, TESTS, F:LinRegTTest

                                                                                                                                                  Description

                                                                                                                                                  Like LinReg(ax+b) and similar commands, LinRegTTest finds the best fit line through a set of points. However, LinRegTTest adds another method of checking the quality of the fit, by performing a t-test on the slope, testing the null hypothesis that the slope of the true best fit line is 0 (which implies the absence of correlation between the two variables, since a relation with a slope of zero means the x-variable does not affect the y-variable at all). If the p-value of the test is not low enough, then there is not enough data to assume a linear relation between the variables.

                                                                                                                                                  To use LinRegTTest, you must first store the points to two lists: one of the x-coordinates and one of the y-coordinates, ordered so that the nth element of one list matches up with the nth element of the other list. L₁ and L₂ are the default lists to use, and the List Editor (STAT > Edit…) is a useful window for entering the points.

                                                                                                                                                  In its simplest form, LinRegTTest takes no arguments, and calculates a best fit line through the points in L₁ and L₂:

                                                                                                                                                  :{9,13,21,30,31,31,34→L₁
:{260,320,420,530,560,550,590→L₂
:LinRegTTest

                                                                                                                                                  The output will look as follows:

                                                                                                                                                  LinRegTTest
 y=a+bx
 β≠0 and ρ≠0
 t=53.71561274
 p=4.2285344e-8
 df=5
 a=145.3808831
 b=13.09073265
 s=5.913823968
 r²=.9982701159
 r=.9991346836

                                                                                                                                                  (the last two lines will only appear if diagnostics have been turned on - see DiagnosticOn)

                                                                                                                                                  • β and ρ: this line represents the alternative hypothesis. β is the true value of the statistic b (it is what we would get if the regression was done on the entire population, rather than a sample); ρ is the true value of the statistic r.
                                                                                                                                                  • t is the test statistic, used to calculate p.
                                                                                                                                                  • p is the probability that we'd get a correlation this strong by chance, assuming the null hypothesis that there is no actual correlation. When it's low, as here, this is evidence against the null hypothesis. Since p<.01, the data is significant on a 1% level, so we reject the null hypothesis and conclude that there is a correlation.
                                                                                                                                                  • df is the degrees of freedom, equal to the number of points minus two
                                                                                                                                                  • a and b are the parameters of the equation y=a+bx, the regression line we've calculated
                                                                                                                                                  • s is the standard error about the line, a measure of the typical size of a residual (the numbers stored in ʟRESID). It is the square root of the sum of squares of the residuals divided by the degrees of freedom. Smaller values indicate that the points tend to be close to the fitted line, while large values indicate scattering.
                                                                                                                                                  • r² and r are respectively the coefficients of determination and correlation: a value near 1 or -1 for the former, and near 1 for the latter, indicates a good fit.

                                                                                                                                                  You do not have to do the regression on L₁ and L₂, but if you don't you'll have to enter the names of the lists after the command. For example:

                                                                                                                                                  :{9,13,21,30,31,31,34→FAT
:{260,320,420,530,560,550,590→CALS
:LinRegTTest ʟFAT,ʟCALS

                                                                                                                                                  You can attach frequencies to points, for when a point occurs more than once, by supplying an additional argument - the frequency list. This list does not have to contain integer frequencies. If you add a frequency list, you must supply the names of the x-list and y-list as well, even when they are L₁ and L₂.

                                                                                                                                                  You can add the alternative argument to change the alternative hypothesis from the default (β≠0 and ρ≠0). This is used when you have prior knowledge either that a negative relation is impossible, or that a positive one is impossible. The values of the alternative argument are as follows:

                                                                                                                                                  • negative: the alternative hypothesis is β<0 and ρ<0 (we have prior knowledge that there can be no positive relation)
                                                                                                                                                  • 0: the alternative hypothesis is β≠0 and ρ≠0 (we have no prior knowledge)
                                                                                                                                                  • positive: the alternative hypothesis is β>0 and ρ>0 (we have prior knowledge that there can be no negative relation)

                                                                                                                                                  Obviously, if you want the alternative hypothesis to be β≠0 and ρ≠0, the default, you don't need to supply this argument. However, if you do, you must enter the names of the lists as well, even if they're L₁ and L₂.

                                                                                                                                                  Finally, you can enter an equation variable (such as Y₁) after the command, so that the line of best fit is stored to this equation automatically. This doesn't require you to supply the names of the lists, but if you do, the equation variable must come last. You can use polar, parametric, or sequential variables as well, but since the line of best fit will be in terms of X anyway, this doesn't make much sense.

                                                                                                                                                  An example of LinRegTTest with all the optional arguments:

                                                                                                                                                  :{9,13,21,30,31,31,34→FAT
:{260,320,420,530,560,550,590→CALS
:{2,1,1,1,2,1,1→FREQ
:LinRegTTest ʟFAT,ʟCALS,ʟFREQ,1,Y₁

                                                                                                                                                  Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Myles_Zadok, thornahawk, Timothy Foster.

                                                                                                                                                  History

                                                                                                                                                  Calculator OS Version Description
                                                                                                                                                  TI-83 0.01013 Added
                                                                                                                                                  Property Value
                                                                                                                                                  Hex Value $9C
                                                                                                                                                  Categories
                                                                                                                                                  Localizations
                                                                                                                                                  • FR: Ligne(

                                                                                                                                                  Line(

                                                                                                                                                  Overview

                                                                                                                                                  Draws a line from (X1,Y1) to (X2,Y2) with the following options: erase #: 1,0, color #: 10-24, and line style #: 1-4.

                                                                                                                                                  Availability: Token available everywhere.

                                                                                                                                                  Syntax

                                                                                                                                                  Line(X1,Y1,X2,Y2[,erase#,color#,linestyle#])

                                                                                                                                                  Arguments

                                                                                                                                                  NameTypeOptional
                                                                                                                                                  X1
                                                                                                                                                  Y1
                                                                                                                                                  X2
                                                                                                                                                  Y2
                                                                                                                                                  erase#Yes
                                                                                                                                                  color#colorNumYes
                                                                                                                                                  linestyle#integerYes

                                                                                                                                                  Location

                                                                                                                                                  2nd, draw, DRAW, 2:Line(

                                                                                                                                                  Overview

                                                                                                                                                  Erases a line (erase #: 1,0) from (X1,Y1) to (X2,Y2).

                                                                                                                                                  Availability: Token available everywhere.

                                                                                                                                                  Syntax

                                                                                                                                                  Line(X1,Y1,X2,Y2,0[,line#])

                                                                                                                                                  Arguments

                                                                                                                                                  NameTypeOptional
                                                                                                                                                  X1
                                                                                                                                                  Y1
                                                                                                                                                  X2
                                                                                                                                                  Y2
                                                                                                                                                  line#Yes

                                                                                                                                                  Location

                                                                                                                                                  2nd, draw, DRAW, 2:Line(

                                                                                                                                                  Description

                                                                                                                                                  The Line( command is used to draw lines at any angle, as opposed to only drawing vertical or horizontal lines. Line(X1,Y1,X2,Y2) will draw a line from (X1,Y1) to (X2,Y2). Line( is affected by the window settings, although you can use a friendly window so there is no impact on the command.

                                                                                                                                                  :Line(5,5,20,3)

                                                                                                                                                  Advanced Uses

                                                                                                                                                  Line has an optional fifth argument. It can be any real number, but the default is one. If the fifth argument, erase, is something other than 0, then it will simply draw the line. If erase is 0, then it will erase the line.

                                                                                                                                                  :Line(5,5,20,3,0)

                                                                                                                                                  Leave off the ending argument if you are just drawing the line.

                                                                                                                                                  :Line(5,5,20,3,1)
can be
:Line(5,5,20,3)

                                                                                                                                                  The ending argument can be a formula, which is useful for movement applications and other things such as health bars where the lines drawn are constantly different. The following draws or erases a line depending on whether a key is pressed.

                                                                                                                                                  :getKey
:Line(5,5,20,3,not(Ans

                                                                                                                                                  If working on a TI 84+CSE or TI 84+CE, then the fifth argument of the Line( command can be a color name or ID number:

                                                                                                                                                  :Line(5,5,20,3,BROWN

                                                                                                                                                  The last argument, line style, is an optional argument that chooses what style of line to draw on the color calculators.

                                                                                                                                                  1 pixel wide line
:Line(5,5,20,3,RED,1
2 pixel wide line
:Line(5,5,20,3,RED,2
shaded above
:Line(5,5,20,3,RED,3
shaded below
:Line(5,5,20,3,RED,4

                                                                                                                                                  Command Timings

                                                                                                                                                  If you are drawing horizontal or vertical lines that stretch the entire graph screen, such as a border, it is better to use Vertical or Horizontal. These are smaller and are usually faster as well.

                                                                                                                                                  See Also

                                                                                                                                                  Source: parts of this page were written by the following TI|BD contributors: basickevin, burr, DarkerLine, GoVegan, kg583, Lionel Foxcroft, Weregoose, Xphoenix.

                                                                                                                                                  History

                                                                                                                                                  Calculator OS Version Description
                                                                                                                                                  TI-82 1.0 Added
                                                                                                                                                  Property Value
                                                                                                                                                  Hex Value $BB3A
                                                                                                                                                  Categories
                                                                                                                                                  Localizations
                                                                                                                                                  • FR: List►matr(

                                                                                                                                                  List►matr(

                                                                                                                                                  Overview

                                                                                                                                                  Fills matrixname column by column with the elements from each specified listname.

                                                                                                                                                  Availability: Token available everywhere.

                                                                                                                                                  Syntax

                                                                                                                                                  List►matr(listname1,...,listname n,matrixname)

                                                                                                                                                  Arguments

                                                                                                                                                  NameTypeOptional
                                                                                                                                                  listname1listName
                                                                                                                                                  ...
                                                                                                                                                  listname nlist
                                                                                                                                                  matrixnamematrix

                                                                                                                                                  Location

                                                                                                                                                  2nd, list, OPS, 0:List, matr(

                                                                                                                                                  Description

                                                                                                                                                  The List►matr( builds a matrix by combining several list expressions, and stores it to the specified variable ([A] through [J]). Each list specifies a column of the matrix: the first list will be stored down the first (leftmost) column, the second list down the second column, and so on. For example:

                                                                                                                                                  List►matr({1,2,3},{10,20,30},{100,200,300},[A]
        Done
[A]
        [[1 10 100]
         [2 20 200]
         [3 30 300]]

                                                                                                                                                  Advanced Uses

                                                                                                                                                  The calculator can actually handle lists that are not the same size. It will pad zeroes to the shorter lists, until they have the same length as the longest list.

                                                                                                                                                  List►matr({1,2,3},{10},{100,200},[A]
        Done
[A]
        [[1 10 100]
         [2  0 200]
         [3  0   0]]

                                                                                                                                                  Error Conditions

                                                                                                                                                  • ERR:ARGUMENT is thrown if there are more than 99 lists (since a matrix can be at most 99x99)
                                                                                                                                                  • ERR:INVALID DIM is thrown if one of the lists is longer than 99 elements (since a matrix can be at most 99x99)

                                                                                                                                                  Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, thornahawk, Timothy Foster.

                                                                                                                                                  History

                                                                                                                                                  Calculator OS Version Description
                                                                                                                                                  TI-83 0.01013 Added
                                                                                                                                                  Property Value
                                                                                                                                                  Hex Value $BB3A
                                                                                                                                                  Categories
                                                                                                                                                  Localizations
                                                                                                                                                  • FR: List►matr(

                                                                                                                                                  List►matr(

                                                                                                                                                  Overview

                                                                                                                                                  Fills matrixname column by column with the elements from each specified listname.

                                                                                                                                                  Availability: Token available everywhere.

                                                                                                                                                  Syntax

                                                                                                                                                  List►matr(listname1,...,listname n,matrixname)

                                                                                                                                                  Arguments

                                                                                                                                                  NameTypeOptional
                                                                                                                                                  listname1listName
                                                                                                                                                  ...
                                                                                                                                                  listname nlist
                                                                                                                                                  matrixnamematrix

                                                                                                                                                  Location

                                                                                                                                                  2nd, list, OPS, 0:List, matr(

                                                                                                                                                  Description

                                                                                                                                                  The List►matr( builds a matrix by combining several list expressions, and stores it to the specified variable ([A] through [J]). Each list specifies a column of the matrix: the first list will be stored down the first (leftmost) column, the second list down the second column, and so on. For example:

                                                                                                                                                  List►matr({1,2,3},{10,20,30},{100,200,300},[A]
        Done
[A]
        [[1 10 100]
         [2 20 200]
         [3 30 300]]

                                                                                                                                                  Advanced Uses

                                                                                                                                                  The calculator can actually handle lists that are not the same size. It will pad zeroes to the shorter lists, until they have the same length as the longest list.

                                                                                                                                                  List►matr({1,2,3},{10},{100,200},[A]
        Done
[A]
        [[1 10 100]
         [2  0 200]
         [3  0   0]]

                                                                                                                                                  Error Conditions

                                                                                                                                                  • ERR:ARGUMENT is thrown if there are more than 99 lists (since a matrix can be at most 99x99)
                                                                                                                                                  • ERR:INVALID DIM is thrown if one of the lists is longer than 99 elements (since a matrix can be at most 99x99)

                                                                                                                                                  Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, thornahawk, Timothy Foster.

                                                                                                                                                  History

                                                                                                                                                  Calculator OS Version Description
                                                                                                                                                  TI-83 0.01013 Added
                                                                                                                                                  Property Value
                                                                                                                                                  Hex Value $F6
                                                                                                                                                  Categories
                                                                                                                                                  Localizations
                                                                                                                                                  • FR: RegLn

                                                                                                                                                  LnReg

                                                                                                                                                  Overview

                                                                                                                                                  Fits a logarithmic regression model to Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ.

                                                                                                                                                  Availability: Token available everywhere.

                                                                                                                                                  Syntax

                                                                                                                                                  LnReg [Xlistname,Ylistname,freqlist,regequ]

                                                                                                                                                  Arguments

                                                                                                                                                  NameTypeOptional
                                                                                                                                                  XlistnamelistYes
                                                                                                                                                  YlistnamelistYes
                                                                                                                                                  freqlistlistYes
                                                                                                                                                  regequYes

                                                                                                                                                  Location

                                                                                                                                                  stat, CALC, 9:LnReg

                                                                                                                                                  Description

                                                                                                                                                  LnReg tries to fit a logarithmic curve (y=a+b*lnx) through a set of points. To use it, you must first store the points to two lists: one of the x-coordinates and one of the y-coordinates, ordered so that the nth element of one list matches up with the nth element of the other list. L₁ and L₂ are the default lists to use, and the List Editor (STAT > Edit…) is a useful window for entering the points.

                                                                                                                                                  The calculator does this regression by taking the natural log ln( of the x-coordinates (this isn't stored anywhere) and then doing a linear regression. This means that if any x-coordinates are negative or 0, the calculator will instantly quit with ERR:DOMAIN.

                                                                                                                                                  In its simplest form, LnReg takes no arguments, and fits a logarithmic curve through the points in L₁ and L₂:

                                                                                                                                                  :{9,13,21,30,31,31,34→L₁
:{260,320,420,530,560,550,590→L₂
:LnReg

                                                                                                                                                  On the home screen, or as the last line of a program, this will display the equation of the curve: you'll be shown the format, y=a+b*ln(x), and the values of a and b. It will also be stored in the RegEQ variable, but you won't be able to use this variable in a program - accessing it just pastes the equation wherever your cursor was. Finally, the statistical variables a, b, r, and r² will be set as well. These latter two variables will be displayed only if "Diagnostic Mode" is turned on (see DiagnosticOn and DiagnosticOff).

                                                                                                                                                  You don't have to do the regression on L₁ and L₂, but if you don't you'll have to enter the names of the lists after the command. For example:

                                                                                                                                                  :{9,13,21,30,31,31,34→FAT
:{260,320,420,530,560,550,590→CALS
:LnReg ʟFAT,ʟCALS

                                                                                                                                                  You can attach frequencies to points, for when a point occurs more than once, by supplying an additional argument - the frequency list. This list does not have to contain integer frequencies. If you add a frequency list, you must supply the names of the x-list and y-list as well, even when they're L₁ and L₂.

                                                                                                                                                  Finally, you can enter an equation variable (such as Y₁) after the command, so that the curve's equation is stored to this variable automatically. This doesn't require you to supply the names of the lists, but if you do, the equation variable must come last. You can use polar, parametric, or sequential variables as well, but since the equation will be in terms of X anyway, this doesn't make much sense.

                                                                                                                                                  An example of LnReg with all the optional arguments:

                                                                                                                                                  :{9,13,21,30,31,31,34→FAT
:{260,320,420,530,560,550,590→CALS
:{2,1,1,1,2,1,1→FREQ
:LnReg ʟFAT,ʟCALS,ʟFREQ,Y₁

                                                                                                                                                  Error Conditions

                                                                                                                                                  • ERR:DOMAIN is thrown if any x-coordinates are negative or 0.

                                                                                                                                                  Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, thornahawk, Timothy Foster.

                                                                                                                                                  History

                                                                                                                                                  Calculator OS Version Description
                                                                                                                                                  TI-82 1.0 Added
                                                                                                                                                  Property Value
                                                                                                                                                  Hex Value $BB33
                                                                                                                                                  Categories
                                                                                                                                                  Localizations
                                                                                                                                                  • FR: Logistique

                                                                                                                                                  Logistic

                                                                                                                                                  Overview

                                                                                                                                                  Fits a logistic regression model toXlistnameand Ylistname with frequency freqlist, and stores the regression equation to regequ.

                                                                                                                                                  Availability: Token available everywhere.

                                                                                                                                                  Syntax

                                                                                                                                                  Logistic [Xlistname,Ylistname,freqlist,regequ]

                                                                                                                                                  Arguments

                                                                                                                                                  NameTypeOptional
                                                                                                                                                  XlistnamelistYes
                                                                                                                                                  YlistnamelistYes
                                                                                                                                                  freqlistlistYes
                                                                                                                                                  regequYes

                                                                                                                                                  Location

                                                                                                                                                  CALC, B:Logistic

                                                                                                                                                  Description

                                                                                                                                                  Logistic tries to fit a logistic curve (y=c/(1+ae-bx)) through a set of points. To use it, you must first store the points to two lists: one of the x-coordinates and one of the y-coordinates, ordered so that the ith element of one list matches up with the ith element of the other list. L₁ and L₂ are the default lists used, and the List Editor (STAT > Edit…) is a useful window for entering the points.

                                                                                                                                                  The explanation for the odd format of a logistic curve is that it is the solution to a differential equation that models population growth with a limiting factor: a population that grows according to a logistic curve will start out growing exponentially, but will slow down before reaching a carrying capacity and approach this critical value without reaching it. The logistic curve also has applications, for example, in physics.

                                                                                                                                                  In its simplest form, Logistic takes no arguments, and fits a logistic curve through the points in L₁ and L₂:

                                                                                                                                                  :{9,13,21,30,31,31,34→L₁
:{260,320,420,530,560,550,590→L₂
:Logistic

                                                                                                                                                  On the home screen, or as the last line of a program, this will display the equation of the curve: you'll be shown the format, y=c/(1+a__e^(-b_x)), and the values of _a, b and c. It will also be stored in the RegEQ variable, but you won't be able to use this variable in a program - accessing it just pastes the equation wherever your cursor was. Finally, the statistical variables a, b, and c will be set as well. There are no correlation statistics available for Logistic even if Diagnostic Mode is turned on (see DiagnosticOn and DiagnosticOff).

                                                                                                                                                  You do not have to do the regression on L₁ and L₂, in which case you will have to enter the names of the lists after the command. For example:

                                                                                                                                                  :{9,13,21,30,31,31,34→FAT
:{260,320,420,530,560,550,590→CALS
:Logistic ʟFAT,ʟCALS

                                                                                                                                                  You can attach frequencies to points, for when a point occurs more than once, by supplying an additional argument - the frequency list. This list does not have to contain integer frequencies. If you add a frequency list, you must supply the names of the x-list and y-list as well, even when they're L₁ and L₂.

                                                                                                                                                  Finally, you can enter an equation variable (such as Y₁) after the command, so that the curve's equation is stored to this variable automatically. This does not require you to supply the names of the lists, but if you do, the equation variable must come last. You can use polar, parametric, or sequential variables as well, but since the equation will be in terms of X anyway, this doesn't make much sense.

                                                                                                                                                  An example of Logistic with all the optional arguments:

                                                                                                                                                  :{9,13,21,30,31,31,34→FAT
:{260,320,420,530,560,550,590→CALS
:{2,1,1,1,2,1,1→FREQ
:Logistic ʟFAT,ʟCALS,ʟFREQ,Y₁

                                                                                                                                                  Warning: if your data is not even slightly logistic in nature, then the calculator may return an error such as ERR:OVERFLOW. This happens when the calculator tries to calculate a carrying capacity, c, for the data, but since the rate of change in data doesn't seem to be slowing down, it assumes that the carrying capacity is still very far off, and tries large values for it. These values may get so large as to cause an overflow.

                                                                                                                                                  The Levenberg-Marquardt nonlinear least-squares algorithm is used by Logistic.

                                                                                                                                                  Error Conditions

                                                                                                                                                  • ERR:ARGUMENT is thrown by using only one list.
                                                                                                                                                  • ERR:DIM MISMATCH is thrown if the dimensions of two lists do not match.
                                                                                                                                                  • ERR:DOMAIN is thrown if Logistic is left without using lists or enough instructions.
                                                                                                                                                  • ERR:DATA TYPE is thrown if lists are not used, or a list contains a number like "4i".

                                                                                                                                                  Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, nap386, thornahawk, Timothy Foster.___

                                                                                                                                                  History

                                                                                                                                                  Calculator OS Version Description
                                                                                                                                                  TI-83 0.01013 Added
                                                                                                                                                  Property Value
                                                                                                                                                  Hex Value $5D00
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                                                                                                                                                  • FR: L₁

                                                                                                                                                  L₁

                                                                                                                                                  Overview

                                                                                                                                                  Availability: Token available everywhere.

                                                                                                                                                  Syntax

                                                                                                                                                  L₁

                                                                                                                                                  Description

                                                                                                                                                  Examples

                                                                                                                                                  Explanation 1

                                                                                                                                                  code 1

                                                                                                                                                  Explanation 2

                                                                                                                                                  code 2

                                                                                                                                                  Error Conditions

                                                                                                                                                  Advanced Notes

                                                                                                                                                  History

                                                                                                                                                  Calculator OS Version Description
                                                                                                                                                  TI-82 1.0 Added
                                                                                                                                                  Property Value
                                                                                                                                                  Hex Value $5D01
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                                                                                                                                                  • FR: L₂

                                                                                                                                                  L₂

                                                                                                                                                  Overview

                                                                                                                                                  Availability: Token available everywhere.

                                                                                                                                                  Syntax

                                                                                                                                                  L₂

                                                                                                                                                  Description

                                                                                                                                                  Examples

                                                                                                                                                  Explanation 1

                                                                                                                                                  code 1

                                                                                                                                                  Explanation 2

                                                                                                                                                  code 2

                                                                                                                                                  Error Conditions

                                                                                                                                                  Advanced Notes

                                                                                                                                                  History

                                                                                                                                                  Calculator OS Version Description
                                                                                                                                                  TI-82 1.0 Added
                                                                                                                                                  Property Value
                                                                                                                                                  Hex Value $5D02
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                                                                                                                                                  • FR: L₃

                                                                                                                                                  L₃

                                                                                                                                                  Overview

                                                                                                                                                  Availability: Token available everywhere.

                                                                                                                                                  Syntax

                                                                                                                                                  L₃

                                                                                                                                                  Description

                                                                                                                                                  Examples

                                                                                                                                                  Explanation 1

                                                                                                                                                  code 1

                                                                                                                                                  Explanation 2

                                                                                                                                                  code 2

                                                                                                                                                  Error Conditions

                                                                                                                                                  Advanced Notes

                                                                                                                                                  History

                                                                                                                                                  Calculator OS Version Description
                                                                                                                                                  TI-82 1.0 Added
                                                                                                                                                  Property Value
                                                                                                                                                  Hex Value $5D03
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                                                                                                                                                  • FR: L₄

                                                                                                                                                  L₄

                                                                                                                                                  Overview

                                                                                                                                                  Availability: Token available everywhere.

                                                                                                                                                  Syntax

                                                                                                                                                  L₄

                                                                                                                                                  Description

                                                                                                                                                  Examples

                                                                                                                                                  Explanation 1

                                                                                                                                                  code 1

                                                                                                                                                  Explanation 2

                                                                                                                                                  code 2

                                                                                                                                                  Error Conditions

                                                                                                                                                  Advanced Notes

                                                                                                                                                  History

                                                                                                                                                  Calculator OS Version Description
                                                                                                                                                  TI-82 1.0 Added
                                                                                                                                                  Property Value
                                                                                                                                                  Hex Value $5D04
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                                                                                                                                                  • FR: L₅

                                                                                                                                                  L₅

                                                                                                                                                  Overview

                                                                                                                                                  Availability: Token available everywhere.

                                                                                                                                                  Syntax

                                                                                                                                                  L₅

                                                                                                                                                  Description

                                                                                                                                                  Examples

                                                                                                                                                  Explanation 1

                                                                                                                                                  code 1

                                                                                                                                                  Explanation 2

                                                                                                                                                  code 2

                                                                                                                                                  Error Conditions

                                                                                                                                                  Advanced Notes

                                                                                                                                                  History

                                                                                                                                                  Calculator OS Version Description
                                                                                                                                                  TI-82 1.0 Added
                                                                                                                                                  Property Value
                                                                                                                                                  Hex Value $5D05
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                                                                                                                                                  • FR: L₆

                                                                                                                                                  L₆

                                                                                                                                                  Overview

                                                                                                                                                  Availability: Token available everywhere.

                                                                                                                                                  Syntax

                                                                                                                                                  L₆

                                                                                                                                                  Description

                                                                                                                                                  Examples

                                                                                                                                                  Explanation 1

                                                                                                                                                  code 1

                                                                                                                                                  Explanation 2

                                                                                                                                                  code 2

                                                                                                                                                  Error Conditions

                                                                                                                                                  Advanced Notes

                                                                                                                                                  History

                                                                                                                                                  Calculator OS Version Description
                                                                                                                                                  TI-82 1.0 Added
                                                                                                                                                  Property Value
                                                                                                                                                  Hex Value $4D
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                                                                                                                                                  • FR: M

                                                                                                                                                  M

                                                                                                                                                  Overview

                                                                                                                                                  Availability: Token available everywhere.

                                                                                                                                                  Syntax

                                                                                                                                                  M

                                                                                                                                                  Description

                                                                                                                                                  Examples

                                                                                                                                                  Explanation 1

                                                                                                                                                  code 1

                                                                                                                                                  Explanation 2

                                                                                                                                                  code 2

                                                                                                                                                  Error Conditions

                                                                                                                                                  Advanced Notes

                                                                                                                                                  History

                                                                                                                                                  Calculator OS Version Description
                                                                                                                                                  TI-82 1.0 Added
                                                                                                                                                  Property Value
                                                                                                                                                  Hex Value $EF44
                                                                                                                                                  Categories
                                                                                                                                                  Localizations
                                                                                                                                                  • FR: MAGENTA

                                                                                                                                                  MAGENTA

                                                                                                                                                  Overview

                                                                                                                                                  Availability: Token available everywhere.

                                                                                                                                                  Syntax

                                                                                                                                                  MAGENTA

                                                                                                                                                  Description

                                                                                                                                                  Examples

                                                                                                                                                  Explanation 1

                                                                                                                                                  code 1

                                                                                                                                                  Explanation 2

                                                                                                                                                  code 2

                                                                                                                                                  Error Conditions

                                                                                                                                                  Advanced Notes

                                                                                                                                                  History

                                                                                                                                                  Calculator OS Version Description
                                                                                                                                                  TI-84+CSE 4.0 Added
                                                                                                                                                  Property Value
                                                                                                                                                  Hex Value $EF37
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                                                                                                                                                    Localizations
                                                                                                                                                    • FR: MATHPRINT

                                                                                                                                                    MATHPRINT

                                                                                                                                                    Overview

                                                                                                                                                    Displays most entries and answers the way they are displayed in textbooks, such as .

                                                                                                                                                    Availability: Token available everywhere.

                                                                                                                                                    Syntax

                                                                                                                                                    MATHPRINT

                                                                                                                                                    Location

                                                                                                                                                    mode

                                                                                                                                                    Description

                                                                                                                                                    MATHPRINT will put the calculator into Mathprint mode as opposed to Classic mode. In MathPrint mode, enhanced homescreen input formatting is available. The Classic mode will make the calculator display everything as a calculator of lower OS would, including input. For instance, rather than superscripting exponents as Mathprint mode would, Classic mode uses the simple caret syntax (^).

                                                                                                                                                    Mathprint mode:
                                                                                                                                                    24
                                                                                                                                                         16

                                                                                                                                                    Classic mode:
                                                                                                                                                    2^4
                                                                                                                                                         16

                                                                                                                                                    When in Mathprint mode, text and numbers are displayed much slower than classic on the home screen and the function menus load slower. This can be inconvenient in games that use the home screen, but can also make solving equations that involve fractions and exponents easier as the numbers are in their correct positions and are the appropriate size.

                                                                                                                                                    Source: parts of this page were written by the following TI|BD contributors: burr, jonbush, Kydapoot.

                                                                                                                                                    History

                                                                                                                                                    Calculator OS Version Description
                                                                                                                                                    TI-84+ 2.53 Added
                                                                                                                                                    Property Value
                                                                                                                                                    Hex Value $EF4D
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                                                                                                                                                    • FR: GRIS MOY

                                                                                                                                                    MEDGRAY

                                                                                                                                                    Overview

                                                                                                                                                    Availability: Token available everywhere.

                                                                                                                                                    Syntax

                                                                                                                                                    MEDGRAY

                                                                                                                                                    Description

                                                                                                                                                    Examples

                                                                                                                                                    Explanation 1

                                                                                                                                                    code 1

                                                                                                                                                    Explanation 2

                                                                                                                                                    code 2

                                                                                                                                                    Error Conditions

                                                                                                                                                    Advanced Notes

                                                                                                                                                    History

                                                                                                                                                    Calculator OS Version Description
                                                                                                                                                    TI-84+CSE 4.0 Added
                                                                                                                                                    Property Value
                                                                                                                                                    Hex Value $EF16
                                                                                                                                                    Categories
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                                                                                                                                                      • FR: Manual-Fit

                                                                                                                                                      Manual-Fit

                                                                                                                                                      Overview

                                                                                                                                                      Fits a linear equation to a scatter plot with specified color and line style.
                                                                                                                                                      Color#: 10 - 24 or color name pasted from [vars] COLOR.
                                                                                                                                                      line style #: 1-4.

                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                      Syntax

                                                                                                                                                      Manual-Fit[equname,color#,line style#]

                                                                                                                                                      Arguments

                                                                                                                                                      NameTypeOptional
                                                                                                                                                      equnameYes
                                                                                                                                                      color#colorNumYes
                                                                                                                                                      line style#Yes

                                                                                                                                                      Location

                                                                                                                                                      stat, CALC, D:Manual-Fit

                                                                                                                                                      Description

                                                                                                                                                      This command will allow the user to create a line of best fit according to their judgment. Activate the command by just pasting it on the screen. Then, click on a point for the line to begin followed by an end point. The calculator will then draw your line and display its equation at the top left corner of the screen. You can modify it by selecting the equation part and pressing enter. Input your desired value for the calculator to change it. The equation is stored into Y₁. If you specify what equation you want to store it to, then it will store to that function.

                                                                                                                                                      :Manual-Fit
(this activates the command and stores to Y₁
:Manual-Fit Y₃
(this stores to Y₃ instead)

                                                                                                                                                      One note about this is that it only graphs linear models. It is written in the form y=mx+b, and you can modify m or b.
                                                                                                                                                      Exit out by 2nd QUIT.

                                                                                                                                                      Advanced Uses

                                                                                                                                                      This command is able to function in a program, but you cannot modify the values. This is a unique form of gathering user input that stores into the specified Y= function. Of course, this draws a line across the graph screen. You can then convert the function into a different form, like this:

                                                                                                                                                      :Manual-Fit
:Equ▶String(Y₁,Str1

                                                                                                                                                      This will turn the equation the user drew into a string which can then be used for output or calculations.

                                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: burr, thornahawk, Timothy Foster.

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-84+ 0.46 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $BB39
                                                                                                                                                      Categories
                                                                                                                                                      Localizations
                                                                                                                                                      • FR: Matr►list(

                                                                                                                                                      Matr►list(

                                                                                                                                                      Overview

                                                                                                                                                      Fills each listname with elements from each column in matrix.

                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                      Syntax

                                                                                                                                                      Matr►list(matrix,listnameA,...,listname n)

                                                                                                                                                      Arguments

                                                                                                                                                      NameTypeOptional
                                                                                                                                                      matrixmatrix
                                                                                                                                                      listnameAlist
                                                                                                                                                      ...
                                                                                                                                                      listname nlist

                                                                                                                                                      Location

                                                                                                                                                      2nd, list, OPS, A:Matr►list(

                                                                                                                                                      Overview

                                                                                                                                                      Fills a listname with elements from a specified column# in matrix.

                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                      Syntax

                                                                                                                                                      Matr►list(matrix,column#,listname)

                                                                                                                                                      Arguments

                                                                                                                                                      NameTypeOptional
                                                                                                                                                      matrixmatrix
                                                                                                                                                      column#
                                                                                                                                                      listnamelist

                                                                                                                                                      Location

                                                                                                                                                      2nd, list, OPS, A:Matr►list(

                                                                                                                                                      Description

                                                                                                                                                      The Matr►list( command stores one or more columns of a matrix (or expression resulting in a matrix) to list variables. The syntax is simple: first enter the matrix, then enter the list or lists you want to store columns to. The first (leftmost) column will be stored to the first list entered, the second column will be stored to the second list, and so on. For example:

                                                                                                                                                      [[11,12,13,14][21,22,23,24][31,32,33,34
        [[11 12 13 14]
         [21 22 23 24]
         [31 32 33 34]]
Matr►list(Ans,L1,L2
        Done
L1
        {11 21 31}
L2
        {12 22 32}

                                                                                                                                                      If there are more lists than columns in the matrix when doing Matr►list(, the extra lists will be ignored.

                                                                                                                                                      Matr►list( can also be used to extract a specific column of a matrix to a list. The order of the arguments is: matrix, column number, list name.

                                                                                                                                                      [[11,12,13,14][21,22,23,24][31,32,33,34
        [[11 12 13 14]
         [21 22 23 24]
         [31 32 33 34]]
Matr►list(Ans,4,L1
        Done
L1
        {14 24 34}

                                                                                                                                                      Advanced Uses

                                                                                                                                                      While the command deals with columns, occasionally you might want to store the matrix to lists by rows. The T (transpose) command is your friend here: applying it to the matrix will flip it diagonally, so that all rows will become columns and vice-versa. For example:

                                                                                                                                                      [[11,12,13,14][21,22,23,24][31,32,33,34
                                                                                                                                                               [[11 12 13 14]
                                                                                                                                                               [21 22 23 24]
                                                                                                                                                               [31 32 33 34]]
                                                                                                                                                      Matr►list(AnsT,L1,L2
                                                                                                                                                               Done
                                                                                                                                                      L1
                                                                                                                                                               {11 12 13 14}
                                                                                                                                                      L2
                                                                                                                                                               {21 22 23 24}

                                                                                                                                                      Optimizations

                                                                                                                                                      When using Matr►list( to store to named lists, only the first list must have an ʟ in front of its name — it can be omitted for the rest. For example:

                                                                                                                                                      :Matr►list([A],ʟCOL1,ʟCOL2,ʟCOL3
can be
:Matr►list([A],ʟCOL1,COL2,COL3

                                                                                                                                                      On the other hand, when storing a specific column of a matrix to a named list, the list does not need to be preceded by an ʟ.

                                                                                                                                                      :Matr►list([A],N,ʟCOL1
can be
:Matr►list([A],N,COL1

                                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, thornahawk, Timothy Foster.

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-83 0.01013 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $BB39
                                                                                                                                                      Categories
                                                                                                                                                      Localizations
                                                                                                                                                      • FR: Matr►list(

                                                                                                                                                      Matr►list(

                                                                                                                                                      Overview

                                                                                                                                                      Fills each listname with elements from each column in matrix.

                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                      Syntax

                                                                                                                                                      Matr►list(matrix,listnameA,...,listname n)

                                                                                                                                                      Arguments

                                                                                                                                                      NameTypeOptional
                                                                                                                                                      matrixmatrix
                                                                                                                                                      listnameAlist
                                                                                                                                                      ...
                                                                                                                                                      listname nlist

                                                                                                                                                      Location

                                                                                                                                                      2nd, list, OPS, A:Matr►list(

                                                                                                                                                      Overview

                                                                                                                                                      Fills a listname with elements from a specified column# in matrix.

                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                      Syntax

                                                                                                                                                      Matr►list(matrix,column#,listname)

                                                                                                                                                      Arguments

                                                                                                                                                      NameTypeOptional
                                                                                                                                                      matrixmatrix
                                                                                                                                                      column#
                                                                                                                                                      listnamelist

                                                                                                                                                      Location

                                                                                                                                                      2nd, list, OPS, A:Matr►list(

                                                                                                                                                      Description

                                                                                                                                                      The Matr►list( command stores one or more columns of a matrix (or expression resulting in a matrix) to list variables. The syntax is simple: first enter the matrix, then enter the list or lists you want to store columns to. The first (leftmost) column will be stored to the first list entered, the second column will be stored to the second list, and so on. For example:

                                                                                                                                                      [[11,12,13,14][21,22,23,24][31,32,33,34
        [[11 12 13 14]
         [21 22 23 24]
         [31 32 33 34]]
Matr►list(Ans,L1,L2
        Done
L1
        {11 21 31}
L2
        {12 22 32}

                                                                                                                                                      If there are more lists than columns in the matrix when doing Matr►list(, the extra lists will be ignored.

                                                                                                                                                      Matr►list( can also be used to extract a specific column of a matrix to a list. The order of the arguments is: matrix, column number, list name.

                                                                                                                                                      [[11,12,13,14][21,22,23,24][31,32,33,34
        [[11 12 13 14]
         [21 22 23 24]
         [31 32 33 34]]
Matr►list(Ans,4,L1
        Done
L1
        {14 24 34}

                                                                                                                                                      Advanced Uses

                                                                                                                                                      While the command deals with columns, occasionally you might want to store the matrix to lists by rows. The T (transpose) command is your friend here: applying it to the matrix will flip it diagonally, so that all rows will become columns and vice-versa. For example:

                                                                                                                                                      [[11,12,13,14][21,22,23,24][31,32,33,34
                                                                                                                                                               [[11 12 13 14]
                                                                                                                                                               [21 22 23 24]
                                                                                                                                                               [31 32 33 34]]
                                                                                                                                                      Matr►list(AnsT,L1,L2
                                                                                                                                                               Done
                                                                                                                                                      L1
                                                                                                                                                               {11 12 13 14}
                                                                                                                                                      L2
                                                                                                                                                               {21 22 23 24}

                                                                                                                                                      Optimizations

                                                                                                                                                      When using Matr►list( to store to named lists, only the first list must have an ʟ in front of its name — it can be omitted for the rest. For example:

                                                                                                                                                      :Matr►list([A],ʟCOL1,ʟCOL2,ʟCOL3
can be
:Matr►list([A],ʟCOL1,COL2,COL3

                                                                                                                                                      On the other hand, when storing a specific column of a matrix to a named list, the list does not need to be preceded by an ʟ.

                                                                                                                                                      :Matr►list([A],N,ʟCOL1
can be
:Matr►list([A],N,COL1

                                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, thornahawk, Timothy Foster.

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-83 0.01013 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $F8
                                                                                                                                                      Categories
                                                                                                                                                      Localizations
                                                                                                                                                      • FR: Med-Med

                                                                                                                                                      Med-Med

                                                                                                                                                      Overview

                                                                                                                                                      Fits a median-median model to Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ.

                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                      Syntax

                                                                                                                                                      Med-Med [Xlistname,Ylistname,freqlist,regequ]

                                                                                                                                                      Arguments

                                                                                                                                                      NameTypeOptional
                                                                                                                                                      XlistnamelistYes
                                                                                                                                                      YlistnamelistYes
                                                                                                                                                      freqlistlistYes
                                                                                                                                                      regequYes

                                                                                                                                                      Location

                                                                                                                                                      stat, CALC, 3:Med-Med

                                                                                                                                                      Description

                                                                                                                                                      The Med-Med command is one of several that can calculate a line of best fit through a set of points. However, unlike the LinReg(ax+b) and LinReg(a+bx) commands, which generate the same result in different formats, Med-Med produces a different line entirely, known as the 'median fit line' or the 'median-median model'. This model is more resistant to outliers than the best-fit line produced by LinReg(ax+b)-type commands, in much the same way that the median of a set of data is more resistant to outliers than the mean. The process of calculating a median fit line is roughly as follows (reference):

                                                                                                                                                      1. Divide the data into three equal groups by their x-values (the smallest third, the middle third, and the largest third)
                                                                                                                                                      2. Find the "median point" for each group by pairing the median x-value in the group with the median y-value (this need not be an actual data point).
                                                                                                                                                      3. These points are stored to (x₁,y₁), (x₂,y₂), and (x₃,y₃) on the calculator.
                                                                                                                                                      4. Find the line passing through the median point for the first and third group.
                                                                                                                                                      5. Shift this line one-third of the way toward the median point of the second group.

                                                                                                                                                      To use the Med-Med command, you must first store the points to two lists: one of the x-coordinates and one of the y-coordinates, ordered so that the nth element of one list matches up with the nth element of the other list. L₁ and L₂ are the default lists to use, and the List Editor (STAT > Edit…) is a useful window for entering the points. As you can see from the steps shown above, Med-Med requires at least three points with different x-values to work with.

                                                                                                                                                      In its simplest form, Med-Med takes no arguments, and calculates a regression line through the points in L₁ and L₂:

                                                                                                                                                      :{9,13,21,30,31,31,34→L₁
:{260,320,420,530,560,550,590→L₂
:Med-Med

                                                                                                                                                      On the home screen, or as the last line of a program, this will display the equation of the regression line: you'll be shown the format, y=ax+b, and the values of a and b. It will also be stored in the RegEQ variable, but you won't be able to use this variable in a program - accessing it just pastes the equation wherever your cursor was. Finally, the statistical variables a and b will be set as well. There are no diagnostics available for the Med-Med command, so r and r² will not be calculated or displayed even if you run DiagnosticOn.

                                                                                                                                                      You don't have to do the regression on L₁ and L₂, but if you don't you'll have to enter the names of the lists after the command. For example:

                                                                                                                                                      :{9,13,21,30,31,31,34→FAT
:{260,320,420,530,560,550,590→CALS
:Med-Med ʟFAT,ʟCALS

                                                                                                                                                      You can attach frequencies to points, for when a point occurs more than once, by supplying an additional argument - the frequency list. This list does not have to contain integer frequencies. If you add a frequency list, you must supply the names of the x-list and y-list as well, even when they're L₁ and L₂.

                                                                                                                                                      Finally, you can enter an equation variable (such as Y₁) after the command, so that the line of best fit is stored to this equation automatically. This doesn't require you to supply the names of the lists, but if you do, the equation variable must come last. You can use polar, parametric, or sequential variables as well, but since the line of best fit will be in terms of X anyway, this doesn't make much sense.

                                                                                                                                                      An example of Med-Med with all the optional arguments:

                                                                                                                                                      :{9,13,21,30,31,31,34→FAT
:{260,320,420,530,560,550,590→CALS
:{2,1,1,1,2,1,1→FREQ
:Med-Med ʟFAT,ʟCALS,ʟFREQ,Y₁

                                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, thornahawk, Timothy Foster.

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $E6
                                                                                                                                                      Categories
                                                                                                                                                      Localizations
                                                                                                                                                      • FR: Menu(

                                                                                                                                                      Menu(

                                                                                                                                                      Overview

                                                                                                                                                      Generates a menu of up to seven items during program execution.

                                                                                                                                                      Availability: Token only available from within the Basic editor.

                                                                                                                                                      Syntax

                                                                                                                                                      Menu("title","text1",label1[,...,"text7",label7])

                                                                                                                                                      Arguments

                                                                                                                                                      NameTypeOptional
                                                                                                                                                      title
                                                                                                                                                      text1string
                                                                                                                                                      label1
                                                                                                                                                      ...Yes
                                                                                                                                                      text7stringYes
                                                                                                                                                      label7Yes

                                                                                                                                                      Location

                                                                                                                                                      prgm, CTL, C:Menu(

                                                                                                                                                      Description

                                                                                                                                                      Menus are used for organization, to provide a list of choices for the user to select from, as well as a good way for users to interact with and navigate programs. Although using the Menu( command requires branching (which is generally frowned upon in most circumstances), the menu looks like a generic built-in menu, so it is familiar and easy to use for the user.

                                                                                                                                                      When the Menu( command is encountered during a program, the menu screen is displayed with the specified menu title in white-on-black text on the top line and each menu item listed below on its own line, the pause indicator turns on, and execution pauses until the user selects a menu item. There is a cursor that the user can move up and down the menu to select a menu item.

                                                                                                                                                      The menu title can be 16 characters or less on monochrome calculators (because of the screen width), and 26 characters or less on color calculators, and must be enclosed in a pair of quotation marks. The menu title looks best if you center it on the screen (using spaces to fill in the rest of the line), so that the entire top line will be highlighted. The menu can have up to seven menu items on monochrome and up to nine on color calculators (because of the screen height and the menu title on top).

                                                                                                                                                      After the menu title, you put a comma and then the menu items. There are two parts to a menu item: the text that will be displayed on the screen and the label that program execution will continue at if the user presses ENTER on the menu item or presses its corresponding number. The text can be fourteen characters or less on monochrome and 24 or less on color (because the menu item number is displayed on the left) and must be enclosed in a pair of quotation marks, and you have to separate the text and label with a comma.

                                                                                                                                                      PROGRAM:MENU
:Lbl NY
:Menu(" Select A Place ","NY",NY,"LA",NY,"MN",MN
:Lbl MN
:Disp "Good Choice!

                                                                                                                                                      Advanced Uses

                                                                                                                                                      When a program needs more than seven (or nine on color calculators) menu items, you will have to create another menu and then link to that menu from the first menu with one of the menu items. Similarly, you can also have two menu items go to the same label (you do not need two labels if they are right next to each other).

                                                                                                                                                      If you get tired of using the Menu( command every time you want to make a menu, the alternative is to make your own custom menu. A custom menu provides a richer experience for the user, and isn't much more work than using the Menu( command. In addition, as you get more experienced as a programmer, you'll come to enjoy using custom menus.

                                                                                                                                                      You can use a string variable for the menu title and menu item text instead of the text in quotes, which may sometimes be smaller if the text is used at other places in the program. Similarly, its possible to place all the menu titles in one string variable, and then just access the respective menu title as a substring Unfortunately, variables will not work for the menu item labels. You can also leave the menu title blank to give the illusion that there is no menu title by using two quotes side by side (i.e. "").

                                                                                                                                                      For many programs, including text-based programs (where menus are heavily used), there is a main menu that is used for navigating to the different parts of the program. While each program's main menu is unique, two of the most standard menu items on a main menu are Start and Quit — Start goes to the beginning of the program, while Quit goes to the end. It is also fairly common to place a label right before the main menu, so you can return to it again later in the program.

                                                                                                                                                      Problems

                                                                                                                                                      1. There is only one line for the title.
                                                                                                                                                      2. There are only seven (or nine on color calculators) slots for the menu items and no scrolling (you CAN add a "next" at the bottom, but that just looks bad, especially if you have a "back" and/or "exit" down there already)
                                                                                                                                                      3. The screen refreshes or blinks when you press down at the bottom to go back to the top.
                                                                                                                                                      4. During the loading of the menu, you can see what is written on the home screen.

                                                                                                                                                      Optimization

                                                                                                                                                      Because the Menu( command displays the menu screen instead of clearing the home screen, you do not need to put the ClrHome command before it.

                                                                                                                                                      :ClrHome
:Menu("Choose","Right",1,"Wrong",2
Remove ClrHome
:Menu("Choose","Right",1,"Wrong",2

                                                                                                                                                      Error Conditions

                                                                                                                                                      • ERR:INVALID occurs if this statement is used outside a program.
                                                                                                                                                      • ERR:LABEL is thrown when an option is chosen whose label doesn't exist.

                                                                                                                                                      See Also

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                                                                                                                                                      Featured Article

                                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: burr, CloudVariable, DarkerLine, GoVegan, Myles_Zadok, olin3434, Timothy Foster, Trenly.

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $BB5A
                                                                                                                                                      Categories
                                                                                                                                                      Localizations
                                                                                                                                                      • FR: GraphBoitMoust

                                                                                                                                                      ModBoxplot

                                                                                                                                                      Overview

                                                                                                                                                      Used as the "type" argument in the command.
                                                                                                                                                      Where # gives Plot1, Plot2 or Plot3.

                                                                                                                                                      Availability: Token only available from within the Basic editor.

                                                                                                                                                      Syntax

                                                                                                                                                      Plot#(type,Xlist[,freqlist,color#])

                                                                                                                                                      Arguments

                                                                                                                                                      NameTypeOptional
                                                                                                                                                      typeModBoxplot token
                                                                                                                                                      Xlistlist
                                                                                                                                                      freqlistlist
                                                                                                                                                      color#colorNum

                                                                                                                                                      Location

                                                                                                                                                      2nd, stat plot, TYPE

                                                                                                                                                      Description

                                                                                                                                                      The commands Plot1(, Plot2(, and Plot3(, which are identical except for which stat plot (1, 2, or 3) they affect, define their corresponding stat plot. When the stat plot is defined, it is also turned on so no PlotsOn command is necessary.

                                                                                                                                                      The first argument of the commands is always the type of plot, and is one of Scatter, xyLine, Histogram, Boxplot, ModBoxplot, and NormProbPlot - these types are found in the TYPE submenu of the stat plot menu. The other arguments vary. For all but Histogram and Boxplot, there is a mark argument - this is a dot, a cross, or a box, symbols that can be found in the MARK submenu of the stat plot menu. On color calculators, there is an optional final argument to specify the color of the plot.

                                                                                                                                                      Scatter plot

                                                                                                                                                      Plot#(Scatter, x-list, y-list, mark) defines a scatter plot. The points defined by x-list and y-list are plotted using mark on the graph screen.

                                                                                                                                                      x-list and y-list must be the same length.

                                                                                                                                                      xyLine plot

                                                                                                                                                      Plot#(xyLine, x-list, y-list, mark) defines an xyLine plot. Similarly to a scatter plot, the points defined by x-list and y-list are plotted using mark on the graph screen, but with an xyLine plot they are also connected by a line, in the order that they occur in the lists.

                                                                                                                                                      x-list and y-list must be the same length.

                                                                                                                                                      Histogram plot

                                                                                                                                                      Plot#(Histogram, x-list, freq list) defines a Histogram plot. The x-axis is divided into intervals that are Xscl wide. A bar is drawn in in each interval whose height corresponds to the number of points in the interval. Points that are not between Xmin and Xmax are not tallied.

                                                                                                                                                      Xscl must not be too small - it can divide the screen into no more than 47 different bars.

                                                                                                                                                      Box plot

                                                                                                                                                      Plot#(Boxplot, x-list, freq list) defines a box plot. A rectangular box is drawn whose left edge is Q1 (the first quartile) of the data, and whose right edge is Q3 (the third quartile). A vertical segment is drawn within the box at the median, and 'whiskers' are drawn from the box to the minimum and maximum data points.

                                                                                                                                                      The box plot ignores the Ymax and Ymin dimensions of the screen, and any plots that aren't box plots or modified box plots. Each box plot takes approximately 1/3 of the screen in height, and if more than one are plotted, they will take up different areas of the screen.

                                                                                                                                                      Modified box plot

                                                                                                                                                      Plot#(ModBoxplot, x-list, freq list, mark) defines a modified box plot. This is almost entirely like the normal box plot, except that it also draws outliers. Whiskers are only drawn to the furthers point within 1.5 times the interquartile range (Q3-Q1) of the box. Beyond this point, data points are drawn individually, using mark.

                                                                                                                                                      The box plot ignores the Ymax and Ymin dimensions of the screen, and any plots that aren't box plots or modified box plots. Each box plot takes approximately 1/3 of the screen in height, and if more than one are plotted, they will take up different areas of the screen.

                                                                                                                                                      Normal probability plot

                                                                                                                                                      Plot#(NormProbPlot, data list, data axis, mark) defines a normal probability plot. The mean and standard deviation of the data are calculated. Then for each point, the number of standard deviations it is from the mean is calculated, and the point is plotted against this number using mark. data axis can be either X or Y: it determines whether the value of a point determines it's x-coordinate or y-coordinate.

                                                                                                                                                      The point behind this rather convoluted process is to test the extent to which the data is normally distributed. If it follows the normal distribution closely, then the result will be close to a straight line - otherwise it will be curved.

                                                                                                                                                      Advanced Uses

                                                                                                                                                      After doing a regression, a scatter plot of ʟRESID against the x-list is a useful measure of the effectiveness of the regression. If the plot appears random, this is a good sign; if there is a pattern to the plot, this means it's likely that a better regression model exists.

                                                                                                                                                      Optimization

                                                                                                                                                      The ʟ symbol at the beginning of list names can be omitted everywhere in this command.

                                                                                                                                                      In addition, every element except the plot type and the data list or data lists are optional, and take on the following default values:

                                                                                                                                                      • freq list is 1 by default, meaning that all frequencies are 1.
                                                                                                                                                      • mark is the box by default.
                                                                                                                                                      • data axis is X by default.

                                                                                                                                                      Error Conditions

                                                                                                                                                      • ERR:DIM MISMATCH is thrown if the x and y lists, or the data and frequency lists, have different dimensions.
                                                                                                                                                      • ERR:STAT is thrown if Xscl is too small in the case of a Histogram.

                                                                                                                                                      All errors are thrown when plotting the stat plot, as opposed to when the command is executed, and do not provide a 2:Goto option.

                                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Myles_Zadok.

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-83 0.01013 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $4E
                                                                                                                                                      Categories
                                                                                                                                                      Localizations
                                                                                                                                                      • FR: N

                                                                                                                                                      N

                                                                                                                                                      Overview

                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                      Syntax

                                                                                                                                                      N

                                                                                                                                                      Description

                                                                                                                                                      Examples

                                                                                                                                                      Explanation 1

                                                                                                                                                      code 1

                                                                                                                                                      Explanation 2

                                                                                                                                                      code 2

                                                                                                                                                      Error Conditions

                                                                                                                                                      Advanced Notes

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $EF48
                                                                                                                                                      Categories
                                                                                                                                                      Localizations
                                                                                                                                                      • FR: BLEU MRN

                                                                                                                                                      NAVY

                                                                                                                                                      Overview

                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                      Syntax

                                                                                                                                                      NAVY

                                                                                                                                                      Description

                                                                                                                                                      Examples

                                                                                                                                                      Explanation 1

                                                                                                                                                      code 1

                                                                                                                                                      Explanation 2

                                                                                                                                                      code 2

                                                                                                                                                      Error Conditions

                                                                                                                                                      Advanced Notes

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-84+CSE 4.0 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $632B
                                                                                                                                                      Categories
                                                                                                                                                      Localizations
                                                                                                                                                      • FR: 𝗡

                                                                                                                                                      𝗡

                                                                                                                                                      Overview

                                                                                                                                                      Syntax

                                                                                                                                                      𝗡

                                                                                                                                                      Description

                                                                                                                                                      Examples

                                                                                                                                                      Explanation 1

                                                                                                                                                      code 1

                                                                                                                                                      Explanation 2

                                                                                                                                                      code 2

                                                                                                                                                      Error Conditions

                                                                                                                                                      Advanced Notes

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-83 0.01013 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $BB5B
                                                                                                                                                      Categories
                                                                                                                                                      Localizations
                                                                                                                                                      • FR: GraphProbNorm

                                                                                                                                                      NormProbPlot

                                                                                                                                                      Overview

                                                                                                                                                      Used as the "type" argument in the command
                                                                                                                                                      Where # gives Plot1, Plot2 or Plot3.

                                                                                                                                                      Availability: Token only available from within the Basic editor.

                                                                                                                                                      Syntax

                                                                                                                                                      Plot#(type,Xlist[,freqlist,color#])

                                                                                                                                                      Arguments

                                                                                                                                                      NameTypeOptional
                                                                                                                                                      typeNormProbPlot token
                                                                                                                                                      Xlistlist
                                                                                                                                                      freqlistlist
                                                                                                                                                      color#colorNum

                                                                                                                                                      Location

                                                                                                                                                      2nd, stat plot, TYPE

                                                                                                                                                      Description

                                                                                                                                                      The commands Plot1(, Plot2(, and Plot3(, which are identical except for which stat plot (1, 2, or 3) they affect, define their corresponding stat plot. When the stat plot is defined, it is also turned on so no PlotsOn command is necessary.

                                                                                                                                                      The first argument of the commands is always the type of plot, and is one of Scatter, xyLine, Histogram, Boxplot, ModBoxplot, and NormProbPlot - these types are found in the TYPE submenu of the stat plot menu. The other arguments vary. For all but Histogram and Boxplot, there is a mark argument - this is a dot, a cross, or a box, symbols that can be found in the MARK submenu of the stat plot menu. On color calculators, there is an optional final argument to specify the color of the plot.

                                                                                                                                                      Scatter plot

                                                                                                                                                      Plot#(Scatter, x-list, y-list, mark) defines a scatter plot. The points defined by x-list and y-list are plotted using mark on the graph screen.

                                                                                                                                                      x-list and y-list must be the same length.

                                                                                                                                                      xyLine plot

                                                                                                                                                      Plot#(xyLine, x-list, y-list, mark) defines an xyLine plot. Similarly to a scatter plot, the points defined by x-list and y-list are plotted using mark on the graph screen, but with an xyLine plot they are also connected by a line, in the order that they occur in the lists.

                                                                                                                                                      x-list and y-list must be the same length.

                                                                                                                                                      Histogram plot

                                                                                                                                                      Plot#(Histogram, x-list, freq list) defines a Histogram plot. The x-axis is divided into intervals that are Xscl wide. A bar is drawn in in each interval whose height corresponds to the number of points in the interval. Points that are not between Xmin and Xmax are not tallied.

                                                                                                                                                      Xscl must not be too small - it can divide the screen into no more than 47 different bars.

                                                                                                                                                      Box plot

                                                                                                                                                      Plot#(Boxplot, x-list, freq list) defines a box plot. A rectangular box is drawn whose left edge is Q1 (the first quartile) of the data, and whose right edge is Q3 (the third quartile). A vertical segment is drawn within the box at the median, and 'whiskers' are drawn from the box to the minimum and maximum data points.

                                                                                                                                                      The box plot ignores the Ymax and Ymin dimensions of the screen, and any plots that aren't box plots or modified box plots. Each box plot takes approximately 1/3 of the screen in height, and if more than one are plotted, they will take up different areas of the screen.

                                                                                                                                                      Modified box plot

                                                                                                                                                      Plot#(ModBoxplot, x-list, freq list, mark) defines a modified box plot. This is almost entirely like the normal box plot, except that it also draws outliers. Whiskers are only drawn to the furthers point within 1.5 times the interquartile range (Q3-Q1) of the box. Beyond this point, data points are drawn individually, using mark.

                                                                                                                                                      The box plot ignores the Ymax and Ymin dimensions of the screen, and any plots that aren't box plots or modified box plots. Each box plot takes approximately 1/3 of the screen in height, and if more than one are plotted, they will take up different areas of the screen.

                                                                                                                                                      Normal probability plot

                                                                                                                                                      Plot#(NormProbPlot, data list, data axis, mark) defines a normal probability plot. The mean and standard deviation of the data are calculated. Then for each point, the number of standard deviations it is from the mean is calculated, and the point is plotted against this number using mark. data axis can be either X or Y: it determines whether the value of a point determines it's x-coordinate or y-coordinate.

                                                                                                                                                      The point behind this rather convoluted process is to test the extent to which the data is normally distributed. If it follows the normal distribution closely, then the result will be close to a straight line - otherwise it will be curved.

                                                                                                                                                      Advanced Uses

                                                                                                                                                      After doing a regression, a scatter plot of ʟRESID against the x-list is a useful measure of the effectiveness of the regression. If the plot appears random, this is a good sign; if there is a pattern to the plot, this means it's likely that a better regression model exists.

                                                                                                                                                      Optimization

                                                                                                                                                      The ʟ symbol at the beginning of list names can be omitted everywhere in this command.

                                                                                                                                                      In addition, every element except the plot type and the data list or data lists are optional, and take on the following default values:

                                                                                                                                                      • freq list is 1 by default, meaning that all frequencies are 1.
                                                                                                                                                      • mark is the box by default.
                                                                                                                                                      • data axis is X by default.

                                                                                                                                                      Error Conditions

                                                                                                                                                      • ERR:DIM MISMATCH is thrown if the x and y lists, or the data and frequency lists, have different dimensions.
                                                                                                                                                      • ERR:STAT is thrown if Xscl is too small in the case of a Histogram.

                                                                                                                                                      All errors are thrown when plotting the stat plot, as opposed to when the command is executed, and do not provide a 2:Goto option.

                                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Myles_Zadok.

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-83 0.01013 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $66
                                                                                                                                                      Categories
                                                                                                                                                      Localizations
                                                                                                                                                      • FR: Normal

                                                                                                                                                      Normal

                                                                                                                                                      Overview

                                                                                                                                                      Sets normal display mode.

                                                                                                                                                      Availability: Token only available from within the Basic editor.

                                                                                                                                                      Syntax

                                                                                                                                                      Normal

                                                                                                                                                      Location

                                                                                                                                                      mode, Normal

                                                                                                                                                      Description

                                                                                                                                                      The Normal command puts the calculator in normal number mode, in which it only uses scientific notation for large enough numbers (10 000 000 000 or higher), negative numbers large enough in absolute value (-10 000 000 000 or lower), or numbers close enough to 0 (less than .001 and greater than -.001)

                                                                                                                                                      The other possible settings are Sci (which always uses scientific notation), or Eng (which uses a specific form of scientific notation based on powers of 1000)

                                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan.

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $4F
                                                                                                                                                      Categories
                                                                                                                                                      Localizations
                                                                                                                                                      • FR: O

                                                                                                                                                      O

                                                                                                                                                      Overview

                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                      Syntax

                                                                                                                                                      O

                                                                                                                                                      Description

                                                                                                                                                      Examples

                                                                                                                                                      Explanation 1

                                                                                                                                                      code 1

                                                                                                                                                      Explanation 2

                                                                                                                                                      code 2

                                                                                                                                                      Error Conditions

                                                                                                                                                      Advanced Notes

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $EF46
                                                                                                                                                      Categories
                                                                                                                                                      Localizations
                                                                                                                                                      • FR: ORANGE

                                                                                                                                                      ORANGE

                                                                                                                                                      Overview

                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                      Syntax

                                                                                                                                                      ORANGE

                                                                                                                                                      Description

                                                                                                                                                      Examples

                                                                                                                                                      Explanation 1

                                                                                                                                                      code 1

                                                                                                                                                      Explanation 2

                                                                                                                                                      code 2

                                                                                                                                                      Error Conditions

                                                                                                                                                      Advanced Notes

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-84+CSE 4.0 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $BBAC
                                                                                                                                                      Categories
                                                                                                                                                      Localizations
                                                                                                                                                      • FR: Ω

                                                                                                                                                      Ω

                                                                                                                                                      Overview

                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                      Syntax

                                                                                                                                                      Ω

                                                                                                                                                      Description

                                                                                                                                                      Examples

                                                                                                                                                      Explanation 1

                                                                                                                                                      code 1

                                                                                                                                                      Explanation 2

                                                                                                                                                      code 2

                                                                                                                                                      Error Conditions

                                                                                                                                                      Advanced Notes

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-83+ 1.03 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $EF11
                                                                                                                                                      Categories
                                                                                                                                                      Localizations
                                                                                                                                                      • FR: OuvrirBiblio(

                                                                                                                                                      OpenLib(

                                                                                                                                                      Overview

                                                                                                                                                      Extends TI-Basic. (Not available.)

                                                                                                                                                      Availability: Token only available from within the Basic editor.

                                                                                                                                                      Syntax

                                                                                                                                                      OpenLib(

                                                                                                                                                      Location

                                                                                                                                                      prgm, CTL, J:OpenLib(

                                                                                                                                                      Description

                                                                                                                                                      Together with ExecLib, OpenLib( is used on the TI-84 Plus and TI-84 Plus SE for running routines from a Flash App library. This only works, of course, with libraries that have been specifically written for this purpose. The only such library so far is usb8x, for advanced interfacing with the USB port.

                                                                                                                                                      The following program, which displays the version of usb8x, is an example of how to use OpenLib( and ExecLib:

                                                                                                                                                      :OpenLib(USBDRV8X
:{6
:ExecLib
:Ans(2)+.01Ans(3

                                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, kg583, seb83.

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-84+ 0.01 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $E0
                                                                                                                                                      Categories
                                                                                                                                                      Localizations
                                                                                                                                                      • FR: Output(

                                                                                                                                                      Output(

                                                                                                                                                      Overview

                                                                                                                                                      Displays text beginning at specified row and columnof the home screen.

                                                                                                                                                      Availability: Token only available from within the Basic editor.

                                                                                                                                                      Syntax

                                                                                                                                                      Output(row,column,"text")

                                                                                                                                                      Arguments

                                                                                                                                                      NameTypeOptional
                                                                                                                                                      row
                                                                                                                                                      column
                                                                                                                                                      textstring

                                                                                                                                                      Location

                                                                                                                                                      prgm, I/O, 6:Output(

                                                                                                                                                      Overview

                                                                                                                                                      Displays value beginning at specified row and columnof the home screen.

                                                                                                                                                      Availability: Token only available from within the Basic editor.

                                                                                                                                                      Syntax

                                                                                                                                                      Output(row,column,value)

                                                                                                                                                      Arguments

                                                                                                                                                      NameTypeOptional
                                                                                                                                                      row
                                                                                                                                                      column
                                                                                                                                                      value

                                                                                                                                                      Location

                                                                                                                                                      prgm, I/O, 6:Output(

                                                                                                                                                      Description

                                                                                                                                                      The Output( command is the fastest way to display text on the home screen. It takes three arguments: the row (1-8) at which you want to display something, the column (1-16), and whatever it is you want to display. It allows for more freedom than the Disp command.

                                                                                                                                                      Although off-screen values for the row and column values will cause an error, it's okay if part of the text displayed goes off the screen. When text goes past the last (16th on monochrome calculators, 26th on color calculators) column, it will wrap to the first column of the next row. If the text goes past the last column of the last row, the remainder will be truncated. Output( will never cause the screen to scroll.

                                                                                                                                                      When the horizontal screen split mode is activated, only the first four rows of the home screen are available for the Output( command, which may cause undesirable behavior, and trying to output to the last four rows will cause an error. It is advisable to use the Full command at the beginning of a program that relies on Output(.

                                                                                                                                                      Like other text display commands, you can display each function and command as text. However, this is not without problems as each function and command is counted as one character. The two characters that you can't display are quotation marks (") and the store command (→). However, you can mimic these respectively by using two apostrophes (' ' ), and two subtract signs and a greater than sign (—>).

                                                                                                                                                      Advanced Uses

                                                                                                                                                      If the last text display command of a program is an Output( command, then "Done" will not be displayed as the program finishes. Some programmers use this to get rid of the Done message by using an empty Output( command at the end (there is no text after the quote):

                                                                                                                                                      :Output(1,1,"

                                                                                                                                                      This trick does not work on recent "MathPrint" OSes.

                                                                                                                                                      You can also use Output( to get rid of the run indicator. Unfortunately, it only silences it for a moment and needs to be repeated in a loop to make it appear to be gone. In a game, it should be incorporated into the main loop. The run indicator is momentarily stopped every time that you output something to the upper right corner, it just needs to be repeated for it to appear to be gone. If you're on the graph screen, you can accomplish the same thing using the Text( command.

                                                                                                                                                      :Output(1,16," "

                                                                                                                                                      Since the text displayed by an Output( command wraps, a single command can be used to overwrite the entire screen by displaying 816=128 (1026=260 for color calculators) characters of text starting from row 1, column 1. Since every space on the screen is overwritten, this does not require a ClrHome to clear previously displayed characters. Keep in mind that exactly 16 (26 on color calculators) characters will be on each line.

                                                                                                                                                      Optimization

                                                                                                                                                      Output( does not allow for more than one expression to be displayed by a single command. However, if several strings are going to be displayed next to each other by several commands they might be combined into one (keep in mind how wrapping works):

                                                                                                                                                      :Output(3,3,"Some Text Here
:Output(4,3,"More Text Here
can be
:Output(3,3,"Some Text Here    More Text Here

                                                                                                                                                      In addition, if you are displaying text on the entire home screen, you can place the all the text in a string and then simply display the string. This is especially useful when combined with movement because you can shift the screen quite easily.

                                                                                                                                                      :Output(1,1,Str1

                                                                                                                                                      Command Timings

                                                                                                                                                      The Output( command is the fastest possible way of displaying text (short of storing text to a picture and then recalling it). In particular, when going for speed, it should be preferred instead of Disp.

                                                                                                                                                      Error Conditions

                                                                                                                                                      • ERR:DOMAIN is thrown when the starting row or column are not integers in the valid range (this is affected by split screen mode).
                                                                                                                                                      • ERR:INVALID occurs if this statement is used outside a program.
                                                                                                                                                      • An error is not thrown when the argument is an empty list (unlike with Disp or pretty much anything else, really)

                                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: burr, CloudVariable, DarkerLine, GoVegan, kg583, Myles_Zadok, persalteas, Sleight, Trenly.

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $50
                                                                                                                                                      Categories
                                                                                                                                                      Localizations
                                                                                                                                                      • FR: P

                                                                                                                                                      P

                                                                                                                                                      Overview

                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                      Syntax

                                                                                                                                                      P

                                                                                                                                                      Description

                                                                                                                                                      Examples

                                                                                                                                                      Explanation 1

                                                                                                                                                      code 1

                                                                                                                                                      Explanation 2

                                                                                                                                                      code 2

                                                                                                                                                      Error Conditions

                                                                                                                                                      Advanced Notes

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $632E
                                                                                                                                                      Categories
                                                                                                                                                      Localizations
                                                                                                                                                      • FR: PMT

                                                                                                                                                      PMT

                                                                                                                                                      Overview

                                                                                                                                                      Syntax

                                                                                                                                                      PMT

                                                                                                                                                      Description

                                                                                                                                                      Examples

                                                                                                                                                      Explanation 1

                                                                                                                                                      code 1

                                                                                                                                                      Explanation 2

                                                                                                                                                      code 2

                                                                                                                                                      Error Conditions

                                                                                                                                                      Advanced Notes

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-83 0.01013 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $1D
                                                                                                                                                      Categories
                                                                                                                                                      Localizations
                                                                                                                                                      • FR: P►Rx(

                                                                                                                                                      P►Rx(

                                                                                                                                                      Overview

                                                                                                                                                      Returns X, given polar coordinates r and θ or a list of polar coordinates.

                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                      Syntax

                                                                                                                                                      P►Rx(r,θ)

                                                                                                                                                      Arguments

                                                                                                                                                      NameTypeOptional
                                                                                                                                                      r
                                                                                                                                                      θ

                                                                                                                                                      Location

                                                                                                                                                      2nd, angle, ANGLE, 7:P, Rx(

                                                                                                                                                      Description

                                                                                                                                                      P►Rx( (polar►rectangular x-coordinate) calculates the x-coordinate of a polar point. Polar coordinates are of the form (r,θ), where θ is the counterclockwise angle made with the positive x-axis, and r is the distance away from the origin (the point (0,0)). The conversion identity x=r*cos(θ) is used to calculate P►Rx(.

                                                                                                                                                      The value returned depends on whether the calculator is in radian or degree mode. A full rotation around a circle is 2π radians, which is equal to 360°. The conversion from radians to degrees is angle180/π and from degrees to radians is angleπ/180. The P►Rx( command also accepts a list of points.

                                                                                                                                                      P►Rx(5,π/4)
    3.535533906
5*cos(π/4)
    3.535533906
P►Rx({1,2},{π/4,π/3})
    {.7071067812 1}

                                                                                                                                                      Advanced Uses

                                                                                                                                                      You can bypass the mode setting by using the ° (degree) and ʳ (radian) symbols. This next command will return the same values no matter if your calculator is in degrees or radians:

                                                                                                                                                      P►Rx(1,{π/4^^r,60°})
    {.7071067812 .5}

                                                                                                                                                      Optimization

                                                                                                                                                      In most cases P►Rx(r,θ) can be replaced by r*cos(θ) to save a byte:

                                                                                                                                                      :P►Rx(5,π/12)
can be
:5cos(π/12)

                                                                                                                                                      Conversely, complicated expressions multiplied by a cosine factor can be simplified by using P►Rx(r,θ) instead.

                                                                                                                                                      :(A+BX)cos(π/5)
can be
:P►Rx(A+BX,π/5)

                                                                                                                                                      Error Conditions

                                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: CloudVariable, DarkerLine, GoVegan, simplethinker, thornahawk.

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $1E
                                                                                                                                                      Categories
                                                                                                                                                      Localizations
                                                                                                                                                      • FR: P►Ry(

                                                                                                                                                      P►Ry(

                                                                                                                                                      Overview

                                                                                                                                                      Returns Y, given polar coordinates r and θ or a list of polar coordinates.

                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                      Syntax

                                                                                                                                                      P►Ry(r,θ)

                                                                                                                                                      Arguments

                                                                                                                                                      NameTypeOptional
                                                                                                                                                      r
                                                                                                                                                      θ

                                                                                                                                                      Location

                                                                                                                                                      2nd, angle, ANGLE, 8:P, Ry(

                                                                                                                                                      Description

                                                                                                                                                      P►Ry( (polar to rectangular y-coordinate) calculates the y-coordinate of a polar point. Polar coordinates are of the form (r,θ), where θ is the counterclockwise angle made with the positive x-axis, and r is the distance away from the origin (the point (0,0)). The conversion identity y=r*sin(θ) is used to calculate P►Ry(.

                                                                                                                                                      The value returned depends on whether the calculator is in radian or degree mode. A full rotation around a circle is 2π radians, which is equal to 360°. The conversion from radians to degrees is angle180/π and from degrees to radians is angleπ/180. The P►Ry( command also accepts a list of points.

                                                                                                                                                      P►Ry(5,π/4)
    3.535533906
5*sin(π/4)
    3.535533906
P►Ry({1,2},{π/4,π/3})
    {.7071067812 1.732050808}

                                                                                                                                                      Advanced Uses

                                                                                                                                                      You can bypass the mode setting by using the ° (degree) and ʳ (radian) symbols. This next command will return the same values no matter if your calculator is in degrees or radians:

                                                                                                                                                      P►Ry(1,{π/4^^r,60°})
    {.7071067812 .8660254038}

                                                                                                                                                      Optimization

                                                                                                                                                      In most cases P►Ry(r,θ) can be replaced by r*sin(θ) to save a byte:

                                                                                                                                                      :P►Ry(5,π/12)
can be
:5sin(π/12)

                                                                                                                                                      Conversely, complicated expressions multiplied by a sine factor can be simplified by using P►Ry(r,θ) instead.

                                                                                                                                                      :(A+BX)sin(π/5)
can be
:P►Ry(A+BX,π/5)

                                                                                                                                                      Error Conditions

                                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, thornahawk.

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $632D
                                                                                                                                                      Categories
                                                                                                                                                      Localizations
                                                                                                                                                      • FR: VA

                                                                                                                                                      PV

                                                                                                                                                      Overview

                                                                                                                                                      Syntax

                                                                                                                                                      PV

                                                                                                                                                      Description

                                                                                                                                                      Examples

                                                                                                                                                      Explanation 1

                                                                                                                                                      code 1

                                                                                                                                                      Explanation 2

                                                                                                                                                      code 2

                                                                                                                                                      Error Conditions

                                                                                                                                                      Advanced Notes

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-83 0.01013 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $6330
                                                                                                                                                      Categories
                                                                                                                                                      Localizations
                                                                                                                                                      • FR: |P/Y

                                                                                                                                                      |P/Y

                                                                                                                                                      Overview

                                                                                                                                                      Syntax

                                                                                                                                                      |P/Y

                                                                                                                                                      Description

                                                                                                                                                      Examples

                                                                                                                                                      Explanation 1

                                                                                                                                                      code 1

                                                                                                                                                      Explanation 2

                                                                                                                                                      code 2

                                                                                                                                                      Error Conditions

                                                                                                                                                      Advanced Notes

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-83 0.01013 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $77
                                                                                                                                                      Categories
                                                                                                                                                      Localizations
                                                                                                                                                      • FR: Param

                                                                                                                                                      Param

                                                                                                                                                      Overview

                                                                                                                                                      Sets parametric graphing mode.

                                                                                                                                                      Availability: Token only available from within the Basic editor.

                                                                                                                                                      Syntax

                                                                                                                                                      Param

                                                                                                                                                      Location

                                                                                                                                                      mode, Par

                                                                                                                                                      Description

                                                                                                                                                      The Param command enables parametric graphing mode.

                                                                                                                                                      Parametric mode is in many ways a generalization of function mode. Instead of writing y as a function of x, both x and y are written as a function of a parameter t (hence the name, parametric mode). You can easily see that equations in function mode are just a special case of equations in parametric mode: if you set x equal to t, then writing y=f(t) is equivalent to writing y=f(x). Of course, graphing a function this way on a calculator will be slightly slower than doing it in function mode directly, because of the overhead.

                                                                                                                                                      Parametric mode allows you the greatest freedom of all the possible graphing modes - nearly every curve you could encounter can be expressed in parametric form.

                                                                                                                                                      In mathematics, the parameter t is commonly allowed to take on all values from negative to positive infinity. However, this would be impossible to do on a calculator, since the equation would never stop graphing (unlike function mode, there's no easy way to check for which values of t the equation will go off the screen and there's no need to graph it). Instead, the calculator has window variables Tmin, Tmax, and Tstep: it will evaluate the parameter at every value from Tmin to Tmax, increasing by Tstep each time, and 'connect the dots'.

                                                                                                                                                      Polar mode, which you'll read about in the next section, is also a special case of parametric mode: To graph r=f(θ), you can instead graph x=f(t)cos(t) and y=f(t)sin(t), with t graphed over the same interval as θ.

                                                                                                                                                      Advanced Uses

                                                                                                                                                      The window variables that apply to parametric mode are:

                                                                                                                                                      • Tmin — Determines the minimum T-value graphed for equations.
                                                                                                                                                      • Tmax — Determines the maximum T-value graphed for equations.
                                                                                                                                                      • Tstep — Determines the difference between consecutive T-values.
                                                                                                                                                      • Xmin — Determines the minimum X-value shown on the screen.
                                                                                                                                                      • Xmax — Determines the maximum X-value shown on the screen.
                                                                                                                                                      • Xscl — Determines the horizontal space between marks on the X-axis in AxesOn mode or dots in GridOn mode.
                                                                                                                                                      • Ymin — Determines the minimum Y-value shown on the screen.
                                                                                                                                                      • Ymax — Determines the maximum Y-value shown on the screen.
                                                                                                                                                      • Yscl — Determines the vertical space between marks on the Y-axis in AxesOn mode or dots in GridOn mode.

                                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan.

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $EFA3
                                                                                                                                                      Categories
                                                                                                                                                      Localizations
                                                                                                                                                      • FR: Coller ligne ↓

                                                                                                                                                      Paste Line Below

                                                                                                                                                      Overview

                                                                                                                                                      Comment:CE OS 5.3+

                                                                                                                                                      Syntax

                                                                                                                                                      Paste Line Below

                                                                                                                                                      Description

                                                                                                                                                      Examples

                                                                                                                                                      Explanation 1

                                                                                                                                                      code 1

                                                                                                                                                      Explanation 2

                                                                                                                                                      code 2

                                                                                                                                                      Error Conditions

                                                                                                                                                      Advanced Notes

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-84+CE 5.3.0 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $D8
                                                                                                                                                      Categories
                                                                                                                                                      Localizations
                                                                                                                                                      • FR: Pause

                                                                                                                                                      Pause

                                                                                                                                                      Overview

                                                                                                                                                      Suspends program execution until you press 【enter】.

                                                                                                                                                      Availability: Token only available from within the Basic editor.

                                                                                                                                                      Syntax

                                                                                                                                                      Pause

                                                                                                                                                      Location

                                                                                                                                                      prgm, CTL, 8:Pause

                                                                                                                                                      Overview

                                                                                                                                                      Displays value; suspends program execution until you press 【enter】.

                                                                                                                                                      Availability: Token only available from within the Basic editor.

                                                                                                                                                      Syntax

                                                                                                                                                      Pause [value]

                                                                                                                                                      Arguments

                                                                                                                                                      NameTypeOptional
                                                                                                                                                      valueYes

                                                                                                                                                      Location

                                                                                                                                                      prgm, CTL, 8:Pause

                                                                                                                                                      Overview

                                                                                                                                                      Displays value on the current home screen and execution of the program continues after the time period specified. For time only, use Pause “”,time where the value is a blank string. Time is in seconds.
                                                                                                                                                      Pause value,time.

                                                                                                                                                      Availability: Token only available from within the Basic editor.

                                                                                                                                                      Syntax

                                                                                                                                                      Pause [value, time]

                                                                                                                                                      Arguments

                                                                                                                                                      NameTypeOptional
                                                                                                                                                      valueYes
                                                                                                                                                      timeYes

                                                                                                                                                      Location

                                                                                                                                                      prgm, 8:Pause

                                                                                                                                                      Description

                                                                                                                                                      The Pause command is used for suspending the execution of a program at a certain point. This is useful when you have text or instructions on the home screen that you want the user to read before the program continues on to the next thing. While the program is paused, the pause indicator turns on in the top-right corner of the screen (it is the dotted line that moves around).

                                                                                                                                                      After the user is done reading the text or instructions, they must press ENTER to resume program execution. One place the Pause command is commonly used is right before clearing the screen with ClrHome, because otherwise the text on the screen will show up for a split second before it is erased. The Pause command gives the user ample time to look at and read the text.

                                                                                                                                                      :Pause

                                                                                                                                                      An alternative to the Pause command that is commonly used is a Repeat loop with a getKey command as the condition. This is sometimes more appropriate in a program if you don't want to bring the program to a complete standstill, and you want the user to be able to resume program execution with any key instead of just ENTER (see usability for more information).

                                                                                                                                                      :Repeat getKey
:End

                                                                                                                                                      Advanced Uses

                                                                                                                                                      The Pause command has an optional argument that can either be text, a number, a variable, or an expression. This argument will be displayed on the next available blank line on the home screen while the program is paused, and it can be scrolled if it is larger than the screen. Although the Pause command can be used with the graph screen, the argument will still be displayed on the home screen.

                                                                                                                                                      Caution: Unlike any other text command, or indeed any other command at all, this optional argument will be stored to Ans after the pause! This could be used to your advantage, but most of the time, it's a nuisance, and if you use Ans for optimization, watch out for this side effect.

                                                                                                                                                      Displaying text with the Pause command follows the same pattern as the Disp command, so text is displayed on the left and everything else is displayed on the right. It also means that if there is already text on the seventh row, it will automatically move everything up one row so it can display its text. In addition, the Pause command is affected by the Output( command and its text.

                                                                                                                                                      PROGRAM:PAUSE
:ClrHome
:"World!
:Disp " Hello "+Ans
:Output(2,2,"Goodbye
:Pause Ans

                                                                                                                                                      When the calculator is paused, it is possible for another linked calculator to use the GetCalc( command to transfer a variable.

                                                                                                                                                      + Show TI-84+CE specific information

                                                                                                                                                      - Hide TI-84+CE specific information

                                                                                                                                                      The TI-84+CE also introduced an optional second argument to the Pause command. With this argument, you can specify the amount of time you wish to wait for in seconds:

                                                                                                                                                      :Pause "HELLO",2

                                                                                                                                                      Using the empty string "" with the optional second argument will cause the Pause command to wait for the specified amount of time without displaying anything on the screen:

                                                                                                                                                      :Pause "",3.5

                                                                                                                                                      The more recent Wait command can do this as well. Here’s the first example, but using Wait:

                                                                                                                                                      :Disp “HELLO
:Wait 2

                                                                                                                                                      Optimization

                                                                                                                                                      When you have a Disp command before a Pause command, you can take the text or variable from the Disp command and place it after the Pause command as its optional argument. This allows you to remove the Disp command. If the Disp command has multiple arguments, you just take the last one off and put it as the optional argument.

                                                                                                                                                      :Disp A
:Pause
can be
:Pause A

                                                                                                                                                      When using the optional argument of Pause, it is stored to Ans, and this can in rare cases be used for optimization. The most common one would probably be using Pause to show work for a calculation, as in the following program:

                                                                                                                                                      :Disp "A+B=
:Pause A+B
:Disp "(A+B)²=
:Pause Ans²
:Disp "(A+B)²-C²=
:Pause Ans-C²

                                                                                                                                                      Error Conditions

                                                                                                                                                      • ERR:INVALID occurs if this statement is used outside a program.

                                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: alexrudd, burr, CloudVariable, DarkerLine, GoVegan, iPhoenixOnTIBD, jonbush, kg583, Myles_Zadok, Trenly.

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $BBAB
                                                                                                                                                      Categories
                                                                                                                                                      Localizations
                                                                                                                                                      • FR: Φ

                                                                                                                                                      Φ

                                                                                                                                                      Overview

                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                      Syntax

                                                                                                                                                      Φ

                                                                                                                                                      Description

                                                                                                                                                      Examples

                                                                                                                                                      Explanation 1

                                                                                                                                                      code 1

                                                                                                                                                      Explanation 2

                                                                                                                                                      code 2

                                                                                                                                                      Error Conditions

                                                                                                                                                      Advanced Notes

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-83+ 1.03 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $6009
                                                                                                                                                      Categories
                                                                                                                                                      Localizations
                                                                                                                                                      • FR: Img0

                                                                                                                                                      Pic0

                                                                                                                                                      Overview

                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                      Syntax

                                                                                                                                                      Pic0

                                                                                                                                                      Description

                                                                                                                                                      Examples

                                                                                                                                                      Explanation 1

                                                                                                                                                      code 1

                                                                                                                                                      Explanation 2

                                                                                                                                                      code 2

                                                                                                                                                      Error Conditions

                                                                                                                                                      Advanced Notes

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-83 0.01013 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $6000
                                                                                                                                                      Categories
                                                                                                                                                      Localizations
                                                                                                                                                      • FR: Img1

                                                                                                                                                      Pic1

                                                                                                                                                      Overview

                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                      Syntax

                                                                                                                                                      Pic1

                                                                                                                                                      Description

                                                                                                                                                      Examples

                                                                                                                                                      Explanation 1

                                                                                                                                                      code 1

                                                                                                                                                      Explanation 2

                                                                                                                                                      code 2

                                                                                                                                                      Error Conditions

                                                                                                                                                      Advanced Notes

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $6001
                                                                                                                                                      Categories
                                                                                                                                                      Localizations
                                                                                                                                                      • FR: Img2

                                                                                                                                                      Pic2

                                                                                                                                                      Overview

                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                      Syntax

                                                                                                                                                      Pic2

                                                                                                                                                      Description

                                                                                                                                                      Examples

                                                                                                                                                      Explanation 1

                                                                                                                                                      code 1

                                                                                                                                                      Explanation 2

                                                                                                                                                      code 2

                                                                                                                                                      Error Conditions

                                                                                                                                                      Advanced Notes

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $6002
                                                                                                                                                      Categories
                                                                                                                                                      Localizations
                                                                                                                                                      • FR: Img3

                                                                                                                                                      Pic3

                                                                                                                                                      Overview

                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                      Syntax

                                                                                                                                                      Pic3

                                                                                                                                                      Description

                                                                                                                                                      Examples

                                                                                                                                                      Explanation 1

                                                                                                                                                      code 1

                                                                                                                                                      Explanation 2

                                                                                                                                                      code 2

                                                                                                                                                      Error Conditions

                                                                                                                                                      Advanced Notes

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $6003
                                                                                                                                                      Categories
                                                                                                                                                      Localizations
                                                                                                                                                      • FR: Img4

                                                                                                                                                      Pic4

                                                                                                                                                      Overview

                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                      Syntax

                                                                                                                                                      Pic4

                                                                                                                                                      Description

                                                                                                                                                      Examples

                                                                                                                                                      Explanation 1

                                                                                                                                                      code 1

                                                                                                                                                      Explanation 2

                                                                                                                                                      code 2

                                                                                                                                                      Error Conditions

                                                                                                                                                      Advanced Notes

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $6004
                                                                                                                                                      Categories
                                                                                                                                                      Localizations
                                                                                                                                                      • FR: Img5

                                                                                                                                                      Pic5

                                                                                                                                                      Overview

                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                      Syntax

                                                                                                                                                      Pic5

                                                                                                                                                      Description

                                                                                                                                                      Examples

                                                                                                                                                      Explanation 1

                                                                                                                                                      code 1

                                                                                                                                                      Explanation 2

                                                                                                                                                      code 2

                                                                                                                                                      Error Conditions

                                                                                                                                                      Advanced Notes

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $6005
                                                                                                                                                      Categories
                                                                                                                                                      Localizations
                                                                                                                                                      • FR: Img6

                                                                                                                                                      Pic6

                                                                                                                                                      Overview

                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                      Syntax

                                                                                                                                                      Pic6

                                                                                                                                                      Description

                                                                                                                                                      Examples

                                                                                                                                                      Explanation 1

                                                                                                                                                      code 1

                                                                                                                                                      Explanation 2

                                                                                                                                                      code 2

                                                                                                                                                      Error Conditions

                                                                                                                                                      Advanced Notes

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $6006
                                                                                                                                                      Categories
                                                                                                                                                      Localizations
                                                                                                                                                      • FR: Img7

                                                                                                                                                      Pic7

                                                                                                                                                      Overview

                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                      Syntax

                                                                                                                                                      Pic7

                                                                                                                                                      Description

                                                                                                                                                      Examples

                                                                                                                                                      Explanation 1

                                                                                                                                                      code 1

                                                                                                                                                      Explanation 2

                                                                                                                                                      code 2

                                                                                                                                                      Error Conditions

                                                                                                                                                      Advanced Notes

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-83 0.01013 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $6007
                                                                                                                                                      Categories
                                                                                                                                                      Localizations
                                                                                                                                                      • FR: Img8

                                                                                                                                                      Pic8

                                                                                                                                                      Overview

                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                      Syntax

                                                                                                                                                      Pic8

                                                                                                                                                      Description

                                                                                                                                                      Examples

                                                                                                                                                      Explanation 1

                                                                                                                                                      code 1

                                                                                                                                                      Explanation 2

                                                                                                                                                      code 2

                                                                                                                                                      Error Conditions

                                                                                                                                                      Advanced Notes

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-83 0.01013 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $6008
                                                                                                                                                      Categories
                                                                                                                                                      Localizations
                                                                                                                                                      • FR: Img9

                                                                                                                                                      Pic9

                                                                                                                                                      Overview

                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                      Syntax

                                                                                                                                                      Pic9

                                                                                                                                                      Description

                                                                                                                                                      Examples

                                                                                                                                                      Explanation 1

                                                                                                                                                      code 1

                                                                                                                                                      Explanation 2

                                                                                                                                                      code 2

                                                                                                                                                      Error Conditions

                                                                                                                                                      Advanced Notes

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-83 0.01013 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $EC
                                                                                                                                                      Categories
                                                                                                                                                      Localizations
                                                                                                                                                      • FR: Graph1(

                                                                                                                                                      Plot1(

                                                                                                                                                      Overview

                                                                                                                                                      Defines Plot# (1, 2, or 3) of type Scatter or xyLine for Xlist and Ylist using markand color.
                                                                                                                                                      Color#: 10 - 24 or color name pasted from [vars] COLOR.
                                                                                                                                                      Note: Xlistand Ylistrepresent the Xlist and Ylist names.

                                                                                                                                                      Availability: Token only available from within the Basic editor.

                                                                                                                                                      Syntax

                                                                                                                                                      Plot#(type,Xlist,Ylist[,mark,color#])

                                                                                                                                                      Arguments

                                                                                                                                                      NameTypeOptional
                                                                                                                                                      #
                                                                                                                                                      type
                                                                                                                                                      Xlistlist
                                                                                                                                                      Ylistlist
                                                                                                                                                      markYes
                                                                                                                                                      color#colorNumYes

                                                                                                                                                      Location

                                                                                                                                                      2nd, stat plot, STAT PLOTS, 1:Plot12:Plot23:Plot3

                                                                                                                                                      Overview

                                                                                                                                                      Defines Plot# (1, 2, or 3) of type Histogram or Boxplot for Xlist with frequency freqlistand color #.
                                                                                                                                                      Color#: 10 - 24 or color name pasted from [vars] COLOR.
                                                                                                                                                      Note: Xlistrepresents the Xlist name.

                                                                                                                                                      Availability: Token only available from within the Basic editor.

                                                                                                                                                      Syntax

                                                                                                                                                      Plot#(type,Xlist[,freqlist,color#])

                                                                                                                                                      Arguments

                                                                                                                                                      NameTypeOptional
                                                                                                                                                      #
                                                                                                                                                      type
                                                                                                                                                      Xlistlist
                                                                                                                                                      freqlistlistYes
                                                                                                                                                      color#colorNumYes

                                                                                                                                                      Location

                                                                                                                                                      2nd, stat plot, STAT PLOTS, 1:Plot12:Plot23:Plot3

                                                                                                                                                      Overview

                                                                                                                                                      Defines Plot# (1, 2, or 3) of type ModBoxplot for Xlist with frequency freqlist using markand color #.
                                                                                                                                                      Color#: 10 - 24 or color name pasted from [vars] COLOR.
                                                                                                                                                      Note: Xlistrepresents the Xlist name.

                                                                                                                                                      Availability: Token only available from within the Basic editor.

                                                                                                                                                      Syntax

                                                                                                                                                      Plot#(type,Xlist[,freqlist,mark,color#])

                                                                                                                                                      Arguments

                                                                                                                                                      NameTypeOptional
                                                                                                                                                      #
                                                                                                                                                      type
                                                                                                                                                      Xlistlist
                                                                                                                                                      freqlistlistYes
                                                                                                                                                      markYes
                                                                                                                                                      color#colorNumYes

                                                                                                                                                      Location

                                                                                                                                                      2nd, stat plot, STAT PLOTS, 1:Plot12:Plot23:Plot3

                                                                                                                                                      Overview

                                                                                                                                                      Defines Plot# (1, 2, or 3) of type NormProbPlot for datalist on data axis using markand color # data axis can be X or Y.
                                                                                                                                                      Color#: 10 - 24 or color name pasted from [vars] COLOR.
                                                                                                                                                      Note: datalistrepresents the datalist name.

                                                                                                                                                      Availability: Token only available from within the Basic editor.

                                                                                                                                                      Syntax

                                                                                                                                                      Plot#(type,datalist[,data axis,mark,color#])

                                                                                                                                                      Arguments

                                                                                                                                                      NameTypeOptional
                                                                                                                                                      #
                                                                                                                                                      type
                                                                                                                                                      datalistlist
                                                                                                                                                      data axisYes
                                                                                                                                                      markYes
                                                                                                                                                      color#colorNumYes

                                                                                                                                                      Location

                                                                                                                                                      2nd, stat plot, STAT PLOTS, 1:Plot12:Plot23:Plot3

                                                                                                                                                      Description

                                                                                                                                                      The commands Plot1(, Plot2(, and Plot3(, which are identical except for which stat plot (1, 2, or 3) they affect, define their corresponding stat plot. When the stat plot is defined, it is also turned on so no PlotsOn command is necessary.

                                                                                                                                                      The first argument of the commands is always the type of plot, and is one of Scatter, xyLine, Histogram, Boxplot, ModBoxplot, and NormProbPlot - these types are found in the TYPE submenu of the stat plot menu. The other arguments vary. For all but Histogram and Boxplot, there is a mark argument - this is a dot, a cross, or a box, symbols that can be found in the MARK submenu of the stat plot menu. On color calculators, there is an optional final argument to specify the color of the plot.

                                                                                                                                                      Scatter plot

                                                                                                                                                      Plot#(Scatter, x-list, y-list, mark) defines a scatter plot. The points defined by x-list and y-list are plotted using mark on the graph screen.

                                                                                                                                                      x-list and y-list must be the same length.

                                                                                                                                                      xyLine plot

                                                                                                                                                      Plot#(xyLine, x-list, y-list, mark) defines an xyLine plot. Similarly to a scatter plot, the points defined by x-list and y-list are plotted using mark on the graph screen, but with an xyLine plot they are also connected by a line, in the order that they occur in the lists.

                                                                                                                                                      x-list and y-list must be the same length.

                                                                                                                                                      Histogram plot

                                                                                                                                                      Plot#(Histogram, x-list, freq list) defines a Histogram plot. The x-axis is divided into intervals that are Xscl wide. A bar is drawn in in each interval whose height corresponds to the number of points in the interval. Points that are not between Xmin and Xmax are not tallied.

                                                                                                                                                      Xscl must not be too small - it can divide the screen into no more than 47 different bars.

                                                                                                                                                      Box plot

                                                                                                                                                      Plot#(Boxplot, x-list, freq list) defines a box plot. A rectangular box is drawn whose left edge is Q1 (the first quartile) of the data, and whose right edge is Q3 (the third quartile). A vertical segment is drawn within the box at the median, and 'whiskers' are drawn from the box to the minimum and maximum data points.

                                                                                                                                                      The box plot ignores the Ymax and Ymin dimensions of the screen, and any plots that aren't box plots or modified box plots. Each box plot takes approximately 1/3 of the screen in height, and if more than one are plotted, they will take up different areas of the screen.

                                                                                                                                                      Modified box plot

                                                                                                                                                      Plot#(ModBoxplot, x-list, freq list, mark) defines a modified box plot. This is almost entirely like the normal box plot, except that it also draws outliers. Whiskers are only drawn to the furthers point within 1.5 times the interquartile range (Q3-Q1) of the box. Beyond this point, data points are drawn individually, using mark.

                                                                                                                                                      The box plot ignores the Ymax and Ymin dimensions of the screen, and any plots that aren't box plots or modified box plots. Each box plot takes approximately 1/3 of the screen in height, and if more than one are plotted, they will take up different areas of the screen.

                                                                                                                                                      Normal probability plot

                                                                                                                                                      Plot#(NormProbPlot, data list, data axis, mark) defines a normal probability plot. The mean and standard deviation of the data are calculated. Then for each point, the number of standard deviations it is from the mean is calculated, and the point is plotted against this number using mark. data axis can be either X or Y: it determines whether the value of a point determines it's x-coordinate or y-coordinate.

                                                                                                                                                      The point behind this rather convoluted process is to test the extent to which the data is normally distributed. If it follows the normal distribution closely, then the result will be close to a straight line - otherwise it will be curved.

                                                                                                                                                      Advanced Uses

                                                                                                                                                      After doing a regression, a scatter plot of ʟRESID against the x-list is a useful measure of the effectiveness of the regression. If the plot appears random, this is a good sign; if there is a pattern to the plot, this means it's likely that a better regression model exists.

                                                                                                                                                      Optimization

                                                                                                                                                      The ʟ symbol at the beginning of list names can be omitted everywhere in this command.

                                                                                                                                                      In addition, every element except the plot type and the data list or data lists are optional, and take on the following default values:

                                                                                                                                                      • freq list is 1 by default, meaning that all frequencies are 1.
                                                                                                                                                      • mark is the box by default.
                                                                                                                                                      • data axis is X by default.

                                                                                                                                                      Error Conditions

                                                                                                                                                      • ERR:DIM MISMATCH is thrown if the x and y lists, or the data and frequency lists, have different dimensions.
                                                                                                                                                      • ERR:STAT is thrown if Xscl is too small in the case of a Histogram.

                                                                                                                                                      All errors are thrown when plotting the stat plot, as opposed to when the command is executed, and do not provide a 2:Goto option.

                                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Myles_Zadok.

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $ED
                                                                                                                                                      Categories
                                                                                                                                                      Localizations
                                                                                                                                                      • FR: Graph2(

                                                                                                                                                      Plot2(

                                                                                                                                                      Overview

                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                      Syntax

                                                                                                                                                      Plot2(

                                                                                                                                                      Description

                                                                                                                                                      The commands Plot1(, Plot2(, and Plot3(, which are identical except for which stat plot (1, 2, or 3) they affect, define their corresponding stat plot. When the stat plot is defined, it is also turned on so no PlotsOn command is necessary.

                                                                                                                                                      The first argument of the commands is always the type of plot, and is one of Scatter, xyLine, Histogram, Boxplot, ModBoxplot, and NormProbPlot - these types are found in the TYPE submenu of the stat plot menu. The other arguments vary. For all but Histogram and Boxplot, there is a mark argument - this is a dot, a cross, or a box, symbols that can be found in the MARK submenu of the stat plot menu. On color calculators, there is an optional final argument to specify the color of the plot.

                                                                                                                                                      Scatter plot

                                                                                                                                                      Plot#(Scatter, x-list, y-list, mark) defines a scatter plot. The points defined by x-list and y-list are plotted using mark on the graph screen.

                                                                                                                                                      x-list and y-list must be the same length.

                                                                                                                                                      xyLine plot

                                                                                                                                                      Plot#(xyLine, x-list, y-list, mark) defines an xyLine plot. Similarly to a scatter plot, the points defined by x-list and y-list are plotted using mark on the graph screen, but with an xyLine plot they are also connected by a line, in the order that they occur in the lists.

                                                                                                                                                      x-list and y-list must be the same length.

                                                                                                                                                      Histogram plot

                                                                                                                                                      Plot#(Histogram, x-list, freq list) defines a Histogram plot. The x-axis is divided into intervals that are Xscl wide. A bar is drawn in in each interval whose height corresponds to the number of points in the interval. Points that are not between Xmin and Xmax are not tallied.

                                                                                                                                                      Xscl must not be too small - it can divide the screen into no more than 47 different bars.

                                                                                                                                                      Box plot

                                                                                                                                                      Plot#(Boxplot, x-list, freq list) defines a box plot. A rectangular box is drawn whose left edge is Q1 (the first quartile) of the data, and whose right edge is Q3 (the third quartile). A vertical segment is drawn within the box at the median, and 'whiskers' are drawn from the box to the minimum and maximum data points.

                                                                                                                                                      The box plot ignores the Ymax and Ymin dimensions of the screen, and any plots that aren't box plots or modified box plots. Each box plot takes approximately 1/3 of the screen in height, and if more than one are plotted, they will take up different areas of the screen.

                                                                                                                                                      Modified box plot

                                                                                                                                                      Plot#(ModBoxplot, x-list, freq list, mark) defines a modified box plot. This is almost entirely like the normal box plot, except that it also draws outliers. Whiskers are only drawn to the furthers point within 1.5 times the interquartile range (Q3-Q1) of the box. Beyond this point, data points are drawn individually, using mark.

                                                                                                                                                      The box plot ignores the Ymax and Ymin dimensions of the screen, and any plots that aren't box plots or modified box plots. Each box plot takes approximately 1/3 of the screen in height, and if more than one are plotted, they will take up different areas of the screen.

                                                                                                                                                      Normal probability plot

                                                                                                                                                      Plot#(NormProbPlot, data list, data axis, mark) defines a normal probability plot. The mean and standard deviation of the data are calculated. Then for each point, the number of standard deviations it is from the mean is calculated, and the point is plotted against this number using mark. data axis can be either X or Y: it determines whether the value of a point determines it's x-coordinate or y-coordinate.

                                                                                                                                                      The point behind this rather convoluted process is to test the extent to which the data is normally distributed. If it follows the normal distribution closely, then the result will be close to a straight line - otherwise it will be curved.

                                                                                                                                                      Advanced Uses

                                                                                                                                                      After doing a regression, a scatter plot of ʟRESID against the x-list is a useful measure of the effectiveness of the regression. If the plot appears random, this is a good sign; if there is a pattern to the plot, this means it's likely that a better regression model exists.

                                                                                                                                                      Optimization

                                                                                                                                                      The ʟ symbol at the beginning of list names can be omitted everywhere in this command.

                                                                                                                                                      In addition, every element except the plot type and the data list or data lists are optional, and take on the following default values:

                                                                                                                                                      • freq list is 1 by default, meaning that all frequencies are 1.
                                                                                                                                                      • mark is the box by default.
                                                                                                                                                      • data axis is X by default.

                                                                                                                                                      Error Conditions

                                                                                                                                                      • ERR:DIM MISMATCH is thrown if the x and y lists, or the data and frequency lists, have different dimensions.
                                                                                                                                                      • ERR:STAT is thrown if Xscl is too small in the case of a Histogram.

                                                                                                                                                      All errors are thrown when plotting the stat plot, as opposed to when the command is executed, and do not provide a 2:Goto option.

                                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Myles_Zadok.

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $EE
                                                                                                                                                      Categories
                                                                                                                                                      Localizations
                                                                                                                                                      • FR: Graph3(

                                                                                                                                                      Plot3(

                                                                                                                                                      Overview

                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                      Syntax

                                                                                                                                                      Plot3(

                                                                                                                                                      Description

                                                                                                                                                      The commands Plot1(, Plot2(, and Plot3(, which are identical except for which stat plot (1, 2, or 3) they affect, define their corresponding stat plot. When the stat plot is defined, it is also turned on so no PlotsOn command is necessary.

                                                                                                                                                      The first argument of the commands is always the type of plot, and is one of Scatter, xyLine, Histogram, Boxplot, ModBoxplot, and NormProbPlot - these types are found in the TYPE submenu of the stat plot menu. The other arguments vary. For all but Histogram and Boxplot, there is a mark argument - this is a dot, a cross, or a box, symbols that can be found in the MARK submenu of the stat plot menu. On color calculators, there is an optional final argument to specify the color of the plot.

                                                                                                                                                      Scatter plot

                                                                                                                                                      Plot#(Scatter, x-list, y-list, mark) defines a scatter plot. The points defined by x-list and y-list are plotted using mark on the graph screen.

                                                                                                                                                      x-list and y-list must be the same length.

                                                                                                                                                      xyLine plot

                                                                                                                                                      Plot#(xyLine, x-list, y-list, mark) defines an xyLine plot. Similarly to a scatter plot, the points defined by x-list and y-list are plotted using mark on the graph screen, but with an xyLine plot they are also connected by a line, in the order that they occur in the lists.

                                                                                                                                                      x-list and y-list must be the same length.

                                                                                                                                                      Histogram plot

                                                                                                                                                      Plot#(Histogram, x-list, freq list) defines a Histogram plot. The x-axis is divided into intervals that are Xscl wide. A bar is drawn in in each interval whose height corresponds to the number of points in the interval. Points that are not between Xmin and Xmax are not tallied.

                                                                                                                                                      Xscl must not be too small - it can divide the screen into no more than 47 different bars.

                                                                                                                                                      Box plot

                                                                                                                                                      Plot#(Boxplot, x-list, freq list) defines a box plot. A rectangular box is drawn whose left edge is Q1 (the first quartile) of the data, and whose right edge is Q3 (the third quartile). A vertical segment is drawn within the box at the median, and 'whiskers' are drawn from the box to the minimum and maximum data points.

                                                                                                                                                      The box plot ignores the Ymax and Ymin dimensions of the screen, and any plots that aren't box plots or modified box plots. Each box plot takes approximately 1/3 of the screen in height, and if more than one are plotted, they will take up different areas of the screen.

                                                                                                                                                      Modified box plot

                                                                                                                                                      Plot#(ModBoxplot, x-list, freq list, mark) defines a modified box plot. This is almost entirely like the normal box plot, except that it also draws outliers. Whiskers are only drawn to the furthers point within 1.5 times the interquartile range (Q3-Q1) of the box. Beyond this point, data points are drawn individually, using mark.

                                                                                                                                                      The box plot ignores the Ymax and Ymin dimensions of the screen, and any plots that aren't box plots or modified box plots. Each box plot takes approximately 1/3 of the screen in height, and if more than one are plotted, they will take up different areas of the screen.

                                                                                                                                                      Normal probability plot

                                                                                                                                                      Plot#(NormProbPlot, data list, data axis, mark) defines a normal probability plot. The mean and standard deviation of the data are calculated. Then for each point, the number of standard deviations it is from the mean is calculated, and the point is plotted against this number using mark. data axis can be either X or Y: it determines whether the value of a point determines it's x-coordinate or y-coordinate.

                                                                                                                                                      The point behind this rather convoluted process is to test the extent to which the data is normally distributed. If it follows the normal distribution closely, then the result will be close to a straight line - otherwise it will be curved.

                                                                                                                                                      Advanced Uses

                                                                                                                                                      After doing a regression, a scatter plot of ʟRESID against the x-list is a useful measure of the effectiveness of the regression. If the plot appears random, this is a good sign; if there is a pattern to the plot, this means it's likely that a better regression model exists.

                                                                                                                                                      Optimization

                                                                                                                                                      The ʟ symbol at the beginning of list names can be omitted everywhere in this command.

                                                                                                                                                      In addition, every element except the plot type and the data list or data lists are optional, and take on the following default values:

                                                                                                                                                      • freq list is 1 by default, meaning that all frequencies are 1.
                                                                                                                                                      • mark is the box by default.
                                                                                                                                                      • data axis is X by default.

                                                                                                                                                      Error Conditions

                                                                                                                                                      • ERR:DIM MISMATCH is thrown if the x and y lists, or the data and frequency lists, have different dimensions.
                                                                                                                                                      • ERR:STAT is thrown if Xscl is too small in the case of a Histogram.

                                                                                                                                                      All errors are thrown when plotting the stat plot, as opposed to when the command is executed, and do not provide a 2:Goto option.

                                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Myles_Zadok.

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $631B
                                                                                                                                                      Categories
                                                                                                                                                      Localizations
                                                                                                                                                      • FR: PlotStart

                                                                                                                                                      PlotStart

                                                                                                                                                      Overview

                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                      Syntax

                                                                                                                                                      PlotStart

                                                                                                                                                      Description

                                                                                                                                                      Examples

                                                                                                                                                      Explanation 1

                                                                                                                                                      code 1

                                                                                                                                                      Explanation 2

                                                                                                                                                      code 2

                                                                                                                                                      Error Conditions

                                                                                                                                                      Advanced Notes

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-82 1.0 𝑛Min added
                                                                                                                                                      TI-83 0.01013 Renamed 𝑛Min to PlotStart
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $6334
                                                                                                                                                      Categories
                                                                                                                                                      Localizations
                                                                                                                                                      • FR: GraphPas

                                                                                                                                                      PlotStep

                                                                                                                                                      Overview

                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                      Syntax

                                                                                                                                                      PlotStep

                                                                                                                                                      Description

                                                                                                                                                      Examples

                                                                                                                                                      Explanation 1

                                                                                                                                                      code 1

                                                                                                                                                      Explanation 2

                                                                                                                                                      code 2

                                                                                                                                                      Error Conditions

                                                                                                                                                      Advanced Notes

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-83 0.01013 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $EA
                                                                                                                                                      Categories
                                                                                                                                                      Localizations
                                                                                                                                                      • FR: GraphNAff

                                                                                                                                                      PlotsOff

                                                                                                                                                      Overview

                                                                                                                                                      Deselects all stat plots or one or more specified stat plots (1, 2, or 3).

                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                      Syntax

                                                                                                                                                      PlotsOff [1,2,3]

                                                                                                                                                      Location

                                                                                                                                                      2nd, stat plot, STAT PLOTS, 4:PlotsOff

                                                                                                                                                      Description

                                                                                                                                                      By itself, the command will turn off all three stat plots.

                                                                                                                                                      If it is given arguments, there can be any number of them (actually, no more than 255, but this won't stop most people), but they must all be numbers 1 to 3. Then, the command will only turn off the specified plots. Unlike some commands, it is okay to give PlotsOff an expression as an argument (for example, PlotsOff X), as long as it has a value of 1, 2, or 3.

                                                                                                                                                      Error Conditions

                                                                                                                                                      • ERR:DOMAIN is thrown if a plot that is not 1, 2, or 3 is specified.

                                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $E9
                                                                                                                                                      Categories
                                                                                                                                                      Localizations
                                                                                                                                                      • FR: GraphAff

                                                                                                                                                      PlotsOn

                                                                                                                                                      Overview

                                                                                                                                                      Selects all stat plots or one or more specified stat plots (1, 2, or 3).

                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                      Syntax

                                                                                                                                                      PlotsOn [1,2,3]

                                                                                                                                                      Location

                                                                                                                                                      2nd, stat plot, STAT PLOTS, 5:PlotsOn

                                                                                                                                                      Description

                                                                                                                                                      By itself, the command will turn on all three stat plots.

                                                                                                                                                      If it is given arguments, there can be any number of them (actually, no more than 255, but this won't stop most people), but they must all be numbers 1 to 3. Then, the command will only turn on the specified plots. Unlike some commands, it is okay to give PlotsOn an expression as an argument (for example, PlotsOn X), as long as it has a value of 1, 2, or 3.

                                                                                                                                                      Error Conditions

                                                                                                                                                      • ERR:DOMAIN is thrown if a plot that is not 1, 2, or 3 is specified.

                                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $BB4C
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                                                                                                                                                      • FR: Pmt_Déb

                                                                                                                                                      Pmt_Bgn

                                                                                                                                                      Overview

                                                                                                                                                      Specifies an annuity due, where payments occur at the beginning of each payment period.

                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                      Syntax

                                                                                                                                                      Pmt_Bgn

                                                                                                                                                      Location

                                                                                                                                                      apps, 1:Finance, CALC, F:Pmt_Bgn

                                                                                                                                                      Description

                                                                                                                                                      The Pmt_Bgn and Pmt_End commands toggle a setting with the finance solver. In Pmt_Bgn mode, the calculator assumes that the payments are made at the beginning of each time period, rather than at the end.

                                                                                                                                                      Make sure to set the calculator to one of the modes before using the finance solving commands in a program, since otherwise the result is unpredictable.

                                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-83 0.01013 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $BB4B
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                                                                                                                                                      • FR: Pmt_Fin

                                                                                                                                                      Pmt_End

                                                                                                                                                      Overview

                                                                                                                                                      Specifies an ordinary annuity, where payments occur at the end of each payment period.

                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                      Syntax

                                                                                                                                                      Pmt_End

                                                                                                                                                      Location

                                                                                                                                                      apps, 1:Finance, CALC, E:Pmt_End

                                                                                                                                                      Description

                                                                                                                                                      The Pmt_End and Pmt_Bgn commands toggle a setting with the finance solver. In Pmt_End mode, the calculator assumes that the payments are made at the end of each time period, rather than at the beginning.

                                                                                                                                                      Make sure to set the calculator to one of the modes before using the finance solving commands in a program, since otherwise the result is unpredictable.

                                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-83 0.01013 Added
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                                                                                                                                                      Hex Value $78
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                                                                                                                                                      • FR: Polaire

                                                                                                                                                      Polar

                                                                                                                                                      Overview

                                                                                                                                                      Sets polar graphing mode.

                                                                                                                                                      Availability: Token only available from within the Basic editor.

                                                                                                                                                      Syntax

                                                                                                                                                      Polar

                                                                                                                                                      Location

                                                                                                                                                      mode, Polar

                                                                                                                                                      Description

                                                                                                                                                      The Polar command enables the polar graphing mode.

                                                                                                                                                      Unlike the previous modes, polar mode doesn't use the more common (x,y) coordinates. Instead, the coordinates (r,θ) are used, where θ is the counterclockwise angle made with the positive x-axis, and r is the distance away from the origin (the point (0,0)). Although it's possible to translate from one system to the other, polar coordinates are more useful for some expressions (and, of course, less useful for others).

                                                                                                                                                      In particular, they're very good at graphing anything circle-related. The equation for a circle in polar mode is just r=1 (or any other number, for a circle of different radius).

                                                                                                                                                      Like in parametric mode, the parameter θ uses the window variables θmin, θmax, and θstep to determine which points are graphed. A common situation is θmin=0, θmax=2π: in Radian mode, this corresponds to going all the way around the circle. Of course, you could use Degree mode and set θmax to be 360, but this is uncommon in mathematics.

                                                                                                                                                      Advanced Uses

                                                                                                                                                      The window variables that apply to polar mode are:

                                                                                                                                                      • θmin — Determines the minimum θ-value graphed for equations.
                                                                                                                                                      • θmax — Determines the maximum θ-value graphed for equations.
                                                                                                                                                      • θstep — Determines the difference between consecutive θ-values.
                                                                                                                                                      • Xmin — Determines the minimum X-value shown on the screen.
                                                                                                                                                      • Xmax — Determines the maximum X-value shown on the screen.
                                                                                                                                                      • Xscl — Determines the horizontal space between marks on the X-axis in AxesOn mode or dots in GridOn mode.
                                                                                                                                                      • Ymin — Determines the minimum Y-value shown on the screen.
                                                                                                                                                      • Ymax — Determines the maximum Y-value shown on the screen.
                                                                                                                                                      • Yscl — Determines the vertical space between marks on the Y-axis in AxesOn mode or dots in GridOn mode.

                                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $7E02
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                                                                                                                                                      • FR: CoordPol

                                                                                                                                                      PolarGC

                                                                                                                                                      Overview

                                                                                                                                                      Sets polar graphing coordinates format.

                                                                                                                                                      Availability: Token only available from within the Basic editor.

                                                                                                                                                      Syntax

                                                                                                                                                      PolarGC

                                                                                                                                                      Location

                                                                                                                                                      2nd, format, PolarGC

                                                                                                                                                      Description

                                                                                                                                                      The PolarGC ("Polar Grid Coordinates") command (like its opposite, the RectGC) command, affects how the coordinates of a point on the graph screen are displayed. When PolarGC is enabled, the coordinates of a point are displayed as (R,θ).

                                                                                                                                                      The polar coordinates of a point can be interpreted as the distance R it is away from the origin (0,0), and the direction θ. θ is the angle that a ray to the point would make with the positive X-axis (so polar coordinates are affected by Degree/Radian mode). An angle of 0 means the point is to the left of the origin; an angle of 90° (π/2 radians) means it's up from the origin, and so on. So, for example, the point with R=2 and θ=270° (3π/2 radians) would be two units down from the origin.

                                                                                                                                                      Of course, coordinates are only displayed with the CoordOn setting; however, with CoordOff, RectGC and PolarGC are still useful, because in a variety of cases, the coordinates of a point are also stored to variables. PolarGC doesn't change the fact that they're stored to X and Y, as with RectGC; however, with PolarGC, they are also stored to R and θ.

                                                                                                                                                      Although the PolarGC command naturally goes with Polar graphing mode, the two settings are independent; you can use both PolarGC and RectGC with any graphing mode.

                                                                                                                                                      Advanced

                                                                                                                                                      The following situations involve storing coordinates of a point to variables:

                                                                                                                                                      • Graphing an equation
                                                                                                                                                      • Tracing an equation or plot
                                                                                                                                                      • Moving the cursor on the graph screen
                                                                                                                                                      • Using the interactive mode of one of the 2nd DRAW commands
                                                                                                                                                      • Using one of DrawF, DrawInv, or Tangent(
                                                                                                                                                      • Anything in the 2nd CALC menu.

                                                                                                                                                      Naturally, any command like Input or Select( which involves the above, will also store coordinates of a point.

                                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan.

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-82 1.0 Added
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                                                                                                                                                      Hex Value $91
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                                                                                                                                                      • FR: PrintScreen

                                                                                                                                                      PrintScreen

                                                                                                                                                      Overview

                                                                                                                                                      Comment:Not available (only token)

                                                                                                                                                      Syntax

                                                                                                                                                      PrintScreen

                                                                                                                                                      Description

                                                                                                                                                      Examples

                                                                                                                                                      Explanation 1

                                                                                                                                                      code 1

                                                                                                                                                      Explanation 2

                                                                                                                                                      code 2

                                                                                                                                                      Error Conditions

                                                                                                                                                      Advanced Notes

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $DD
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                                                                                                                                                      • FR: Prompt

                                                                                                                                                      Prompt

                                                                                                                                                      Overview

                                                                                                                                                      Prompts for value for variableA, then variableB, and so on.

                                                                                                                                                      Availability: Token only available from within the Basic editor.

                                                                                                                                                      Syntax

                                                                                                                                                      Prompt variableA[,variableB,...,variable n]

                                                                                                                                                      Arguments

                                                                                                                                                      NameTypeOptional
                                                                                                                                                      variableA
                                                                                                                                                      variableBYes
                                                                                                                                                      ...Yes
                                                                                                                                                      variable nYes

                                                                                                                                                      Location

                                                                                                                                                      prgm, I/O, 2:Prompt

                                                                                                                                                      Description

                                                                                                                                                      The Prompt command is the simplest way of getting user input on the home screen (getting user input on the graph screen is only possible with the getKey command). Prompt displays variables one per line, with an equal sign and question mark (=?) displayed to the right of each variable. After the user enters a value or expression for the variables and presses ENTER, the values will be stored to the variables and program execution will resume.

                                                                                                                                                      Prompt can be used with every variable, but some of the variables have to be entered in a certain way. If the variable is a string or equation, the user must put quotes ("") around the value; the user must also put curly braces ({}) around lists and square brackets ([]) around matrices. Of course, ending quotes, braces, and brackets can be left off as usual.

                                                                                                                                                      When you use Prompt to input a named list, the ʟ in front of the name is dropped (so Prompt ʟNAME will display NAME=?). This can be confusing with single-letter names: Prompt ʟX and Prompt X both display X=?. Further enhancing the confusion, if the user enters a list for Prompt X, the list will be stored to ʟX instead.

                                                                                                                                                      During the Prompt, the user can press [2nd][MODE] to quit the program immediately.

                                                                                                                                                      Advanced Uses

                                                                                                                                                      Because simply displaying what variable the value will be stored to does not really tell the user what the variable will be used for, you can put a Disp command before Prompt to give the user some more insight into what an appropriate value for the variable would be. The Prompt command will be displayed one line lower, though, because the Disp command automatically creates a new line after itself. (Of course, you could also just use the Input command.)

                                                                                                                                                      :Disp "Enter the Score
:Prompt A

                                                                                                                                                      Optimizations

                                                                                                                                                      When you have a list of Prompt commands (and each one has its own variable), you can just use the first Prompt command and combine the rest of the other Prompt commands with it. You remove the Prompt commands and combine the arguments, separating each argument with a comma. The arguments can be composed of whatever combination of variables is desired.

                                                                                                                                                      The advantages of combining Prompt commands are that it makes scrolling through code faster, and it is more compact (i.e. smaller) and easier to write than using the individual Prompt commands. The primary disadvantage is that it is easier to accidentally erase a Prompt command with multiple arguments.

                                                                                                                                                      :Prompt A
:Prompt Str1
Combine the Prompts
:Prompt A,Str1

                                                                                                                                                      Error Conditions

                                                                                                                                                      • ERR:INVALID occurs if this statement is used outside a program.

                                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583, merthsoft.

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-82 1.0 Added
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                                                                                                                                                      Hex Value $A0
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                                                                                                                                                      • FR: Pt-Change(

                                                                                                                                                      Pt-Change(

                                                                                                                                                      Overview

                                                                                                                                                      Toggles a point on or off at (x,y) on the graph area. Off will be in the Background color and On will be the specified
                                                                                                                                                      Color#: 10 - 24 or color name pasted from [vars] COLOR.

                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                      Syntax

                                                                                                                                                      Pt-Change(x,y[,color#])

                                                                                                                                                      Arguments

                                                                                                                                                      NameTypeOptional
                                                                                                                                                      x
                                                                                                                                                      y
                                                                                                                                                      color#colorNumYes

                                                                                                                                                      Location

                                                                                                                                                      2nd, draw, POINTS, 3:Pt-Change(

                                                                                                                                                      Description

                                                                                                                                                      The Pt-Change( command is used to toggle a point (a pixel on the screen) on the graph screen at the given (X,Y) coordinates. If the point is on, it will be turned off and vice versa. Pt-Change( is affected by the window settings, which means you have to change the window settings accordingly, otherwise the point won't show up correctly on the screen.

                                                                                                                                                      Pt-Change( can be an interactive command: when on the graph screen, you can select it from the draw menu, and rather than have to input coordinates, be able to draw directly on the screen. Since you can both draw and erase points easily with Pt-Change(, this use of it is often more convenient than the Pen tool.

                                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $9F
                                                                                                                                                      Categories
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                                                                                                                                                      • FR: Pt-Naff(

                                                                                                                                                      Pt-Off(

                                                                                                                                                      Overview

                                                                                                                                                      Erases a point at (x,y) on the graph area using mark. The Off state may be the background color determined by the ImageVar or color setting.
                                                                                                                                                      Color#: 10 - 24 or color name pasted from [vars] COLOR.

                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                      Syntax

                                                                                                                                                      Pt-Off(x,y[,mark])

                                                                                                                                                      Arguments

                                                                                                                                                      NameTypeOptional
                                                                                                                                                      x
                                                                                                                                                      y
                                                                                                                                                      markYes

                                                                                                                                                      Location

                                                                                                                                                      2nd, draw, POINTS, 2:Pt-Off(

                                                                                                                                                      Description

                                                                                                                                                      The Pt-Off( command is used to turn off a point (a pixel on the screen) on the graph screen at the given (X,Y) coordinates. Pt-Off( is affected by the window settings, which means you have to change the window settings accordingly, otherwise the point won't show up correctly on the screen.

                                                                                                                                                      Advanced Uses

                                                                                                                                                      The Pt-Off( command has an optional third argument that determines the shape of the point (its mark). The mark can be 1 (dot), 2 (3x3 box), 3 (3x3 cross), 6 (3x3 box), or 7 (3x3 cross). Note that by using the 3x3 shapes the X,Y coördinates will be the center of the shape and not the upperleft corner of the shape. You don't need to specify the mark when using the first mark because it is the default; also, any value that isn't 2, 3, 6, or 7 will be treated as the default of 1.

                                                                                                                                                      :Pt-Off(5,5,1
Remove Mark
:Pt-Off(5,5

                                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, my_name, Skwerlman.

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $9E
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                                                                                                                                                      • FR: Pt-Aff(

                                                                                                                                                      Pt-On(

                                                                                                                                                      Overview

                                                                                                                                                      Draws a point at (x,y) on the graph area using markand the specified color#.
                                                                                                                                                      Color#: 10 - 24 or color name pasted from [vars] COLOR.

                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                      Syntax

                                                                                                                                                      Pt-On(x,y[,mark,color#])

                                                                                                                                                      Arguments

                                                                                                                                                      NameTypeOptional
                                                                                                                                                      x
                                                                                                                                                      y
                                                                                                                                                      markYes
                                                                                                                                                      color#colorNumYes

                                                                                                                                                      Location

                                                                                                                                                      2nd, draw, POINTS, 1:Pt-On(

                                                                                                                                                      Description

                                                                                                                                                      The Pt-On( command is used to draw a point on the graph screen at the given (X,Y) coordinates. Pt-On( is affected by the window settings Xmin, Xmax, Ymin, and Ymax. Make sure to change these accordingly when using it in a program, otherwise, you don't know where the point will show up.

                                                                                                                                                      Advanced Uses

                                                                                                                                                      The Pt-On( command has an optional third argument that determines the shape of the point (its mark). The mark can be 1 (dot), 2 (3x3 box), 3 (3x3 cross), 6 (3x3 box), or 7 (3x3 cross). Note that by using the 3x3 shapes the X,Y coordinates will be the center of the shape and not the upperleft corner of the shape. You don't need to specify the mark when using the first mark because it is the default; also, any value that isn't 2, 3, 6, or 7 will be treated as the default of 1. Remember to use the same mark when turning a point off as you used to turn it on. Note that the mark arguments 6 and 7 are not supported on the TI-84+CE, and using them will return a domain error. The color calculators also include a color argument after the mark argument, which can be used to change the color of the point. Note that the leaving the color argument blank will result in the point being plotted with a default color of blue.

                                                                                                                                                      If you need to convert coordinates in pixel format into point coordinate format, it can easily be done with the following formula:

                                                                                                                                                      (X pixel coordinateΔX)-absolute value(Xmax)=X point
                                                                                                                                                      (Y pixel coordinate                                                                                                                                                      ΔY)-absolute value(Ymax)=Y point

                                                                                                                                                      The ΔX and ΔY variables are available under "VARS", "Window", options 8 and 9. These two variables represent the number of points per pixel on the graph screen, so multiplying the pixel value by the ratio of points to pixels will give you the point value, you then subtract the Xmax/Ymax from this value to calibrate it to the center of the screen. This formula is useful in programs that use the pixel commands for their speed advantage, but need a point value for commands such as Circle( or Line(.

                                                                                                                                                      :Pt-On(5,5,1
should be
:Pt-On(5,5

                                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: burr, CloudVariable, DarkerLine, GoVegan, my_name, Skwerlman, tyler999.

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $F7
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                                                                                                                                                      • FR: RegPuiss

                                                                                                                                                      PwrReg

                                                                                                                                                      Overview

                                                                                                                                                      Fits a power regression model to Xlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ.

                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                      Syntax

                                                                                                                                                      PwrReg [Xlistname,Ylistname,freqlist,regequ]

                                                                                                                                                      Arguments

                                                                                                                                                      NameTypeOptional
                                                                                                                                                      XlistnamelistYes
                                                                                                                                                      YlistnamelistYes
                                                                                                                                                      freqlistlistYes
                                                                                                                                                      regequYes

                                                                                                                                                      Location

                                                                                                                                                      stat, CALC, A:PwrReg

                                                                                                                                                      Description

                                                                                                                                                      PwrReg tries to fit a power curve (y=a*xb) through a set of points. To use it, you must first store the points to two lists: one of the x-coordinates and one of the y-coordinates, ordered so that the nth element of one list matches up with the nth element of the other list. L₁ and L₂ are the default lists to use, and the List Editor (STAT > Edit…) is a useful window for entering the points.

                                                                                                                                                      The calculator does this regression by taking the natural log ln( of the x- and of the y-coordinates (this isn't stored anywhere) and then doing a linear regression. The result, ln(y)=bln(x)+ln(a), is transformed into y=eln(a)xb, which is a power curve. This algorithm shows that if any coordinates are negative or 0, the calculator will instantly quit with ERR:DOMAIN.

                                                                                                                                                      In its simplest form, PwrReg takes no arguments, and fits a power curve through the points in L₁ and L₂:

                                                                                                                                                      :{9,13,21,30,31,31,34→L₁
:{260,320,420,530,560,550,590→L₂
:LnReg

                                                                                                                                                      On the home screen, or as the last line of a program, this will display the equation of the curve: you'll be shown the format, y=a*x^b, and the values of a and b. It will also be stored in the RegEQ variable, but you won't be able to use this variable in a program - accessing it just pastes the equation wherever your cursor was. Finally, the statistical variables a, b, r, and r² will be set as well. These latter two variables will be displayed only if "Diagnostic Mode" is turned on (see DiagnosticOn and DiagnosticOff).

                                                                                                                                                      You don't have to do the regression on L₁ and L₂, but if you don't you'll have to enter the names of the lists after the command. For example:

                                                                                                                                                      :{9,13,21,30,31,31,34→FAT
:{260,320,420,530,560,550,590→CALS
:PwrReg ʟFAT,ʟCALS

                                                                                                                                                      You can attach frequencies to points, for when a point occurs more than once, by supplying an additional argument - the frequency list. This list does not have to contain integer frequencies. If you add a frequency list, you must supply the names of the x-list and y-list as well, even when they're L₁ and L₂.

                                                                                                                                                      Finally, you can enter an equation variable (such as Y₁) after the command, so that the curve's equation is stored to this variable automatically. This doesn't require you to supply the names of the lists, but if you do, the equation variable must come last. You can use polar, parametric, or sequential variables as well, but since the equation will be in terms of X anyway, this doesn't make much sense.

                                                                                                                                                      An example of PwrReg with all the optional arguments:

                                                                                                                                                      :{9,13,21,30,31,31,34→FAT
:{260,320,420,530,560,550,590→CALS
:{2,1,1,1,2,1,1→FREQ
:PwrReg ʟFAT,ʟCALS,ʟFREQ,Y1

                                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, thornahawk, Timothy Foster.

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $A3
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                                                                                                                                                      • FR: Pxl-Change(

                                                                                                                                                      Pxl-Change(

                                                                                                                                                      Overview

                                                                                                                                                      Toggles Off to On in the graph area: with specified color# Toggles On to Off in the graph area: Off will display the set Background Image Var or Color.
                                                                                                                                                      Color#: 10 - 24 or color name pasted from [vars] COLOR.

                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                      Syntax

                                                                                                                                                      Pxl-Change(row,column[,color#])

                                                                                                                                                      Arguments

                                                                                                                                                      NameTypeOptional
                                                                                                                                                      row
                                                                                                                                                      column
                                                                                                                                                      color#colorNumYes

                                                                                                                                                      Location

                                                                                                                                                      2nd, draw, POINTS, 6:Pxl-Change(

                                                                                                                                                      Description

                                                                                                                                                      The Pxl-Change( command is used to toggle the pixel at the given (Y,X) coordinates. If the pixel is on, it will be turned off and vice versa. Please note that the coordinates are switched around so that the row comes first and then the column — it's (Y,X) instead of (X,Y) like the Pt-Change( command. Also note that the row decreases as you go up which can confuse users.

                                                                                                                                                      In addition to being easier to use because it is not affected by the window settings (meaning you don't have to set them when using the command), Pxl-Change( is faster than its equivalent Pt-Change( command, so it should generally be used instead whenever possible.

                                                                                                                                                      Error Conditions

                                                                                                                                                      • ERR:DOMAIN is triggered if the coordinates are not whole numbers or not in the right range ([0..62] for row, [0..94] for column). These bounds are also affected by split screen mode.

                                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, iPhoenixOnTIBD.

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $A2
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                                                                                                                                                      • FR: Pxl-Naff(

                                                                                                                                                      Pxl-Off(

                                                                                                                                                      Overview

                                                                                                                                                      The Off state will display the set Background Image Var or COLOR.

                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                      Syntax

                                                                                                                                                      Pxl-Off(row,column)

                                                                                                                                                      Arguments

                                                                                                                                                      NameTypeOptional
                                                                                                                                                      row
                                                                                                                                                      column

                                                                                                                                                      Location

                                                                                                                                                      2nd, draw, POINTS, 5:Pxl-Off(

                                                                                                                                                      Description

                                                                                                                                                      The Pxl-Off( command is used to turn off the pixel at the given (Y,X) coordinates. Please note that the coordinates are switched around so that the row comes first and then the column — it's (Y,X) instead of (X,Y) like the Pt-Off( command. Also note that the (0,0) point is the upper left corner of the Graph screen.

                                                                                                                                                      In addition to being easier to use because it is not affected by the window settings (meaning you don't have to set them when using the command), Pxl-Off( is faster than its equivalent Pt-Off( command, so it should generally be used instead whenever possible.

                                                                                                                                                      Error Conditions

                                                                                                                                                      • ERR:DOMAIN is triggered if the coordinates are not whole numbers or not in the right range ([0..62] for row, [0..94] for column). These bounds are also affected by split screen mode.

                                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, my_name.

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $A1
                                                                                                                                                      Categories
                                                                                                                                                      Localizations
                                                                                                                                                      • FR: Pxl-Aff(

                                                                                                                                                      Pxl-On(

                                                                                                                                                      Overview

                                                                                                                                                      Draws pixel on the graph area at (row,column) in the specified color.
                                                                                                                                                      Color#: 10 - 24 or color name pasted from [vars] COLOR.

                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                      Syntax

                                                                                                                                                      Pxl-On(row,column[,color#])

                                                                                                                                                      Arguments

                                                                                                                                                      NameTypeOptional
                                                                                                                                                      row
                                                                                                                                                      column
                                                                                                                                                      color#colorNumYes

                                                                                                                                                      Location

                                                                                                                                                      2nd, draw, POINTS, 4:Pxl-On(

                                                                                                                                                      Description

                                                                                                                                                      The Pxl-On( command is used to turn on the pixel at the given (Y,X) coordinates. Please note that the coordinates are switched around so that the row comes first and then the column — it's (Y,X) unlike the (X,Y) of the Pt-On( command. Also note that the (0,0) point is the upper left corner of the Graph screen.

                                                                                                                                                      In addition to being easier to use because it is not affected by the window settings (meaning you don't have to set them when using the command), Pxl-On( is faster than its equivalent Pt-On( command, so it should generally be used instead whenever possible.

                                                                                                                                                      Error Conditions

                                                                                                                                                      • ERR:DOMAIN is triggered if the coordinates are not whole numbers or not in the right range ([0..62] for row, [0..94] for column). These bounds are also affected by split screen mode.

                                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, my_name.

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $1D
                                                                                                                                                      Categories
                                                                                                                                                      Localizations
                                                                                                                                                      • FR: P►Rx(

                                                                                                                                                      P►Rx(

                                                                                                                                                      Overview

                                                                                                                                                      Returns X, given polar coordinates r and θ or a list of polar coordinates.

                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                      Syntax

                                                                                                                                                      P►Rx(r,θ)

                                                                                                                                                      Arguments

                                                                                                                                                      NameTypeOptional
                                                                                                                                                      r
                                                                                                                                                      θ

                                                                                                                                                      Location

                                                                                                                                                      2nd, angle, ANGLE, 7:P, Rx(

                                                                                                                                                      Description

                                                                                                                                                      P►Rx( (polar►rectangular x-coordinate) calculates the x-coordinate of a polar point. Polar coordinates are of the form (r,θ), where θ is the counterclockwise angle made with the positive x-axis, and r is the distance away from the origin (the point (0,0)). The conversion identity x=r*cos(θ) is used to calculate P►Rx(.

                                                                                                                                                      The value returned depends on whether the calculator is in radian or degree mode. A full rotation around a circle is 2π radians, which is equal to 360°. The conversion from radians to degrees is angle180/π and from degrees to radians is angleπ/180. The P►Rx( command also accepts a list of points.

                                                                                                                                                      P►Rx(5,π/4)
    3.535533906
5*cos(π/4)
    3.535533906
P►Rx({1,2},{π/4,π/3})
    {.7071067812 1}

                                                                                                                                                      Advanced Uses

                                                                                                                                                      You can bypass the mode setting by using the ° (degree) and ʳ (radian) symbols. This next command will return the same values no matter if your calculator is in degrees or radians:

                                                                                                                                                      P►Rx(1,{π/4^^r,60°})
    {.7071067812 .5}

                                                                                                                                                      Optimization

                                                                                                                                                      In most cases P►Rx(r,θ) can be replaced by r*cos(θ) to save a byte:

                                                                                                                                                      :P►Rx(5,π/12)
can be
:5cos(π/12)

                                                                                                                                                      Conversely, complicated expressions multiplied by a cosine factor can be simplified by using P►Rx(r,θ) instead.

                                                                                                                                                      :(A+BX)cos(π/5)
can be
:P►Rx(A+BX,π/5)

                                                                                                                                                      Error Conditions

                                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: CloudVariable, DarkerLine, GoVegan, simplethinker, thornahawk.

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $1E
                                                                                                                                                      Categories
                                                                                                                                                      Localizations
                                                                                                                                                      • FR: P►Ry(

                                                                                                                                                      P►Ry(

                                                                                                                                                      Overview

                                                                                                                                                      Returns Y, given polar coordinates r and θ or a list of polar coordinates.

                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                      Syntax

                                                                                                                                                      P►Ry(r,θ)

                                                                                                                                                      Arguments

                                                                                                                                                      NameTypeOptional
                                                                                                                                                      r
                                                                                                                                                      θ

                                                                                                                                                      Location

                                                                                                                                                      2nd, angle, ANGLE, 8:P, Ry(

                                                                                                                                                      Description

                                                                                                                                                      P►Ry( (polar to rectangular y-coordinate) calculates the y-coordinate of a polar point. Polar coordinates are of the form (r,θ), where θ is the counterclockwise angle made with the positive x-axis, and r is the distance away from the origin (the point (0,0)). The conversion identity y=r*sin(θ) is used to calculate P►Ry(.

                                                                                                                                                      The value returned depends on whether the calculator is in radian or degree mode. A full rotation around a circle is 2π radians, which is equal to 360°. The conversion from radians to degrees is angle180/π and from degrees to radians is angleπ/180. The P►Ry( command also accepts a list of points.

                                                                                                                                                      P►Ry(5,π/4)
    3.535533906
5*sin(π/4)
    3.535533906
P►Ry({1,2},{π/4,π/3})
    {.7071067812 1.732050808}

                                                                                                                                                      Advanced Uses

                                                                                                                                                      You can bypass the mode setting by using the ° (degree) and ʳ (radian) symbols. This next command will return the same values no matter if your calculator is in degrees or radians:

                                                                                                                                                      P►Ry(1,{π/4^^r,60°})
    {.7071067812 .8660254038}

                                                                                                                                                      Optimization

                                                                                                                                                      In most cases P►Ry(r,θ) can be replaced by r*sin(θ) to save a byte:

                                                                                                                                                      :P►Ry(5,π/12)
can be
:5sin(π/12)

                                                                                                                                                      Conversely, complicated expressions multiplied by a sine factor can be simplified by using P►Ry(r,θ) instead.

                                                                                                                                                      :(A+BX)sin(π/5)
can be
:P►Ry(A+BX,π/5)

                                                                                                                                                      Error Conditions

                                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, thornahawk.

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $51
                                                                                                                                                      Categories
                                                                                                                                                      Localizations
                                                                                                                                                      • FR: Q

                                                                                                                                                      Q

                                                                                                                                                      Overview

                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                      Syntax

                                                                                                                                                      Q

                                                                                                                                                      Description

                                                                                                                                                      Examples

                                                                                                                                                      Explanation 1

                                                                                                                                                      code 1

                                                                                                                                                      Explanation 2

                                                                                                                                                      code 2

                                                                                                                                                      Error Conditions

                                                                                                                                                      Advanced Notes

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $F9
                                                                                                                                                      Categories
                                                                                                                                                      Localizations
                                                                                                                                                      • FR: RegQuad

                                                                                                                                                      QuadReg

                                                                                                                                                      Overview

                                                                                                                                                      Fits a quadratic regression model toXlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ.

                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                      Syntax

                                                                                                                                                      QuadReg [Xlistname,Ylistname,freqlist,regequ]

                                                                                                                                                      Arguments

                                                                                                                                                      NameTypeOptional
                                                                                                                                                      XlistnamelistYes
                                                                                                                                                      YlistnamelistYes
                                                                                                                                                      freqlistlistYes
                                                                                                                                                      regequYes

                                                                                                                                                      Location

                                                                                                                                                      stat, CALC, 5:QuadReg

                                                                                                                                                      Description

                                                                                                                                                      The QuadReg command can calculate the best fit quadratic through a set of points. To use it, you must first store the points to two lists: one of the x-coordinates and one of the y-coordinates, ordered so that the nth element of one list matches up with the nth element of the other list. L₁ and L₂ are the default lists to use, and the List Editor (STAT > Edit…) is a useful window for entering the points. You must have at least 3 points, because there are infinitely many quadratics that can go through 2 points or 1 point.

                                                                                                                                                      In its simplest form, QuadReg takes no arguments, and calculates a quadratic through the points in L₁ and L₂:

                                                                                                                                                      :{9,13,21,30,31,31,34→L₁
:{260,320,420,530,560,550,590→L₂
:QuadReg

                                                                                                                                                      On the home screen, or as the last line of a program, this will display the equation of the quadratic: you'll be shown the format, y=ax²+bx+c, and the values of a, b, and c. It will also be stored in the RegEQ variable, but you won't be able to use this variable in a program - accessing it just pastes the equation wherever your cursor was. Finally, the statistical variables a, b, c, and R² will be set as well. This latter variable will be displayed only if "Diagnostic Mode" is turned on (see DiagnosticOn and DiagnosticOff).

                                                                                                                                                      You don't have to do the regression on L₁ and L₂, but if you don't you'll have to enter the names of the lists after the command. For example:

                                                                                                                                                      :{9,13,21,30,31,31,34→FAT
:{260,320,420,530,560,550,590→CALS
:QuadReg ʟFAT,ʟCALS

                                                                                                                                                      You can attach frequencies to points, for when a point occurs more than once, by supplying an additional argument - the frequency list. This list does not have to contain integer frequencies. If you add a frequency list, you must supply the names of the x-list and y-list as well, even when they're L₁ and L₂.

                                                                                                                                                      Finally, you can enter an equation variable (such as Y₁) after the command, so that the quadratic is stored to this equation automatically. This doesn't require you to supply the names of the lists, but if you do, the equation variable must come last. You can use polar, parametric, or sequential variables as well, but since the quadratic will be in terms of X anyway, this doesn't make much sense.

                                                                                                                                                      An example of QuadReg with all the optional arguments:

                                                                                                                                                      :{9,13,21,30,31,31,34→FAT
:{260,320,420,530,560,550,590→CALS
:{2,1,1,1,2,1,1→FREQ
:QuadReg ʟFAT,ʟCALS,ʟFREQ,Y₁

                                                                                                                                                      Advanced

                                                                                                                                                      Note that even if a relationship is actually linear, since a quadratic regression has all the freedom of a linear regression and more, it will produce a better R² value, especially if the number of terms is small, and may lead you to (falsely) believe that a relationship is quadratic when it actually isn't. Take the correlation constant with a grain of salt, and consider if the fit is really that much better at the expense of added complexity, and if there's any reason to believe the relationship between the variables may be quadratic.

                                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, thornahawk, Timothy Foster.

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $2F
                                                                                                                                                      Categories
                                                                                                                                                      Localizations
                                                                                                                                                      • FR: RegQuatre

                                                                                                                                                      QuartReg

                                                                                                                                                      Overview

                                                                                                                                                      Fits a quartic regression model toXlistname and Ylistname with frequency freqlist, and stores the regression equation to regequ.

                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                      Syntax

                                                                                                                                                      QuartReg [Xlistname,Ylistname,freqlist,regequ]

                                                                                                                                                      Arguments

                                                                                                                                                      NameTypeOptional
                                                                                                                                                      XlistnamelistYes
                                                                                                                                                      YlistnamelistYes
                                                                                                                                                      freqlistlistYes
                                                                                                                                                      regequYes

                                                                                                                                                      Location

                                                                                                                                                      stat, CALC, 7:QuartReg

                                                                                                                                                      Description

                                                                                                                                                      The QuartReg command can calculate the best fit quartic equation through a set of points. To use it, you must first store the points to two lists: one of the x-coordinates and one of the y-coordinates, ordered so that the Nth element of one list matches up with the Nth element of the other list. L1 and L2 are the default lists to use, and the List Editor (STAT > Edit…) is a useful window for entering the points. You must have at least 5 points, because there's infinitely many quadratics that can go through 4 points or less

                                                                                                                                                      In its simplest form, QuartReg takes no arguments, and calculates a quartic through the points in L1 and L2:

                                                                                                                                                      :{9,13,21,30,31,31,34→L1
:{260,320,420,530,560,550,590→L2
:QuartReg

                                                                                                                                                      On the home screen, or as the last line of a program, this will display the equation of the quartic: you'll be shown the format, y=ax4+bx3+cx2+dx+e, and the values of a, b, c, d, and e. It will also be stored in the RegEQ variable, but you won't be able to use this variable in a program - accessing it just pastes the equation wherever your cursor was. Finally, the statistical variables a, b, c, d, e, and R2 will be set as well. This latter variable will be displayed only if "Diagnostic Mode" is turned on (see DiagnosticOn and DiagnosticOff).

                                                                                                                                                      You don't have to do the regression on L1 and L2, but if you don't you'll have to enter the names of the lists after the command. For example:

                                                                                                                                                      :{9,13,21,30,31,31,34→FAT
:{260,320,420,530,560,550,590→CALS
:QuartReg ʟFAT,ʟCALS

                                                                                                                                                      You can attach frequencies to points, for when a point occurs more than once, by supplying an additional argument - the frequency list. This list does not have to contain integer frequencies. If you add a frequency list, you must supply the names of the x-list and y-list as well, even when they're L1 and L2.

                                                                                                                                                      Finally, you can enter an equation variable (such as Y1) after the command, so that the quartic equation is stored to this variable automatically. This doesn't require you to supply the names of the lists, but if you do, the equation variable must come last. You can use polar, parametric, or sequential variables as well, but since the quadratic will be in terms of X anyway, this doesn't make much sense.

                                                                                                                                                      An example of QuartReg with all the optional arguments:

                                                                                                                                                      :{9,13,21,30,31,31,34→FAT
:{260,320,420,530,560,550,590→CALS
:{2,1,1,1,2,1,1→FREQ
:QuartReg ʟFAT,ʟCALS,ʟFREQ,Y1

                                                                                                                                                      Advanced

                                                                                                                                                      Note that even if a relationship is actually linear, since a quartic regression has all the freedom of a linear regression and much more, it will produce a better R2 value, especially if the number of points is small, and may lead you to (falsely) believe that a relationship is quartic when it actually isn't. An extreme example is the case of 5 points which are close to being on a line. The linear regression will be very good, but the quartic will seem even better - it will go through all 5 points and have an R2 value of 1. However, this doesn't make the 5 points special - any 5 (that don't have repeating x-values) will do! Take the correlation constant with a grain of salt, and consider if the fit is really that much better at the expense of much added complexity, and if there's any reason to believe the relationship between the variables may be quartic.

                                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Timothy Foster.

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $EF81
                                                                                                                                                      Categories
                                                                                                                                                      Localizations
                                                                                                                                                      • FR: Quartiles réglage…

                                                                                                                                                      Quartiles Setting…

                                                                                                                                                      Overview

                                                                                                                                                      Comment:CE OS 5.2+

                                                                                                                                                      Syntax

                                                                                                                                                      Quartiles Setting…

                                                                                                                                                      Description

                                                                                                                                                      Examples

                                                                                                                                                      Explanation 1

                                                                                                                                                      code 1

                                                                                                                                                      Explanation 2

                                                                                                                                                      code 2

                                                                                                                                                      Error Conditions

                                                                                                                                                      Advanced Notes

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-84+CE 5.1.0 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $EF81
                                                                                                                                                      Categories
                                                                                                                                                      Localizations
                                                                                                                                                      • FR: Quartiles réglage…

                                                                                                                                                      Quartiles Setting…

                                                                                                                                                      Overview

                                                                                                                                                      Comment:CE OS 5.2+

                                                                                                                                                      Syntax

                                                                                                                                                      Quartiles Setting…

                                                                                                                                                      Description

                                                                                                                                                      Examples

                                                                                                                                                      Explanation 1

                                                                                                                                                      code 1

                                                                                                                                                      Explanation 2

                                                                                                                                                      code 2

                                                                                                                                                      Error Conditions

                                                                                                                                                      Advanced Notes

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-84+CE 5.1.0 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $EF66
                                                                                                                                                      Categories
                                                                                                                                                      Localizations
                                                                                                                                                      • FR: TracéAjust-Éq

                                                                                                                                                      QuickPlot&Fit-EQ

                                                                                                                                                      Overview

                                                                                                                                                      Comment:84+CSE and later

                                                                                                                                                      Syntax

                                                                                                                                                      QuickPlot&Fit-EQ

                                                                                                                                                      Description

                                                                                                                                                      Examples

                                                                                                                                                      Explanation 1

                                                                                                                                                      code 1

                                                                                                                                                      Explanation 2

                                                                                                                                                      code 2

                                                                                                                                                      Error Conditions

                                                                                                                                                      Advanced Notes

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-84+CSE 4.0 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $EFA5
                                                                                                                                                      Categories
                                                                                                                                                      Localizations
                                                                                                                                                      • FR: Quitter

                                                                                                                                                      Quit Editor

                                                                                                                                                      Overview

                                                                                                                                                      Comment:CE OS 5.3+

                                                                                                                                                      Syntax

                                                                                                                                                      Quit Editor

                                                                                                                                                      Description

                                                                                                                                                      Examples

                                                                                                                                                      Explanation 1

                                                                                                                                                      code 1

                                                                                                                                                      Explanation 2

                                                                                                                                                      code 2

                                                                                                                                                      Error Conditions

                                                                                                                                                      Advanced Notes

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-84+CE 5.3.0 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $6214
                                                                                                                                                      Categories
                                                                                                                                                      Localizations
                                                                                                                                                      • FR: Q₁

                                                                                                                                                      Q₁

                                                                                                                                                      Overview

                                                                                                                                                      Syntax

                                                                                                                                                      Q₁

                                                                                                                                                      Description

                                                                                                                                                      Examples

                                                                                                                                                      Explanation 1

                                                                                                                                                      code 1

                                                                                                                                                      Explanation 2

                                                                                                                                                      code 2

                                                                                                                                                      Error Conditions

                                                                                                                                                      Advanced Notes

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $6215
                                                                                                                                                      Categories
                                                                                                                                                      Localizations
                                                                                                                                                      • FR: Q₃

                                                                                                                                                      Q₃

                                                                                                                                                      Overview

                                                                                                                                                      Syntax

                                                                                                                                                      Q₃

                                                                                                                                                      Description

                                                                                                                                                      Examples

                                                                                                                                                      Explanation 1

                                                                                                                                                      code 1

                                                                                                                                                      Explanation 2

                                                                                                                                                      code 2

                                                                                                                                                      Error Conditions

                                                                                                                                                      Advanced Notes

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $52
                                                                                                                                                      Categories
                                                                                                                                                      Localizations
                                                                                                                                                      • FR: R

                                                                                                                                                      R

                                                                                                                                                      Overview

                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                      Syntax

                                                                                                                                                      R

                                                                                                                                                      Description

                                                                                                                                                      Examples

                                                                                                                                                      Explanation 1

                                                                                                                                                      code 1

                                                                                                                                                      Explanation 2

                                                                                                                                                      code 2

                                                                                                                                                      Error Conditions

                                                                                                                                                      Advanced Notes

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $EF42
                                                                                                                                                      Categories
                                                                                                                                                      Localizations
                                                                                                                                                      • FR: ROUGE

                                                                                                                                                      RED

                                                                                                                                                      Overview

                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                      Syntax

                                                                                                                                                      RED

                                                                                                                                                      Description

                                                                                                                                                      Examples

                                                                                                                                                      Explanation 1

                                                                                                                                                      code 1

                                                                                                                                                      Explanation 2

                                                                                                                                                      code 2

                                                                                                                                                      Error Conditions

                                                                                                                                                      Advanced Notes

                                                                                                                                                      History

                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                      TI-84+CSE 4.0 Added
                                                                                                                                                      Property Value
                                                                                                                                                      Hex Value $EF94
                                                                                                                                                      Categories
                                                                                                                                                        Localizations
                                                                                                                                                        • FR: DROITE

                                                                                                                                                        RIGHT

                                                                                                                                                        Overview

                                                                                                                                                        RIGHT is a tail argument for the invNorm( command where the optional argument tail can be LEFT (-∞,-a), CENTER [-a,a] or RIGHT (a, ∞) for Real a.
                                                                                                                                                        See also invNorm(.

                                                                                                                                                        Comment:CE OS 5.2+

                                                                                                                                                        Availability: Token available everywhere.

                                                                                                                                                        Syntax

                                                                                                                                                        RIGHT

                                                                                                                                                        Location

                                                                                                                                                        2nd, catalog

                                                                                                                                                        Description

                                                                                                                                                        Examples

                                                                                                                                                        Explanation 1

                                                                                                                                                        code 1

                                                                                                                                                        Explanation 2

                                                                                                                                                        code 2

                                                                                                                                                        Error Conditions

                                                                                                                                                        Advanced Notes

                                                                                                                                                        History

                                                                                                                                                        Calculator OS Version Description
                                                                                                                                                        TI-84+CE 5.2.0 Added
                                                                                                                                                        Property Value
                                                                                                                                                        Hex Value $1B
                                                                                                                                                        Categories
                                                                                                                                                        Localizations
                                                                                                                                                        • FR: R►Pr(

                                                                                                                                                        R►Pr(

                                                                                                                                                        Overview

                                                                                                                                                        Returns R, given rectangular coordinates x and y or a list of rectangular coordinates.

                                                                                                                                                        Availability: Token available everywhere.

                                                                                                                                                        Syntax

                                                                                                                                                        R►Pr(x,y)

                                                                                                                                                        Arguments

                                                                                                                                                        NameTypeOptional
                                                                                                                                                        x
                                                                                                                                                        y

                                                                                                                                                        Location

                                                                                                                                                        2nd, angle, ANGLE, 5:R, Pr(

                                                                                                                                                        Description

                                                                                                                                                        R►Pr( (Rectangular to polar radius) takes the (x,y) (Cartesian) coordinates, and gives the radius coordinate r of the same point in (r,θ) (polar) mode. The identity used for this conversion is _r_² = _x_²+_y_²

                                                                                                                                                        R►Pr(3,4)
    5
√(3²+4²)
    5
R►Pr({6,5},{8,12})
    {10 13}

                                                                                                                                                        The function works even when the equivalent √(_x_²+_y_²) fails due to overflow:

                                                                                                                                                        R►Pr(3e99,4e99)
    5e99

                                                                                                                                                        Optimization

                                                                                                                                                        R►Pr( is the smallest way to implement the distance formula \(d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\). Just give the values x1-x2 and y1 - y2 as arguments:

                                                                                                                                                        :√((5-2)²+(4-0)²)
can be
:R►Pr(5-2,4-0)

                                                                                                                                                        Error Conditions

                                                                                                                                                        Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Myles_Zadok, thornahawk, Timothy Foster.

                                                                                                                                                        History

                                                                                                                                                        Calculator OS Version Description
                                                                                                                                                        TI-82 1.0 Added
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                                                                                                                                                        Hex Value $1C
                                                                                                                                                        Categories
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                                                                                                                                                        • FR: R►Pθ(

                                                                                                                                                        R►Pθ(

                                                                                                                                                        Overview

                                                                                                                                                        Returns θ, given rectangular coordinates x and y or a list of rectangular coordinates.

                                                                                                                                                        Availability: Token available everywhere.

                                                                                                                                                        Syntax

                                                                                                                                                        R►Pθ(x,y)

                                                                                                                                                        Arguments

                                                                                                                                                        NameTypeOptional
                                                                                                                                                        θ
                                                                                                                                                        x
                                                                                                                                                        y

                                                                                                                                                        Location

                                                                                                                                                        2nd, angle, ANGLE

                                                                                                                                                        Description

                                                                                                                                                        R►Pθ( (Rectangular to polar θ) takes the (x,y) (Cartesian) coordinate, and returns the angle that the ray from (0,0) to (x,y) makes with the positive x-axis. This is the θ-coordinate of the same point in (r,θ) (polar) mode. The identity used for this conversion is tan(θ)=y__/x, with the correct inverse being chosen depending on the quadrant that the point is in. The range of the angle returned is -π<θ≤π. R►Pθ( can also be used on lists.

                                                                                                                                                        R►Pθ( is equivalent to the atan2() instruction seen in C/++ and FORTRAN.

                                                                                                                                                        R►Pθ(3,4)
    .927295218
tanֿ¹(4/3)
    .927295218
R►Pθ(0,{1,-1})
    {1.570796327, -1.57096327}

                                                                                                                                                        R►Pθ( is affected by Degree and Radian mode in its output, which is an angle measured in degrees or radians respectively.

                                                                                                                                                        Advanced Uses

                                                                                                                                                        If you want the result to always be a radian angle, regardless of mode settings, you can divide the result by 1ʳ:

                                                                                                                                                        R►Pθ(x,y)/1^^r

                                                                                                                                                        If you want the result to always be a degree angle, regardless of mode settings, you can divide the result by 1°:

                                                                                                                                                        R►Pθ(x,y)/1°

                                                                                                                                                        Error Conditions

                                                                                                                                                        Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, thornahawk.

                                                                                                                                                        History

                                                                                                                                                        Calculator OS Version Description
                                                                                                                                                        TI-82 1.0 Added
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                                                                                                                                                        • FR: Radian

                                                                                                                                                        Radian

                                                                                                                                                        Overview

                                                                                                                                                        Sets radian angle mode.

                                                                                                                                                        Availability: Token only available from within the Basic editor.

                                                                                                                                                        Syntax

                                                                                                                                                        Radian

                                                                                                                                                        Location

                                                                                                                                                        mode, Radian

                                                                                                                                                        Description

                                                                                                                                                        The Radian command puts the calculator into Radian mode, where the inputs and/or outputs to trig functions are assumed to be radian angles.

                                                                                                                                                        Angles measured in radians range from 0 to 2π. They are defined as the arc length of the arc, on a unit circle (circle with radius 1), that corresponds to the angle when it is placed in the center. This definition actually only differs from degree measurements by a constant factor.

                                                                                                                                                        To convert from a degree angle to a radian angle, multiply by 180/π. To go the other way, and get a radian angle from a degree angle, multiply by π/180.

                                                                                                                                                        The following commands are affected by whether the calculator is in Radian or Degree mode:

                                                                                                                                                        The input is differently interpreted:

                                                                                                                                                        The output is differently expressed:

                                                                                                                                                        However, some commands are notably unaffected by angle mode, even though they involve angles, and this may cause confusion. This happens with the SinReg command, which assumes that the calculator is in Radian mode even when it's not. As a result, the regression model it generates will graph incorrectly in Degree mode.

                                                                                                                                                        Also, complex numbers in polar form are an endless source of confusion. The angle( command, as well as the polar display format, are affected by angle mode. However, complex exponentials (see the e^( command), defined as \(e^{i\theta}=\cos\theta+i\sin\theta\), are evaluated as though in Radian mode, regardless of the angle mode. This gives mysterious results like the following:

                                                                                                                                                        Degree:r𝑒^θ𝑖
        Done
𝑒^(πi)
        1𝑒^(180i)
Ans=𝑒^(180𝑖)
        0 (false)

                                                                                                                                                        Overall, it's better to put your calculator in Radian mode when dealing with polar form of complex numbers, especially since no mathematician would ever use degrees for the purpose anyway.

                                                                                                                                                        Optimization

                                                                                                                                                        It's sometimes beneficial to use the ʳ command instead of switching to Radian mode. The r symbol will make sure a number is interpreted as a radian angle, even in degree mode, so that, for example:

                                                                                                                                                        Degree
                                                                                                                                                        ………………Done
                                                                                                                                                        sin(π)
                                                                                                                                                        ……………….0548036651
                                                                                                                                                        sin(πr)
                                                                                                                                                        ………………0

                                                                                                                                                        This is smaller when only one trig calculation needs to be done. Also, it doesn't change the user's settings, which are good to preserve whenever possible.

                                                                                                                                                        Source: parts of this page were written by the following TI|BD contributors: burr, CloudVariable, DarkerLine, GoVegan, Timothy Foster, Trenly.

                                                                                                                                                        History

                                                                                                                                                        Calculator OS Version Description
                                                                                                                                                        TI-82 1.0 Added
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                                                                                                                                                        Hex Value $BB4D
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                                                                                                                                                        • FR: Réel

                                                                                                                                                        Real

                                                                                                                                                        Overview

                                                                                                                                                        Sets mode to display complex results only when you enter complex numbers.

                                                                                                                                                        Availability: Token only available from within the Basic editor.

                                                                                                                                                        Syntax

                                                                                                                                                        Real

                                                                                                                                                        Location

                                                                                                                                                        mode, Real

                                                                                                                                                        Description

                                                                                                                                                        The Real command puts the calculator in real number-only mode. This shouldn't be taken quite literally, as you can still type in 𝑖 to get complex numbers, and do operations with them (they will be displayed as in a+b𝑖 mode, in that case). However, any operation done with real numbers that comes out to a complex result, such as taking the square root of a negative number, will throw a ERR:NONREAL ANS error.

                                                                                                                                                        There is no real advantage to using Real mode over a+b𝑖 mode — it just adds another error condition that wouldn't be triggered otherwise. However, it is the default setting, and so there's a good chance that the calculator will be in Real mode when someone runs your program. Thus, when using complex numbers implicitly (such as in a quadratic equation solver) you should do something about this.

                                                                                                                                                        Advanced Uses

                                                                                                                                                        Rather than switch to a+b𝑖 mode, you might want to force the calculations to use complex numbers by making the original argument complex. The general way to do this is by adding +0i to the number. However, there may be an optimization in any particular case. See the quadratic formula routine for a good example of this.

                                                                                                                                                        Real
        Done
√(-1)    
        (causes an error)
√(-1+0i)        
        i

                                                                                                                                                        See Also

                                                                                                                                                        Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

                                                                                                                                                        History

                                                                                                                                                        Calculator OS Version Description
                                                                                                                                                        TI-83 0.01013 Added
                                                                                                                                                        Property Value
                                                                                                                                                        Hex Value $9B
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                                                                                                                                                        • FR: RappelBDG

                                                                                                                                                        RecallGDB

                                                                                                                                                        Overview

                                                                                                                                                        Restores all settings stored in the graph database variable GDBn.

                                                                                                                                                        Availability: Token available everywhere.

                                                                                                                                                        Syntax

                                                                                                                                                        RecallGDB n

                                                                                                                                                        Arguments

                                                                                                                                                        NameTypeOptional
                                                                                                                                                        n

                                                                                                                                                        Location

                                                                                                                                                        2nd, draw, STO, 4:RecallGDB

                                                                                                                                                        Description

                                                                                                                                                        The RecallGDB command recalls graph settings a GDB (Graph DataBase) variable, one of GDB1, GDB2, …, GDB0 (as indicated by the argument). These settings can be stored to a GDB using the StoreGDB command.

                                                                                                                                                        The settings stored in a GDB include:

                                                                                                                                                        • The graphing mode currently enabled.
                                                                                                                                                        • All equations in the current graphing mode, but NOT other graphing modes.
                                                                                                                                                        • All window variables applicable to the current graphing mode. This does not include zoom variables, table settings, or irrelevant variables such as Tmin when in function mode.
                                                                                                                                                        • The menu settings relevant to graphing (everything in the 2nd FORMAT menu, as well as Connected/Dot and Sequential/Simul settings in the MODE menu)

                                                                                                                                                        The number passed to RecallGDB must be one of 0 through 9. It has to be a number: RecallGDB X will not work, even if X contains a value 0 through 9.

                                                                                                                                                        Advanced Uses

                                                                                                                                                        The StoreGDB and RecallGDB variables are useful in cleaning up after a program finishes running, preserving the user's settings. If your program heavily relies on the graph screen, it may end up editing window size or other graph settings, which the user might want to be saved. This is easily done:

                                                                                                                                                        Add StoreGDB 1 (or any other number) to the beginning of your program.

                                                                                                                                                        Then, feel free to edit any graph settings you like.

                                                                                                                                                        At the end of your program, add RecallGDB 1, followed by DelVar GDB1, to recall the graph settings stored at the beginning.

                                                                                                                                                        GDBs can also be useful in adding extra string storage. You can store strings to the Yn variables, and back them up in a GDB; to retrieve them later, recall the GDB and use Equ►String( to store the equations to the strings again.

                                                                                                                                                        Error Conditions

                                                                                                                                                        • ERR:DATA TYPE is thrown if the argument is not a number 0 through 9.
                                                                                                                                                        • ERR:UNDEFINED is thrown if the requested GDB does not exist.

                                                                                                                                                        See Also

                                                                                                                                                        Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Zaphod Beeblebrox.

                                                                                                                                                        History

                                                                                                                                                        Calculator OS Version Description
                                                                                                                                                        TI-82 1.0 Added
                                                                                                                                                        Property Value
                                                                                                                                                        Hex Value $99
                                                                                                                                                        Categories
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                                                                                                                                                        • FR: RappelImage

                                                                                                                                                        RecallPic

                                                                                                                                                        Overview

                                                                                                                                                        Displays the graph and adds the picture stored in Picn.

                                                                                                                                                        Availability: Token available everywhere.

                                                                                                                                                        Syntax

                                                                                                                                                        RecallPic n

                                                                                                                                                        Arguments

                                                                                                                                                        NameTypeOptional
                                                                                                                                                        n

                                                                                                                                                        Location

                                                                                                                                                        2nd, draw, STO, 2:RecallPic

                                                                                                                                                        Description

                                                                                                                                                        RecallPic draws a saved picture to the graph screen (to save a picture, draw it on the graph screen, then save it with StorePic). If something is already drawn on the graph screen, RecallPic will draw new pixels where needed, but it will not erase anything. As a result, you often want to ClrDraw before recalling a picture.

                                                                                                                                                        The number passed to RecallPic must be one of 0 through 9. It has to be a number: RecallPic X will not work, even if X contains a value 0 through 9.

                                                                                                                                                        Advanced Uses

                                                                                                                                                        A combination of StorePic and RecallPic can be used to maintain a background over which another sprite moves:

                                                                                                                                                        1. Draw the background, and save it to a picture file with StorePic.
                                                                                                                                                        2. Next, draw the sprite to the screen.
                                                                                                                                                        3. When you want to move the sprite, erase it, then use RecallPic to draw the background again.
                                                                                                                                                        4. Then draw the sprite to its new location on the screen again (this can be done before or after using RecallPic).

                                                                                                                                                        Also, if a screen in your program takes more than a second to draw, and is displayed several times, you might want to consider storing it to a picture the first time it's drawn, and then recalling it every next time you want to draw it.

                                                                                                                                                        Error Conditions

                                                                                                                                                        • ERR:DATA TYPE is thrown if the argument is not a number 0 through 9.
                                                                                                                                                        • ERR:UNDEFINED is thrown if the requested picture does not exist.

                                                                                                                                                        Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583, Zaphod Beeblebrox.

                                                                                                                                                        History

                                                                                                                                                        Calculator OS Version Description
                                                                                                                                                        TI-82 1.0 Added
                                                                                                                                                        Property Value
                                                                                                                                                        Hex Value $7E03
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                                                                                                                                                        • FR: CoordRect

                                                                                                                                                        RectGC

                                                                                                                                                        Overview

                                                                                                                                                        Sets rectangular graphing coordinates format.

                                                                                                                                                        Availability: Token only available from within the Basic editor.

                                                                                                                                                        Syntax

                                                                                                                                                        RectGC

                                                                                                                                                        Location

                                                                                                                                                        2nd, format, RectGC

                                                                                                                                                        Description

                                                                                                                                                        The RectGC ("Rectangular Grid Coordinates") command (like its opposite, the PolarGC) command, affects how the coordinates of a point on the graph screen are displayed. When RectGC is enabled, the coordinates of a point are displayed as (X,Y).

                                                                                                                                                        The X and Y coordinates of a point are interpreted as the horizontal and vertical distance from the origin (the point (0,0)) Up and right are positive directions, while down and left are negative. For example, the point (1,-2) — that is, the point with x-coordinate 1 and y-coordinate -2 — is one horizontal unit right and two horizontal units down from (0,0).

                                                                                                                                                        Of course, coordinates are only displayed with the CoordOn setting; however, with CoordOff, RectGC and PolarGC are still useful, because in a variety of cases, the coordinates of a point are also stored to variables. With RectGC enabled, they are stored to X and Y.

                                                                                                                                                        Advanced

                                                                                                                                                        The following situations involve storing coordinates of a point to variables:

                                                                                                                                                        • Graphing an equation
                                                                                                                                                        • Tracing an equation or plot
                                                                                                                                                        • Moving the cursor on the graph screen
                                                                                                                                                        • Using the interactive mode of one of the 2nd DRAW commands
                                                                                                                                                        • Using one of DrawF, DrawInv, or Tangent(
                                                                                                                                                        • Anything in the 2nd CALC menu.

                                                                                                                                                        Naturally, any command like Input or Select( which involves the above, will also store coordinates of a point.

                                                                                                                                                        Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan.

                                                                                                                                                        History

                                                                                                                                                        Calculator OS Version Description
                                                                                                                                                        TI-82 1.0 Added
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                                                                                                                                                        Hex Value $6201
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                                                                                                                                                        • FR: RegEQ

                                                                                                                                                        RegEQ

                                                                                                                                                        Overview

                                                                                                                                                        Availability: Token available everywhere.

                                                                                                                                                        Syntax

                                                                                                                                                        RegEQ

                                                                                                                                                        Description

                                                                                                                                                        Examples

                                                                                                                                                        Explanation 1

                                                                                                                                                        code 1

                                                                                                                                                        Explanation 2

                                                                                                                                                        code 2

                                                                                                                                                        Error Conditions

                                                                                                                                                        Advanced Notes

                                                                                                                                                        History

                                                                                                                                                        Calculator OS Version Description
                                                                                                                                                        TI-82 1.0 Added
                                                                                                                                                        Property Value
                                                                                                                                                        Hex Value $D2
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                                                                                                                                                        • FR: Repeat

                                                                                                                                                        Repeat

                                                                                                                                                        Overview

                                                                                                                                                        Executes commands until condition is true.

                                                                                                                                                        Availability: Token only available from within the Basic editor.

                                                                                                                                                        Syntax

                                                                                                                                                        Repeatcondition:commands:End:commands

                                                                                                                                                        Arguments

                                                                                                                                                        NameTypeOptional
                                                                                                                                                        condition
                                                                                                                                                        commands
                                                                                                                                                        commands

                                                                                                                                                        Location

                                                                                                                                                        prgm, CTL, 6:Repeat

                                                                                                                                                        Description

                                                                                                                                                        A Repeat loop executes a block of commands between the Repeat and End commands until the specified condition is true. The condition is tested at the end of the loop (when the End command is encountered), so the loop will always be executed at least once. This means that you sometimes don't have to declare or initialize the variables in the condition before the loop.

                                                                                                                                                        After each time the Repeat loop is executed, the condition is checked to see if it is true. If it is true, then the loop is exited and program execution continues after the End command. If the condition is false, the loop is executed again.

                                                                                                                                                        Advanced Uses

                                                                                                                                                        When using Repeat loops, you have to provide the code to break out of the loop (it isn't built into the loop). If there is no code that ends the loop, then you will have an infinite loop. An infinite loop just keeps executing, until you have to manually exit the loop (by pressing the ON key). In the case that you actually want an infinite loop, you can just use 0 as the condition. Because 0 is always false (based on Boolean Logic), the loop will never end.

                                                                                                                                                        :Repeat 0
:statement(s)
:End

                                                                                                                                                        Each time the program enters a Repeat block, the calculator uses 35+(size of the condition) bytes of memory to keep track of this. This memory is given back to you as soon as the program reaches End. This isn't really a problem unless you're low on RAM, or have a lot of nested Repeat statements. However, if you use Goto to jump out of a Repeat block, you lose those bytes for as long as the program is running — and if you keep doing this, you might easily run out of memory, resulting in ERR:MEMORY.

                                                                                                                                                        Optimization

                                                                                                                                                        The Ans variable (last answer) is a temporary variable that can hold any variable. Ans is changed when there is an expression or variable storage or when pausing with the Pause command. It is mostly useful when you are just manipulating one variable. To use Ans just put an expression on a line by itself; it will automatically be stored to Ans. You can then change the expressions on the next line where the variable was called and put Ans there instead.

                                                                                                                                                        Because Repeat loops are executed at least once, you can sometimes put Ans in the condition instead of the variable.

                                                                                                                                                        :Repeat A
:getKey→A
:End
can be
:Repeat Ans
:getKey→A
:End

                                                                                                                                                        Command Timings

                                                                                                                                                        When deciding whether to use a Repeat loop, as opposed to a For or While loop, it's good to know how Repeat loops stack up against them. This comparison comes from the Code Timings page showing the speeds of the three different kinds of loops:

                                                                                                                                                        Format

                                                                                                                                                        Bars

                                                                                                                                                        Pixels

                                                                                                                                                        For(A,0,2000
                                                                                                                                                        End

                                                                                                                                                        4 bars + 4 pixels

                                                                                                                                                        36

                                                                                                                                                        Delvar A
                                                                                                                                                        While A≤2000
                                                                                                                                                        A+1→A
                                                                                                                                                        End

                                                                                                                                                        23 bars

                                                                                                                                                        184

                                                                                                                                                        Delvar A
                                                                                                                                                        Repeat A>2000
                                                                                                                                                        A+1→A
                                                                                                                                                        End

                                                                                                                                                        22 bars + 7 pixels

                                                                                                                                                        183

                                                                                                                                                        The general conclusion you can take away from this table is that For( loops should be used when speed is a priority, and then you should use Repeat or While loops when the appropriate circumstance comes up. Each kind of loop has its own place, so it's still good to know how to use all three of them.

                                                                                                                                                        Error Conditions

                                                                                                                                                        • ERR:INVALID occurs if this statement is used outside a program.

                                                                                                                                                        Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

                                                                                                                                                        History

                                                                                                                                                        Calculator OS Version Description
                                                                                                                                                        TI-82 1.0 Added
                                                                                                                                                        Property Value
                                                                                                                                                        Hex Value $D5
                                                                                                                                                        Categories
                                                                                                                                                        Localizations
                                                                                                                                                        • FR: Return

                                                                                                                                                        Return

                                                                                                                                                        Overview

                                                                                                                                                        Returns to the calling program.

                                                                                                                                                        Availability: Token only available from within the Basic editor.

                                                                                                                                                        Syntax

                                                                                                                                                        Return

                                                                                                                                                        Location

                                                                                                                                                        prgm, CTL, E:Return

                                                                                                                                                        Description

                                                                                                                                                        When the Return command is used in a program it exits the program (terminating the program execution) and returns the user to the home screen. If it is encountered within loops, the loops will be stopped.

                                                                                                                                                        There is some distinction when using Return with subprograms: the Return command will stop the program execution of the subprogram, and program execution will go back to the calling program, continuing right after the subprogram call. If this functionality is not desired, then you should use the Stop command instead. Generally, though, you should use Return instead of Stop.

                                                                                                                                                        :ClrHome
:Input "Guess:",A
:Stop
Replace Stop with Return
:ClrHome
:Input "Guess:",A
:Return

                                                                                                                                                        Optimization

                                                                                                                                                        You don't have to put a Return command at the end of a program or subprogram if you can organize the program so that it just naturally quits. When the calculator reaches the end of a program, it will automatically stop executing as if it had encountered a Return command (the Return is implied).

                                                                                                                                                        :ClrHome
:Input "Guess:",A
:Return
Remove the Return
:ClrHome
:Input "Guess:",A

                                                                                                                                                        Error Conditions

                                                                                                                                                        • ERR:INVALID occurs if this statement is used outside a program.

                                                                                                                                                        See Also

                                                                                                                                                        Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

                                                                                                                                                        History

                                                                                                                                                        Calculator OS Version Description
                                                                                                                                                        TI-82 1.0 Added
                                                                                                                                                        Property Value
                                                                                                                                                        Hex Value $6236
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                                                                                                                                                        • FR: R²

                                                                                                                                                        R²

                                                                                                                                                        Overview

                                                                                                                                                        Syntax

                                                                                                                                                        R²

                                                                                                                                                        Description

                                                                                                                                                        Examples

                                                                                                                                                        Explanation 1

                                                                                                                                                        code 1

                                                                                                                                                        Explanation 2

                                                                                                                                                        code 2

                                                                                                                                                        Error Conditions

                                                                                                                                                        Advanced Notes

                                                                                                                                                        History

                                                                                                                                                        Calculator OS Version Description
                                                                                                                                                        TI-82 1.0 Added
                                                                                                                                                        Property Value
                                                                                                                                                        Hex Value $1B
                                                                                                                                                        Categories
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                                                                                                                                                        • FR: R►Pr(

                                                                                                                                                        R►Pr(

                                                                                                                                                        Overview

                                                                                                                                                        Returns R, given rectangular coordinates x and y or a list of rectangular coordinates.

                                                                                                                                                        Availability: Token available everywhere.

                                                                                                                                                        Syntax

                                                                                                                                                        R►Pr(x,y)

                                                                                                                                                        Arguments

                                                                                                                                                        NameTypeOptional
                                                                                                                                                        x
                                                                                                                                                        y

                                                                                                                                                        Location

                                                                                                                                                        2nd, angle, ANGLE, 5:R, Pr(

                                                                                                                                                        Description

                                                                                                                                                        R►Pr( (Rectangular to polar radius) takes the (x,y) (Cartesian) coordinates, and gives the radius coordinate r of the same point in (r,θ) (polar) mode. The identity used for this conversion is _r_² = _x_²+_y_²

                                                                                                                                                        R►Pr(3,4)
    5
√(3²+4²)
    5
R►Pr({6,5},{8,12})
    {10 13}

                                                                                                                                                        The function works even when the equivalent √(_x_²+_y_²) fails due to overflow:

                                                                                                                                                        R►Pr(3e99,4e99)
    5e99

                                                                                                                                                        Optimization

                                                                                                                                                        R►Pr( is the smallest way to implement the distance formula \(d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\). Just give the values x1-x2 and y1 - y2 as arguments:

                                                                                                                                                        :√((5-2)²+(4-0)²)
can be
:R►Pr(5-2,4-0)

                                                                                                                                                        Error Conditions

                                                                                                                                                        Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Myles_Zadok, thornahawk, Timothy Foster.

                                                                                                                                                        History

                                                                                                                                                        Calculator OS Version Description
                                                                                                                                                        TI-82 1.0 Added
                                                                                                                                                        Property Value
                                                                                                                                                        Hex Value $1C
                                                                                                                                                        Categories
                                                                                                                                                        Localizations
                                                                                                                                                        • FR: R►Pθ(

                                                                                                                                                        R►Pθ(

                                                                                                                                                        Overview

                                                                                                                                                        Returns θ, given rectangular coordinates x and y or a list of rectangular coordinates.

                                                                                                                                                        Availability: Token available everywhere.

                                                                                                                                                        Syntax

                                                                                                                                                        R►Pθ(x,y)

                                                                                                                                                        Arguments

                                                                                                                                                        NameTypeOptional
                                                                                                                                                        θ
                                                                                                                                                        x
                                                                                                                                                        y

                                                                                                                                                        Location

                                                                                                                                                        2nd, angle, ANGLE

                                                                                                                                                        Description

                                                                                                                                                        R►Pθ( (Rectangular to polar θ) takes the (x,y) (Cartesian) coordinate, and returns the angle that the ray from (0,0) to (x,y) makes with the positive x-axis. This is the θ-coordinate of the same point in (r,θ) (polar) mode. The identity used for this conversion is tan(θ)=y__/x, with the correct inverse being chosen depending on the quadrant that the point is in. The range of the angle returned is -π<θ≤π. R►Pθ( can also be used on lists.

                                                                                                                                                        R►Pθ( is equivalent to the atan2() instruction seen in C/++ and FORTRAN.

                                                                                                                                                        R►Pθ(3,4)
    .927295218
tanֿ¹(4/3)
    .927295218
R►Pθ(0,{1,-1})
    {1.570796327, -1.57096327}

                                                                                                                                                        R►Pθ( is affected by Degree and Radian mode in its output, which is an angle measured in degrees or radians respectively.

                                                                                                                                                        Advanced Uses

                                                                                                                                                        If you want the result to always be a radian angle, regardless of mode settings, you can divide the result by 1ʳ:

                                                                                                                                                        R►Pθ(x,y)/1^^r

                                                                                                                                                        If you want the result to always be a degree angle, regardless of mode settings, you can divide the result by 1°:

                                                                                                                                                        R►Pθ(x,y)/1°

                                                                                                                                                        Error Conditions

                                                                                                                                                        Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, thornahawk.

                                                                                                                                                        History

                                                                                                                                                        Calculator OS Version Description
                                                                                                                                                        TI-82 1.0 Added
                                                                                                                                                        Property Value
                                                                                                                                                        Hex Value $53
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                                                                                                                                                        • FR: S

                                                                                                                                                        S

                                                                                                                                                        Overview

                                                                                                                                                        Availability: Token available everywhere.

                                                                                                                                                        Syntax

                                                                                                                                                        S

                                                                                                                                                        Description

                                                                                                                                                        Examples

                                                                                                                                                        Explanation 1

                                                                                                                                                        code 1

                                                                                                                                                        Explanation 2

                                                                                                                                                        code 2

                                                                                                                                                        Error Conditions

                                                                                                                                                        Advanced Notes

                                                                                                                                                        History

                                                                                                                                                        Calculator OS Version Description
                                                                                                                                                        TI-82 1.0 Added
                                                                                                                                                        Property Value
                                                                                                                                                        Hex Value $EF8F
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                                                                                                                                                          • FR: SUITE(𝑛)

                                                                                                                                                          SEQ(𝑛)

                                                                                                                                                          Overview

                                                                                                                                                          In sequence mode, SEQ(n) sets the sequence editor type to enter sequence functions, u, v, or w, as a function of the independent variable n. Can also be set from the Y= editor in SEQ mode.

                                                                                                                                                          Comment:CE OS 5.2+

                                                                                                                                                          Availability: Token only available from within the Basic editor.

                                                                                                                                                          Syntax

                                                                                                                                                          Seq(n)

                                                                                                                                                          Arguments

                                                                                                                                                          NameTypeOptional
                                                                                                                                                          n

                                                                                                                                                          Location

                                                                                                                                                          mode, SEQ(n)

                                                                                                                                                          Description

                                                                                                                                                          Examples

                                                                                                                                                          Explanation 1

                                                                                                                                                          code 1

                                                                                                                                                          Explanation 2

                                                                                                                                                          code 2

                                                                                                                                                          Error Conditions

                                                                                                                                                          Advanced Notes

                                                                                                                                                          History

                                                                                                                                                          Calculator OS Version Description
                                                                                                                                                          TI-84+CE 5.2.0 Added
                                                                                                                                                          Property Value
                                                                                                                                                          Hex Value $EF90
                                                                                                                                                          Categories
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                                                                                                                                                            • FR: SUITE(𝑛+1)

                                                                                                                                                            SEQ(𝑛+1)

                                                                                                                                                            Overview

                                                                                                                                                            In sequence mode, SEQ(n+1) sets the sequence editor type to enter sequence functions, u, v, or w, as a function of the independent variable n+1. Can also be set from the Y= editor in SEQ mode.

                                                                                                                                                            Comment:CE OS 5.2+

                                                                                                                                                            Availability: Token only available from within the Basic editor.

                                                                                                                                                            Syntax

                                                                                                                                                            Seq(n+1)

                                                                                                                                                            Arguments

                                                                                                                                                            NameTypeOptional
                                                                                                                                                            n+1

                                                                                                                                                            Location

                                                                                                                                                            mode, SEQ(n+1)

                                                                                                                                                            Description

                                                                                                                                                            Examples

                                                                                                                                                            Explanation 1

                                                                                                                                                            code 1

                                                                                                                                                            Explanation 2

                                                                                                                                                            code 2

                                                                                                                                                            Error Conditions

                                                                                                                                                            Advanced Notes

                                                                                                                                                            History

                                                                                                                                                            Calculator OS Version Description
                                                                                                                                                            TI-84+CE 5.2.0 Added
                                                                                                                                                            Property Value
                                                                                                                                                            Hex Value $EF91
                                                                                                                                                            Categories
                                                                                                                                                              Localizations
                                                                                                                                                              • FR: SUITE(𝑛+2)

                                                                                                                                                              SEQ(𝑛+2)

                                                                                                                                                              Overview

                                                                                                                                                              In sequence mode, SEQ(n+2) sets the sequence editor type to enter sequence functions, u, v, or w, as a function of the independent variable n+2. Can also be set from the Y= editor in SEQ mode.

                                                                                                                                                              Comment:CE OS 5.2+

                                                                                                                                                              Availability: Token only available from within the Basic editor.

                                                                                                                                                              Syntax

                                                                                                                                                              Seq(n+2)

                                                                                                                                                              Arguments

                                                                                                                                                              NameTypeOptional
                                                                                                                                                              n+2

                                                                                                                                                              Location

                                                                                                                                                              mode, SEQ(n+2)

                                                                                                                                                              Description

                                                                                                                                                              Examples

                                                                                                                                                              Explanation 1

                                                                                                                                                              code 1

                                                                                                                                                              Explanation 2

                                                                                                                                                              code 2

                                                                                                                                                              Error Conditions

                                                                                                                                                              Advanced Notes

                                                                                                                                                              History

                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                              TI-84+CE 5.2.0 Added
                                                                                                                                                              Property Value
                                                                                                                                                              Hex Value $EF8F
                                                                                                                                                              Categories
                                                                                                                                                                Localizations
                                                                                                                                                                • FR: SUITE(𝑛)

                                                                                                                                                                SEQ(𝑛)

                                                                                                                                                                Overview

                                                                                                                                                                In sequence mode, SEQ(n) sets the sequence editor type to enter sequence functions, u, v, or w, as a function of the independent variable n. Can also be set from the Y= editor in SEQ mode.

                                                                                                                                                                Comment:CE OS 5.2+

                                                                                                                                                                Availability: Token only available from within the Basic editor.

                                                                                                                                                                Syntax

                                                                                                                                                                Seq(n)

                                                                                                                                                                Arguments

                                                                                                                                                                NameTypeOptional
                                                                                                                                                                n

                                                                                                                                                                Location

                                                                                                                                                                mode, SEQ(n)

                                                                                                                                                                Description

                                                                                                                                                                Examples

                                                                                                                                                                Explanation 1

                                                                                                                                                                code 1

                                                                                                                                                                Explanation 2

                                                                                                                                                                code 2

                                                                                                                                                                Error Conditions

                                                                                                                                                                Advanced Notes

                                                                                                                                                                History

                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                TI-84+CE 5.2.0 Added
                                                                                                                                                                Property Value
                                                                                                                                                                Hex Value $EF90
                                                                                                                                                                Categories
                                                                                                                                                                  Localizations
                                                                                                                                                                  • FR: SUITE(𝑛+1)

                                                                                                                                                                  SEQ(𝑛+1)

                                                                                                                                                                  Overview

                                                                                                                                                                  In sequence mode, SEQ(n+1) sets the sequence editor type to enter sequence functions, u, v, or w, as a function of the independent variable n+1. Can also be set from the Y= editor in SEQ mode.

                                                                                                                                                                  Comment:CE OS 5.2+

                                                                                                                                                                  Availability: Token only available from within the Basic editor.

                                                                                                                                                                  Syntax

                                                                                                                                                                  Seq(n+1)

                                                                                                                                                                  Arguments

                                                                                                                                                                  NameTypeOptional
                                                                                                                                                                  n+1

                                                                                                                                                                  Location

                                                                                                                                                                  mode, SEQ(n+1)

                                                                                                                                                                  Description

                                                                                                                                                                  Examples

                                                                                                                                                                  Explanation 1

                                                                                                                                                                  code 1

                                                                                                                                                                  Explanation 2

                                                                                                                                                                  code 2

                                                                                                                                                                  Error Conditions

                                                                                                                                                                  Advanced Notes

                                                                                                                                                                  History

                                                                                                                                                                  Calculator OS Version Description
                                                                                                                                                                  TI-84+CE 5.2.0 Added
                                                                                                                                                                  Property Value
                                                                                                                                                                  Hex Value $EF91
                                                                                                                                                                  Categories
                                                                                                                                                                    Localizations
                                                                                                                                                                    • FR: SUITE(𝑛+2)

                                                                                                                                                                    SEQ(𝑛+2)

                                                                                                                                                                    Overview

                                                                                                                                                                    In sequence mode, SEQ(n+2) sets the sequence editor type to enter sequence functions, u, v, or w, as a function of the independent variable n+2. Can also be set from the Y= editor in SEQ mode.

                                                                                                                                                                    Comment:CE OS 5.2+

                                                                                                                                                                    Availability: Token only available from within the Basic editor.

                                                                                                                                                                    Syntax

                                                                                                                                                                    Seq(n+2)

                                                                                                                                                                    Arguments

                                                                                                                                                                    NameTypeOptional
                                                                                                                                                                    n+2

                                                                                                                                                                    Location

                                                                                                                                                                    mode, SEQ(n+2)

                                                                                                                                                                    Description

                                                                                                                                                                    Examples

                                                                                                                                                                    Explanation 1

                                                                                                                                                                    code 1

                                                                                                                                                                    Explanation 2

                                                                                                                                                                    code 2

                                                                                                                                                                    Error Conditions

                                                                                                                                                                    Advanced Notes

                                                                                                                                                                    History

                                                                                                                                                                    Calculator OS Version Description
                                                                                                                                                                    TI-84+CE 5.2.0 Added
                                                                                                                                                                    Property Value
                                                                                                                                                                    Hex Value $EF40
                                                                                                                                                                    Categories
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                                                                                                                                                                      • FR: STATWIZARD OFF

                                                                                                                                                                      STATWIZARD OFF

                                                                                                                                                                      Overview

                                                                                                                                                                      Disables wizard syntax help for statistical commands, distributions, and seq(.

                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                      Syntax

                                                                                                                                                                      STATWIZARD OFF

                                                                                                                                                                      Location

                                                                                                                                                                      2nd, catalog, STATWIZARD OFF

                                                                                                                                                                      Description

                                                                                                                                                                      Examples

                                                                                                                                                                      Explanation 1

                                                                                                                                                                      code 1

                                                                                                                                                                      Explanation 2

                                                                                                                                                                      code 2

                                                                                                                                                                      Error Conditions

                                                                                                                                                                      Advanced Notes

                                                                                                                                                                      History

                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                      TI-84+ 2.55 Added
                                                                                                                                                                      Property Value
                                                                                                                                                                      Hex Value $EF3F
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                                                                                                                                                                        • FR: STATWIZARD ON

                                                                                                                                                                        STATWIZARD ON

                                                                                                                                                                        Overview

                                                                                                                                                                        Enables wizard syntax help for statistical commands, distributions, and seq(.

                                                                                                                                                                        Availability: Token available everywhere.

                                                                                                                                                                        Syntax

                                                                                                                                                                        STATWIZARD ON

                                                                                                                                                                        Location

                                                                                                                                                                        2nd, catalog, STATWIZARD ON(

                                                                                                                                                                        Description

                                                                                                                                                                        Examples

                                                                                                                                                                        Explanation 1

                                                                                                                                                                        code 1

                                                                                                                                                                        Explanation 2

                                                                                                                                                                        code 2

                                                                                                                                                                        Error Conditions

                                                                                                                                                                        Advanced Notes

                                                                                                                                                                        History

                                                                                                                                                                        Calculator OS Version Description
                                                                                                                                                                        TI-84+ 2.55 Added
                                                                                                                                                                        Property Value
                                                                                                                                                                        Hex Value $FE
                                                                                                                                                                        Categories
                                                                                                                                                                        Localizations
                                                                                                                                                                        • FR: Nuage

                                                                                                                                                                        Scatter

                                                                                                                                                                        Overview

                                                                                                                                                                        Used as the "type" argument in the command
                                                                                                                                                                        Where # gives Plot1, Plot2 or Plot3.

                                                                                                                                                                        Availability: Token only available from within the Basic editor.

                                                                                                                                                                        Syntax

                                                                                                                                                                        Plot#(type,Xlist[,freqlist,color#])

                                                                                                                                                                        Arguments

                                                                                                                                                                        NameTypeOptional
                                                                                                                                                                        typeScatter token
                                                                                                                                                                        Xlistlist
                                                                                                                                                                        freqlistlist
                                                                                                                                                                        color#colorNum

                                                                                                                                                                        Location

                                                                                                                                                                        2nd, stat plot, TYPE

                                                                                                                                                                        Description

                                                                                                                                                                        The commands Plot1(, Plot2(, and Plot3(, which are identical except for which stat plot (1, 2, or 3) they affect, define their corresponding stat plot. When the stat plot is defined, it is also turned on so no PlotsOn command is necessary.

                                                                                                                                                                        The first argument of the commands is always the type of plot, and is one of Scatter, xyLine, Histogram, Boxplot, ModBoxplot, and NormProbPlot - these types are found in the TYPE submenu of the stat plot menu. The other arguments vary. For all but Histogram and Boxplot, there is a mark argument - this is a dot, a cross, or a box, symbols that can be found in the MARK submenu of the stat plot menu. On color calculators, there is an optional final argument to specify the color of the plot.

                                                                                                                                                                        Scatter plot

                                                                                                                                                                        Plot#(Scatter, x-list, y-list, mark) defines a scatter plot. The points defined by x-list and y-list are plotted using mark on the graph screen.

                                                                                                                                                                        x-list and y-list must be the same length.

                                                                                                                                                                        xyLine plot

                                                                                                                                                                        Plot#(xyLine, x-list, y-list, mark) defines an xyLine plot. Similarly to a scatter plot, the points defined by x-list and y-list are plotted using mark on the graph screen, but with an xyLine plot they are also connected by a line, in the order that they occur in the lists.

                                                                                                                                                                        x-list and y-list must be the same length.

                                                                                                                                                                        Histogram plot

                                                                                                                                                                        Plot#(Histogram, x-list, freq list) defines a Histogram plot. The x-axis is divided into intervals that are Xscl wide. A bar is drawn in in each interval whose height corresponds to the number of points in the interval. Points that are not between Xmin and Xmax are not tallied.

                                                                                                                                                                        Xscl must not be too small - it can divide the screen into no more than 47 different bars.

                                                                                                                                                                        Box plot

                                                                                                                                                                        Plot#(Boxplot, x-list, freq list) defines a box plot. A rectangular box is drawn whose left edge is Q1 (the first quartile) of the data, and whose right edge is Q3 (the third quartile). A vertical segment is drawn within the box at the median, and 'whiskers' are drawn from the box to the minimum and maximum data points.

                                                                                                                                                                        The box plot ignores the Ymax and Ymin dimensions of the screen, and any plots that aren't box plots or modified box plots. Each box plot takes approximately 1/3 of the screen in height, and if more than one are plotted, they will take up different areas of the screen.

                                                                                                                                                                        Modified box plot

                                                                                                                                                                        Plot#(ModBoxplot, x-list, freq list, mark) defines a modified box plot. This is almost entirely like the normal box plot, except that it also draws outliers. Whiskers are only drawn to the furthers point within 1.5 times the interquartile range (Q3-Q1) of the box. Beyond this point, data points are drawn individually, using mark.

                                                                                                                                                                        The box plot ignores the Ymax and Ymin dimensions of the screen, and any plots that aren't box plots or modified box plots. Each box plot takes approximately 1/3 of the screen in height, and if more than one are plotted, they will take up different areas of the screen.

                                                                                                                                                                        Normal probability plot

                                                                                                                                                                        Plot#(NormProbPlot, data list, data axis, mark) defines a normal probability plot. The mean and standard deviation of the data are calculated. Then for each point, the number of standard deviations it is from the mean is calculated, and the point is plotted against this number using mark. data axis can be either X or Y: it determines whether the value of a point determines it's x-coordinate or y-coordinate.

                                                                                                                                                                        The point behind this rather convoluted process is to test the extent to which the data is normally distributed. If it follows the normal distribution closely, then the result will be close to a straight line - otherwise it will be curved.

                                                                                                                                                                        Advanced Uses

                                                                                                                                                                        After doing a regression, a scatter plot of ʟRESID against the x-list is a useful measure of the effectiveness of the regression. If the plot appears random, this is a good sign; if there is a pattern to the plot, this means it's likely that a better regression model exists.

                                                                                                                                                                        Optimization

                                                                                                                                                                        The ʟ symbol at the beginning of list names can be omitted everywhere in this command.

                                                                                                                                                                        In addition, every element except the plot type and the data list or data lists are optional, and take on the following default values:

                                                                                                                                                                        • freq list is 1 by default, meaning that all frequencies are 1.
                                                                                                                                                                        • mark is the box by default.
                                                                                                                                                                        • data axis is X by default.

                                                                                                                                                                        Error Conditions

                                                                                                                                                                        • ERR:DIM MISMATCH is thrown if the x and y lists, or the data and frequency lists, have different dimensions.
                                                                                                                                                                        • ERR:STAT is thrown if Xscl is too small in the case of a Histogram.

                                                                                                                                                                        All errors are thrown when plotting the stat plot, as opposed to when the command is executed, and do not provide a 2:Goto option.

                                                                                                                                                                        Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Myles_Zadok.

                                                                                                                                                                        History

                                                                                                                                                                        Calculator OS Version Description
                                                                                                                                                                        TI-82 1.0 Added
                                                                                                                                                                        Property Value
                                                                                                                                                                        Hex Value $67
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                                                                                                                                                                        • FR: Sci

                                                                                                                                                                        Sci

                                                                                                                                                                        Overview

                                                                                                                                                                        Sets scientific notation display mode.

                                                                                                                                                                        Availability: Token only available from within the Basic editor.

                                                                                                                                                                        Syntax

                                                                                                                                                                        Sci

                                                                                                                                                                        Location

                                                                                                                                                                        mode, Sci

                                                                                                                                                                        Description

                                                                                                                                                                        The Sci command puts the calculator in scientific notation mode, so that all results are displayed in scientific notation: as a (possibly fractional) number between 1 and 10 (not including 10) multiplied by a power of 10.

                                                                                                                                                                        Sci
        Done
1000
        1e3
{1,2,3}
        {1e0 2e0 3e0}

                                                                                                                                                                        Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan.

                                                                                                                                                                        History

                                                                                                                                                                        Calculator OS Version Description
                                                                                                                                                                        TI-82 1.0 Added
                                                                                                                                                                        Property Value
                                                                                                                                                                        Hex Value $BB58
                                                                                                                                                                        Categories
                                                                                                                                                                        Localizations
                                                                                                                                                                        • FR: Sélect(

                                                                                                                                                                        Select(

                                                                                                                                                                        Overview

                                                                                                                                                                        Selects one or more specific data points from a scatter plot or xyLine plot (only), and then store's the selected data points to two new lists, Xlistname and Ylistname.

                                                                                                                                                                        Availability: Token available everywhere.

                                                                                                                                                                        Syntax

                                                                                                                                                                        Select(Xlistname,Ylistname)

                                                                                                                                                                        Arguments

                                                                                                                                                                        NameTypeOptional
                                                                                                                                                                        Xlistnamelist
                                                                                                                                                                        Ylistnamelist

                                                                                                                                                                        Location

                                                                                                                                                                        2nd, list, OPS, 8:Select(

                                                                                                                                                                        Description

                                                                                                                                                                        When Select( is called, if it has any Scatter or xyLine plots to work with, it displays the graph screen and allows the user to pick a left bound and then a right bound on one of the plots (the left and right keys move from point to point, while the up and down keys switch plots). Then, it stores all the points between those bounds to x-list name and y-list name. Finally, it sets the chosen plot to use x-list name and y-list name as its X and Y lists.

                                                                                                                                                                        Optimization

                                                                                                                                                                        It isn't necessary to add the ʟ symbol before list names:

                                                                                                                                                                        :Select(ʟX,ʟY)
can be
:Select(X,Y)

                                                                                                                                                                        Error Conditions

                                                                                                                                                                        • ERR:INVALID is thrown if there are no enabled Scatter or xyLine plots for the command to work with.

                                                                                                                                                                        Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan.

                                                                                                                                                                        History

                                                                                                                                                                        Calculator OS Version Description
                                                                                                                                                                        TI-83 0.01013 Added
                                                                                                                                                                        Property Value
                                                                                                                                                                        Hex Value $E7
                                                                                                                                                                        Categories
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                                                                                                                                                                        • FR: Envoi(

                                                                                                                                                                        Send(

                                                                                                                                                                        Overview

                                                                                                                                                                        Sends one or more TI-Innovator™ Hub commands to a connected hub.
                                                                                                                                                                        Notes:
                                                                                                                                                                        See also eval( and Get( command related to the Send( command.
                                                                                                                                                                        TI-Innovator™ Hub commands are supported in the HUB submenu in the CE OS v.5.2 program editor.

                                                                                                                                                                        Availability: Token only available from within the Basic editor.

                                                                                                                                                                        Syntax

                                                                                                                                                                        Send(string)

                                                                                                                                                                        Arguments

                                                                                                                                                                        NameTypeOptional
                                                                                                                                                                        stringstring

                                                                                                                                                                        Location

                                                                                                                                                                        prgm, I/O, B:Send(

                                                                                                                                                                        Overview

                                                                                                                                                                        Sends one or more TI-Innovator™ Hub commands to a connected hub.
                                                                                                                                                                        Notes:
                                                                                                                                                                        See also eval( and Get( command related to the Send( command.
                                                                                                                                                                        TI-Innovator™ Hub commands are supported in the HUB submenu in the CE OS v.5.2 program editor.

                                                                                                                                                                        Availability: Token only available from within the Basic editor.

                                                                                                                                                                        Syntax

                                                                                                                                                                        Send(string)

                                                                                                                                                                        Arguments

                                                                                                                                                                        NameTypeOptional
                                                                                                                                                                        stringstring

                                                                                                                                                                        Location

                                                                                                                                                                        prgm, HUB

                                                                                                                                                                        Description

                                                                                                                                                                        The Send( command is used for sending data to a CBL (Calculator Based Laboratory) device (or another compatible device) via a link cable. With some exceptions, Send('s argument must be a variable: a real number, list, matrix, string, equation, picture, or GDB. An expression or a number will not work — Send(5) or Send([A][B]) is invalid.

                                                                                                                                                                        The exceptions are list or matrix elements (that is, you can do Send(A) or Send(L1(2)) without an error) and non-variable lists typed out with { } brackets and commas.

                                                                                                                                                                        Norland Robot

                                                                                                                                                                        You can use Send( with a Get( for a Norland calculator robot. The format called CLR format. C stands for command number, L stands for left axle, and R stands for right axle. If the command number is 1, it makes the robot moves in a direction for the time specified later in the command. If it is 2, the robot moves until the bumper hits a wall. If it is 3, it moves for a specified amount of time and stops when the robot when the bumper hits a wall. For example, send({122,100}) will make the robot move forward for 100 centiseconds, send({222}) makes it go forward until the bumper hits the wall, and send({322,100}) makes the robot move forward for 100 centiseconds and stops it when the bumper is pressed. The last two axle control numbers are like this:
                                                                                                                                                                        0=backwards
                                                                                                                                                                        1=stop
                                                                                                                                                                        2=forwards

                                                                                                                                                                        Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, jonbush, princetonlion.

                                                                                                                                                                        History

                                                                                                                                                                        Calculator OS Version Description
                                                                                                                                                                        TI-82 1.0 Added
                                                                                                                                                                        Property Value
                                                                                                                                                                        Hex Value $79
                                                                                                                                                                        Categories
                                                                                                                                                                        Localizations
                                                                                                                                                                        • FR: Suite

                                                                                                                                                                        Seq

                                                                                                                                                                        Overview

                                                                                                                                                                        Sets sequence graphing mode.

                                                                                                                                                                        Availability: Token only available from within the Basic editor.

                                                                                                                                                                        Syntax

                                                                                                                                                                        Seq

                                                                                                                                                                        Location

                                                                                                                                                                        mode, Seq

                                                                                                                                                                        Description

                                                                                                                                                                        The Seq command enables sequence graphing mode.

                                                                                                                                                                        Sequential mode is used for graphing sequences, which can be thought of as functions from the positive (or non-negative) integers. The TI-83 calculators let n be the independent variable in this situation, and the three sequences, instead of using subscripts, use the letters u, v, and w.

                                                                                                                                                                        One of the main advantages of sequential mode is that it allows recursive definitions: u(n) can be defined in terms of u(n-1) and u(n-2). For recursive definitions to work, an initial case must be defined: this is done using the variables u(_n_Min), v(_n_Min), and w(_n_Min). The constant _n_Min is the initial case, for which the calculator will use a specific value rather than the formula.

                                                                                                                                                                        For example, say a bunny population starts out at 100 and doubles each year. We can describe this situation using the recursive definition u(n)=2u(n-1) (this just says that the _n_th year population is twice the population of the previous year); then we set u(_n_Min)=100. Note that without u(_n_Min), the equation would be meaningless - without the initial population, we have no way to calculate any other population.

                                                                                                                                                                        When you're using more than one previous value — both u(n-1) and u(n-2)) — you need more than one initial value, and then u(_n_Min) becomes a list.

                                                                                                                                                                        Advanced Uses

                                                                                                                                                                        Sequence graphing mode has several submodes that can be selected from the 2nd FORMAT screen. They are Time, Web, uvAxes, uwAxes, and vwAxes. Sequences are still defined in the same way, but these modes control the way that they're graphed.

                                                                                                                                                                        The window variables that apply to sequence mode are:

                                                                                                                                                                        • _n_Min — Determines the minimum n-value calculated for equations.
                                                                                                                                                                        • _n_Max — Determines the maximum n-value calculated for equations.
                                                                                                                                                                        • PlotStart — Determines the first value of n that is actually graphed.
                                                                                                                                                                        • PlotStep — Determines the difference between consecutive graphed values of n.
                                                                                                                                                                        • Xmin — Determines the minimum X-value shown on the screen.
                                                                                                                                                                        • Xmax — Determines the maximum X-value shown on the screen.
                                                                                                                                                                        • Xscl — Determines the horizontal space between marks on the X-axis in AxesOn mode or dots in GridOn mode.
                                                                                                                                                                        • Ymin — Determines the minimum Y-value shown on the screen.
                                                                                                                                                                        • Ymax — Determines the maximum Y-value shown on the screen.
                                                                                                                                                                        • Yscl — Determines the vertical space between marks on the Y-axis in AxesOn mode or dots in GridOn mode.

                                                                                                                                                                        Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

                                                                                                                                                                        History

                                                                                                                                                                        Calculator OS Version Description
                                                                                                                                                                        TI-82 1.0 Added
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                                                                                                                                                                        Hex Value $7E00
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                                                                                                                                                                        • FR: Séquentiel

                                                                                                                                                                        Sequential

                                                                                                                                                                        Overview

                                                                                                                                                                        Sets mode to graph functions sequentially.

                                                                                                                                                                        Availability: Token only available from within the Basic editor.

                                                                                                                                                                        Syntax

                                                                                                                                                                        Sequential

                                                                                                                                                                        Location

                                                                                                                                                                        mode, Sequential

                                                                                                                                                                        Description

                                                                                                                                                                        Puts the calculator into sequential graphing mode (the default). When multiple equations are enabled at the same time, sequential graphing mode means that they will be graphed one after the other (as opposed to Simul mode, in which they will be graphed simultaneously)

                                                                                                                                                                        If you use a list in an equation, as with Y1={1,2,3}X, this will graph several equations that will always graph separately, regardless of this setting, which only affects multiple functions in different equation variables.

                                                                                                                                                                        Make sure not to confuse this with Seq mode, which is referred to in this guide as sequence graphing mode.

                                                                                                                                                                        Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

                                                                                                                                                                        History

                                                                                                                                                                        Calculator OS Version Description
                                                                                                                                                                        TI-82 1.0 Added
                                                                                                                                                                        Property Value
                                                                                                                                                                        Hex Value $BB4A
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                                                                                                                                                                        • FR: ListesDéfaut

                                                                                                                                                                        SetUpEditor

                                                                                                                                                                        Overview

                                                                                                                                                                        Removes all list names from the stat list editor, and then restores list names L1 through L6 to columns 1 through 6.

                                                                                                                                                                        Availability: Token available everywhere.

                                                                                                                                                                        Syntax

                                                                                                                                                                        SetUpEditor

                                                                                                                                                                        Location

                                                                                                                                                                        stat, EDIT, 5:SetUpEditor

                                                                                                                                                                        Overview

                                                                                                                                                                        Removes all list names from the stat list editor, then sets it up to display one or more listnames in the specified order, starting with column 1.

                                                                                                                                                                        Availability: Token available everywhere.

                                                                                                                                                                        Syntax

                                                                                                                                                                        SetUpEditor listname1[,listname2,...,listname20]

                                                                                                                                                                        Arguments

                                                                                                                                                                        NameTypeOptional
                                                                                                                                                                        listname1listName
                                                                                                                                                                        listname2listNameYes
                                                                                                                                                                        ...Yes
                                                                                                                                                                        listname20listNameYes

                                                                                                                                                                        Location

                                                                                                                                                                        stat, EDIT, 5:SetUpEditor

                                                                                                                                                                        Description

                                                                                                                                                                        The SetUpEditor command is used to define which lists are shown in the List Editor (which can be accessed by pressing [STAT] [ENTER] [Edit…]). The list editor provides a convenient interface for viewing and editing items inside lists (especially when the elements of two lists are connected to each other, such as a list for X-coordinates and one for Y-coordinates, since they will be shown in the same row).

                                                                                                                                                                        If the command is called without any arguments, it uses the default six lists: L1, L2, L3, L4, L5, and L6.

                                                                                                                                                                        :SetUpEditor

                                                                                                                                                                        However, you can use it to select any lists that you have defined, or even lists that are archived or not yet defined. To do this, simply put the lists you want as arguments to the command. For example, if you want to edit the lists FOO and BAR, do:

                                                                                                                                                                        :SetUpEditor FOO,BAR

                                                                                                                                                                        Both the list editor itself and the SetUpEditor command support up to 20 lists. If you specify more than 20, the 21st and beyond will be ignored.

                                                                                                                                                                        The List Editor doesn't do anything when you are running a program, so it may seem as though SetUpEditor is nearly useless in programs. This is not the case, however, because of SetUpEditor's powerful side effect: if the lists it is given as arguments are archived, it will unarchive them. If they don't exist, it will create empty lists with zero items. If the lists exist, the items stored inside are not modified.

                                                                                                                                                                        Advanced Uses

                                                                                                                                                                        Due to this side effect, SetUpEditor can be used for lists with external data such as saved games or high scores. When the user first runs the program, the assumption is you don't know anything about the state of those lists: they may be archived, or they may not even exist. You can deal with both of those individually: storing to the dimension will create the list if it didn't exist, and the UnArchive command will move the list to RAM if it wasn't there.

                                                                                                                                                                        However, if you're wrong about the list, both of these commands will cause an error. If the list exists but is archived, storing to its dimension will cause an ERR:ARCHIVE error. If the list doesn't exist, unarchiving it will cause an ERR:UNDEFINED error. Sounds like a vicious circle.

                                                                                                                                                                        The SetUpEditor command allows you to deal with both of these problems at once. Say the program saves its data in LSAVE. Use the SetUpEditor command on it, and from then on you know that the list exists AND that it is unarchived.

                                                                                                                                                                        :SetUpEditor SAVE

                                                                                                                                                                        At the end of the program, you should clean up after yourself, though. You don't want the user to see the list SAVE in the editor (he might be tempted to edit it and give himself a huge high score, for one thing). So you should use the SetUpEditor command again, this time without arguments, to reset the editor to its default state.

                                                                                                                                                                        For more information about using SetUpEditor in the context of saving data, see the page on saving.

                                                                                                                                                                        Similar Commands

                                                                                                                                                                        See Also

                                                                                                                                                                        Source: parts of this page were written by the following TI|BD contributors: 2Tie, burr, DarkerLine, GoVegan, Timothy Foster.

                                                                                                                                                                        History

                                                                                                                                                                        Calculator OS Version Description
                                                                                                                                                                        TI-83 0.01013 Added
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                                                                                                                                                                        Hex Value $A4
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                                                                                                                                                                        • FR: Ombre(

                                                                                                                                                                        Shade(

                                                                                                                                                                        Overview

                                                                                                                                                                        Draws lowerfunc and upperfunc in terms of X on the current graph and uses pattern and patres to shade and color the area bounded by lowerfunc, upperfunc, Xleft, and Xright. lowerfuncand upperfuncare shaded in the same specified color.
                                                                                                                                                                        Color#: 10 - 24 or color name pasted from [vars] COLOR.

                                                                                                                                                                        Availability: Token available everywhere.

                                                                                                                                                                        Syntax

                                                                                                                                                                        Shade(lowerfunc,upperfunc[,Xleft,Xright,pattern,patres,color#])

                                                                                                                                                                        Arguments

                                                                                                                                                                        NameTypeOptional
                                                                                                                                                                        lowerfunc
                                                                                                                                                                        upperfunc
                                                                                                                                                                        XleftYes
                                                                                                                                                                        XrightYes
                                                                                                                                                                        patternYes
                                                                                                                                                                        patresYes
                                                                                                                                                                        color#colorNumYes

                                                                                                                                                                        Location

                                                                                                                                                                        2nd, draw, DRAW, 7:Shade(

                                                                                                                                                                        Description

                                                                                                                                                                        The Shade( command draws two functions and shades the area between them.

                                                                                                                                                                        Shade(lower func, upper func, [xmin, xmax, pattern #, resolution])

                                                                                                                                                                        • lowerfunc and upperfunc are the two functions (whenever lowerfunc<upperfunc, the area between them will be shaded)
                                                                                                                                                                        • xmin and xmax (optional) are left and right boundaries on where to shade.
                                                                                                                                                                        • pattern # (optional) is an integer 1-4 determining which pattern to use:
                                                                                                                                                                          • 1 — vertical shading (default)
                                                                                                                                                                          • 2 — horizontal shading
                                                                                                                                                                          • 3 — diagonal shading (negative slope)
                                                                                                                                                                          • 4 — diagonal shading (positive slope)
                                                                                                                                                                        • resolution (optional) is an integer 1-8 determining the spacing between shading lines. When it's 1 (default), everything is shaded, when it's 2, one pixel is skipped between lines, and so on - when it's 8, seven pixels are skipped.

                                                                                                                                                                        Note that if you don't supply the resolution argument, it defaults to 1 and everything gets shaded regardless of the pattern.

                                                                                                                                                                        Advanced Uses

                                                                                                                                                                        Shade(Ymin,Ymax) is the smallest (though not the fastest) way to shade the entire screen.

                                                                                                                                                                        See Also

                                                                                                                                                                        Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Timothy Foster.

                                                                                                                                                                        History

                                                                                                                                                                        Calculator OS Version Description
                                                                                                                                                                        TI-82 1.0 Added
                                                                                                                                                                        Property Value
                                                                                                                                                                        Hex Value $BB38
                                                                                                                                                                        Categories
                                                                                                                                                                        Localizations
                                                                                                                                                                        • FR: Ombre𝐅(

                                                                                                                                                                        Shade𝐅(

                                                                                                                                                                        Overview

                                                                                                                                                                        Draws the density function for the 𝐅distribution specified by numerator df and denominator df and shades and colors the area between lowerbound and upperbound.
                                                                                                                                                                        Color#: 10 - 24 or color name pasted from [vars] COLOR.

                                                                                                                                                                        Availability: Token available everywhere.

                                                                                                                                                                        Syntax

                                                                                                                                                                        Shade𝐅(lowerbound,upperbound,numerator df,denominator df[,color#])

                                                                                                                                                                        Arguments

                                                                                                                                                                        NameTypeOptional
                                                                                                                                                                        𝐅
                                                                                                                                                                        lowerbound
                                                                                                                                                                        upperbound
                                                                                                                                                                        numerator df
                                                                                                                                                                        denominator dfYes
                                                                                                                                                                        color#colorNumYes

                                                                                                                                                                        Location

                                                                                                                                                                        2nd, distr, DRAW, 4:Shade, (

                                                                                                                                                                        Description

                                                                                                                                                                        Examples

                                                                                                                                                                        Explanation 1

                                                                                                                                                                        code 1

                                                                                                                                                                        Explanation 2

                                                                                                                                                                        code 2

                                                                                                                                                                        Error Conditions

                                                                                                                                                                        Advanced Notes

                                                                                                                                                                        History

                                                                                                                                                                        Calculator OS Version Description
                                                                                                                                                                        TI-83 0.01013 Added
                                                                                                                                                                        Property Value
                                                                                                                                                                        Hex Value $BB35
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                                                                                                                                                                        • FR: OmbreNorm(

                                                                                                                                                                        ShadeNorm(

                                                                                                                                                                        Overview

                                                                                                                                                                        Draws the normal density function specified by μ and σ and shades and colors the area between lowerbound and upperbound.
                                                                                                                                                                        Color#: 10 - 24 or color name pasted from [vars] COLOR.

                                                                                                                                                                        Availability: Token available everywhere.

                                                                                                                                                                        Syntax

                                                                                                                                                                        ShadeNorm(lowerbound,upperbound[,μ,σ,color#])

                                                                                                                                                                        Arguments

                                                                                                                                                                        NameTypeOptional
                                                                                                                                                                        lowerbound
                                                                                                                                                                        upperbound
                                                                                                                                                                        μYes
                                                                                                                                                                        σYes
                                                                                                                                                                        colorYes
                                                                                                                                                                        #Yes

                                                                                                                                                                        Location

                                                                                                                                                                        2nd, distr, DRAW, 1:ShadeNorm(

                                                                                                                                                                        Description

                                                                                                                                                                        ShadeNorm( is equivalent to normalcdf( in terms of the probability it calculates: if a random variable follows the normal distribution, you can use it to calculate the probability that the variable's value falls in a certain interval. However, in addition to calculating the probability, this command also draws the normal curve, and shades the interval whose area represents the probability you want.

                                                                                                                                                                        Note that this command does not actually return the value it calculates in Ans or anywhere else: it's merely displayed on the graph. If you're going to use the value in further calculations, you'll have to use normalcdf( as well.

                                                                                                                                                                        There are two ways to use ShadeNorm(. With two arguments (lower bound and upper bound), the calculator will assume you mean the standard normal distribution, and use that to find the probability corresponding to the interval between "lower bound" and "upper bound". You can also supply two additional arguments to use the normal distribution with a specified mean and standard deviation. For example:

                                                                                                                                                                        for the standard normal distribution
:ShadeNorm(-1,1

for the normal distribution with mean 10 and std. dev. 2.5
:ShadeNorm(5,15,10,2.5

                                                                                                                                                                        Advanced

                                                                                                                                                                        Often, you want to find a "tail probability" - a special case for which the interval has no lower or no upper bound. For example, "what is the probability x is greater than 2?". The TI-83+ has no special symbol for infinity, but you can use E99 to get a very large number that will work equally well in this case (E is the decimal exponent obtained by pressing [2nd] [EE]). Use E99 for positive infinity, and -E99 for negative infinity.

                                                                                                                                                                        It can be hard to find the best window for ShadeNorm( to work in, since it doesn't automatically zoom for you. For the standard curve, the graph doesn't go above y=.5 (a good value for Ymax); Ymin should probably be something small. Xmin and Xmax could be -3 to 3 (3 deviations out); change this around to see more or less of the graph.

                                                                                                                                                                        For nonstandard curves, increasing the standard deviation stretches and flattens the curve; by dividing Ymax and multiplying Xmin and Xmax by the standard deviation, you'll account for this effect. To account for the mean, add it to both Xmin and Xmax. You may also choose to standardize the lower and upper values instead by applying the formula (z-μ)/σ.

                                                                                                                                                                        Keep in mind that ShadeNorm is just a drawing command and not an actual graphed function, so resizing the window, ClrDraw, and a bunch of other things will simply get rid of it.

                                                                                                                                                                        Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

                                                                                                                                                                        History

                                                                                                                                                                        Calculator OS Version Description
                                                                                                                                                                        TI-83 0.01013 Added
                                                                                                                                                                        Property Value
                                                                                                                                                                        Hex Value $BB36
                                                                                                                                                                        Categories
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                                                                                                                                                                        • FR: Ombre_t(

                                                                                                                                                                        Shade_t(

                                                                                                                                                                        Overview

                                                                                                                                                                        Draws the density function for the Student-t distribution specified by degrees of freedom df, and shades or colors the area between lowerbound and upperbound.
                                                                                                                                                                        Color#: 10 - 24 or color name pasted from [vars] COLOR.

                                                                                                                                                                        Availability: Token available everywhere.

                                                                                                                                                                        Syntax

                                                                                                                                                                        Shade_t(lowerbound,upperbound,df[,color#])

                                                                                                                                                                        Arguments

                                                                                                                                                                        NameTypeOptional
                                                                                                                                                                        lowerbound
                                                                                                                                                                        upperbound
                                                                                                                                                                        df
                                                                                                                                                                        color#colorNumYes

                                                                                                                                                                        Location

                                                                                                                                                                        2nd, distr, DRAW, 2:Shade_t(

                                                                                                                                                                        Description

                                                                                                                                                                        Shade_t( is equivalent to tcdf( in terms of the probability it calculates: if a random variable follows the Student's t distribution, you can use it to calculate the probability that the variable's value falls in a certain interval. However, in addition to calculating the probability, this command also draws the distribution, and shades the interval whose area represents the probability you want.

                                                                                                                                                                        Note that this command does not actually return the value it calculates in Ans or anywhere else: it's merely displayed on the graph. If you're going to use the value in further calculations, you'll have to use tcdf( as well.

                                                                                                                                                                        Like tcdf(, Shade_t( takes three arguments: the lower bound, the upper bound, and the degrees of freedom.

                                                                                                                                                                        Advanced

                                                                                                                                                                        Often, you want to find a "tail probability" - a special case for which the interval has no lower or no upper bound. For example, "what is the probability x is greater than 2?". The TI-83+ has no special symbol for infinity, but you can use E99 to get a very large number that will work equally well in this case (E is the decimal exponent obtained by pressing [2nd] [EE]). Use E99 for positive infinity, and -E99 for negative infinity.

                                                                                                                                                                        The Shade_t( command's output is affected by the graphing window, and on many windows you won't be able to get a good idea of what the graph looks like. For best results, Ymin should be either 0 or a small negative number, and Ymax should be 0.5 or less. Xmin and Xmax should be opposites of each other (so the middle of the graph is 0), but how large they are depends on the degrees of freedom and on how much of the graph you want to see: -4 and 4 are good starting places.

                                                                                                                                                                        Keep in mind that Shade_t( is a drawing command and not the graph of an equation, so changing graph settings, the ClrDraw command, and a great deal of other things will erase its output.

                                                                                                                                                                        Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

                                                                                                                                                                        History

                                                                                                                                                                        Calculator OS Version Description
                                                                                                                                                                        TI-83 0.01013 Added
                                                                                                                                                                        Property Value
                                                                                                                                                                        Hex Value $BB37
                                                                                                                                                                        Categories
                                                                                                                                                                        Localizations
                                                                                                                                                                        • FR: Ombreχ²(

                                                                                                                                                                        Shadeχ²(

                                                                                                                                                                        Overview

                                                                                                                                                                        Draws the density function for the χ² distribution specified by degrees of freedom df, and shades and colors the area between lowerbound and upperbound.
                                                                                                                                                                        Color#: 10 - 24 or color name pasted from [vars] COLOR.

                                                                                                                                                                        Availability: Token available everywhere.

                                                                                                                                                                        Syntax

                                                                                                                                                                        Shadeχ²(lowerbound,upperbound,df[,color#])

                                                                                                                                                                        Arguments

                                                                                                                                                                        NameTypeOptional
                                                                                                                                                                        χ²
                                                                                                                                                                        lowerbound
                                                                                                                                                                        upperbound
                                                                                                                                                                        dfYes
                                                                                                                                                                        color#colorNumYes

                                                                                                                                                                        Location

                                                                                                                                                                        2nd, distr, DRAW, 3:Shade, (

                                                                                                                                                                        Description

                                                                                                                                                                        Shadeχ²( is equivalent to χ²cdf( in terms of the probability it calculates: if a random variable follows the χ² distribution, you can use it to calculate the probability that the variable's value falls in a certain interval. However, in addition to calculating the probability, this command also draws the χ² curve, and shades the interval whose area represents the probability you want.

                                                                                                                                                                        Note that this command does not actually return the value it calculates in Ans or anywhere else: it's merely displayed on the graph. If you're going to use the value in further calculations, you'll have to use χ²cdf( as well.

                                                                                                                                                                        The Shadeχ²( command takes three arguments. lower and upper identify the interval you're interested in. df specifies the degrees of freedom (selecting from an infinite family of χ² distributions).

                                                                                                                                                                        Thus, the following code would find the probability of χ² between 0 and 1 on a χ² distribution with 2 degrees of freedom, and shade this interval:

                                                                                                                                                                        :Shadeχ²(0,1,2

                                                                                                                                                                        Advanced

                                                                                                                                                                        Often, you want to find a "tail probability" - a special case for which the interval has no lower or no upper bound. For example, "what is the probability x is greater than 2?". The TI-83+ has no special symbol for infinity, but you can use E99 to get a very large number that will work equally well in this case (E is the decimal exponent obtained by pressing [2nd] [EE]). Use E99 for positive infinity, and -E99 for negative infinity.

                                                                                                                                                                        It can be hard to find the best window for Shadeχ²( to work in, since it doesn't automatically zoom for you. For any number of degrees of freedom (except for 1), the graph doesn't go above y=.5 (a good value for Ymax); Ymin should probably be something small and negative. Xmin should be around 0 (possibly slightly less if you like seeing axes), while Xmax probably shouldn't go above 5.

                                                                                                                                                                        Keep in mind that Shadeχ²( is just a drawing command and not an actual graphed function, so resizing the window, ClrDraw, and other commands that refresh the graphscreen will remove it.

                                                                                                                                                                        Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583.

                                                                                                                                                                        History

                                                                                                                                                                        Calculator OS Version Description
                                                                                                                                                                        TI-83 0.01013 Added
                                                                                                                                                                        Property Value
                                                                                                                                                                        Hex Value $BB37
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                                                                                                                                                                        • FR: Ombreχ²(

                                                                                                                                                                        Shadeχ²(

                                                                                                                                                                        Overview

                                                                                                                                                                        Draws the density function for the χ² distribution specified by degrees of freedom df, and shades and colors the area between lowerbound and upperbound.
                                                                                                                                                                        Color#: 10 - 24 or color name pasted from [vars] COLOR.

                                                                                                                                                                        Availability: Token available everywhere.

                                                                                                                                                                        Syntax

                                                                                                                                                                        Shadeχ²(lowerbound,upperbound,df[,color#])

                                                                                                                                                                        Arguments

                                                                                                                                                                        NameTypeOptional
                                                                                                                                                                        χ²
                                                                                                                                                                        lowerbound
                                                                                                                                                                        upperbound
                                                                                                                                                                        dfYes
                                                                                                                                                                        color#colorNumYes

                                                                                                                                                                        Location

                                                                                                                                                                        2nd, distr, DRAW, 3:Shade, (

                                                                                                                                                                        Description

                                                                                                                                                                        Shadeχ²( is equivalent to χ²cdf( in terms of the probability it calculates: if a random variable follows the χ² distribution, you can use it to calculate the probability that the variable's value falls in a certain interval. However, in addition to calculating the probability, this command also draws the χ² curve, and shades the interval whose area represents the probability you want.

                                                                                                                                                                        Note that this command does not actually return the value it calculates in Ans or anywhere else: it's merely displayed on the graph. If you're going to use the value in further calculations, you'll have to use χ²cdf( as well.

                                                                                                                                                                        The Shadeχ²( command takes three arguments. lower and upper identify the interval you're interested in. df specifies the degrees of freedom (selecting from an infinite family of χ² distributions).

                                                                                                                                                                        Thus, the following code would find the probability of χ² between 0 and 1 on a χ² distribution with 2 degrees of freedom, and shade this interval:

                                                                                                                                                                        :Shadeχ²(0,1,2

                                                                                                                                                                        Advanced

                                                                                                                                                                        Often, you want to find a "tail probability" - a special case for which the interval has no lower or no upper bound. For example, "what is the probability x is greater than 2?". The TI-83+ has no special symbol for infinity, but you can use E99 to get a very large number that will work equally well in this case (E is the decimal exponent obtained by pressing [2nd] [EE]). Use E99 for positive infinity, and -E99 for negative infinity.

                                                                                                                                                                        It can be hard to find the best window for Shadeχ²( to work in, since it doesn't automatically zoom for you. For any number of degrees of freedom (except for 1), the graph doesn't go above y=.5 (a good value for Ymax); Ymin should probably be something small and negative. Xmin should be around 0 (possibly slightly less if you like seeing axes), while Xmax probably shouldn't go above 5.

                                                                                                                                                                        Keep in mind that Shadeχ²( is just a drawing command and not an actual graphed function, so resizing the window, ClrDraw, and other commands that refresh the graphscreen will remove it.

                                                                                                                                                                        Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583.

                                                                                                                                                                        History

                                                                                                                                                                        Calculator OS Version Description
                                                                                                                                                                        TI-83 0.01013 Added
                                                                                                                                                                        Property Value
                                                                                                                                                                        Hex Value $BB38
                                                                                                                                                                        Categories
                                                                                                                                                                        Localizations
                                                                                                                                                                        • FR: Ombre𝐅(

                                                                                                                                                                        Shade𝐅(

                                                                                                                                                                        Overview

                                                                                                                                                                        Draws the density function for the 𝐅distribution specified by numerator df and denominator df and shades and colors the area between lowerbound and upperbound.
                                                                                                                                                                        Color#: 10 - 24 or color name pasted from [vars] COLOR.

                                                                                                                                                                        Availability: Token available everywhere.

                                                                                                                                                                        Syntax

                                                                                                                                                                        Shade𝐅(lowerbound,upperbound,numerator df,denominator df[,color#])

                                                                                                                                                                        Arguments

                                                                                                                                                                        NameTypeOptional
                                                                                                                                                                        𝐅
                                                                                                                                                                        lowerbound
                                                                                                                                                                        upperbound
                                                                                                                                                                        numerator df
                                                                                                                                                                        denominator dfYes
                                                                                                                                                                        color#colorNumYes

                                                                                                                                                                        Location

                                                                                                                                                                        2nd, distr, DRAW, 4:Shade, (

                                                                                                                                                                        Description

                                                                                                                                                                        Examples

                                                                                                                                                                        Explanation 1

                                                                                                                                                                        code 1

                                                                                                                                                                        Explanation 2

                                                                                                                                                                        code 2

                                                                                                                                                                        Error Conditions

                                                                                                                                                                        Advanced Notes

                                                                                                                                                                        History

                                                                                                                                                                        Calculator OS Version Description
                                                                                                                                                                        TI-83 0.01013 Added
                                                                                                                                                                        Property Value
                                                                                                                                                                        Hex Value $EF33
                                                                                                                                                                        Categories
                                                                                                                                                                          Localizations
                                                                                                                                                                          • FR: Σ(

                                                                                                                                                                          Σ(

                                                                                                                                                                          Overview

                                                                                                                                                                          Classic command as shown.
                                                                                                                                                                          In MathPrint™ the summation entry template displays and returns the sum of elements of list from start to end,wherestart<=end.

                                                                                                                                                                          Availability: Token available everywhere.

                                                                                                                                                                          Syntax

                                                                                                                                                                          Σ(expression[,start,end])

                                                                                                                                                                          Arguments

                                                                                                                                                                          NameTypeOptional
                                                                                                                                                                          expressionexpression
                                                                                                                                                                          startYes
                                                                                                                                                                          endYes

                                                                                                                                                                          Location

                                                                                                                                                                          math

                                                                                                                                                                          Description

                                                                                                                                                                          Examples

                                                                                                                                                                          Explanation 1

                                                                                                                                                                          code 1

                                                                                                                                                                          Explanation 2

                                                                                                                                                                          code 2

                                                                                                                                                                          Error Conditions

                                                                                                                                                                          Advanced Notes

                                                                                                                                                                          History

                                                                                                                                                                          Calculator OS Version Description
                                                                                                                                                                          TI-84+ 2.53 Added
                                                                                                                                                                          Property Value
                                                                                                                                                                          Hex Value $BBA9
                                                                                                                                                                          Categories
                                                                                                                                                                          Localizations
                                                                                                                                                                          • FR: Σ

                                                                                                                                                                          Σ

                                                                                                                                                                          Overview

                                                                                                                                                                          Availability: Token available everywhere.

                                                                                                                                                                          Syntax

                                                                                                                                                                          Σ

                                                                                                                                                                          Description

                                                                                                                                                                          Examples

                                                                                                                                                                          Explanation 1

                                                                                                                                                                          code 1

                                                                                                                                                                          Explanation 2

                                                                                                                                                                          code 2

                                                                                                                                                                          Error Conditions

                                                                                                                                                                          Advanced Notes

                                                                                                                                                                          History

                                                                                                                                                                          Calculator OS Version Description
                                                                                                                                                                          TI-83+ 1.03 Added
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                                                                                                                                                                          Hex Value $BB04
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                                                                                                                                                                          • FR: ΣInt(

                                                                                                                                                                          ΣInt(

                                                                                                                                                                          Overview

                                                                                                                                                                          Computes the sum, rounded to roundvalue, of the interest amount between pmt1 and pmt2 for an amortization schedule.

                                                                                                                                                                          Availability: Token available everywhere.

                                                                                                                                                                          Syntax

                                                                                                                                                                          ΣInt(pmt1,pmt2[,roundvalue])

                                                                                                                                                                          Arguments

                                                                                                                                                                          NameTypeOptional
                                                                                                                                                                          Σ
                                                                                                                                                                          pmt1
                                                                                                                                                                          pmt2Yes
                                                                                                                                                                          roundvalueYes

                                                                                                                                                                          Location

                                                                                                                                                                          apps, 1:Finance, CALC, A:Int(

                                                                                                                                                                          Description

                                                                                                                                                                          The ΣInt( command calculates, for an amortization schedule, the interest over a range of payments: the portion of those payments that went toward paying interest. Its two required arguments are payment1 and payment2, which define the range of payments we're interested in. However, it also uses the values of the finance variables PV, PMT, and I% in its calculations.

                                                                                                                                                                          The optional argument, roundvalue, is the number of digits to which the calculator will round all internal calculations. Since this rounding affects further steps, this isn't the same as using round( to round the result of ΣInt( to the same number of digits.

                                                                                                                                                                          Usually, you will know the values of N, PV, and I%, but not PMT. This means you'll have to use the finance solver to solve for PMT before calculating ΣInt(; virtually always, FV will equal 0.

                                                                                                                                                                          Sample Problem

                                                                                                                                                                          Imagine that you have taken out a 30-year fixed-rate mortgage. The loan amount is $100000, and the annual interest rate (APR) is 8%. Payments will be made monthly. How much of the amount that was paid in the first five years went towards interest?

                                                                                                                                                                          We know the values of N, I%, and PV, though we still need to convert them to monthly values (since payments are made monthly). N is 30*12, and I% is 8/12. PV is just 100000.

                                                                                                                                                                          Now, we use the finance solver to solve for PMT. Since you intend to pay out the entire loan, FV is 0. Using either the interactive TVM solver, or the tvm_Pmt command, we get a value of about -$733.76 for PMT.

                                                                                                                                                                          We are ready to use ΣInt(. We are interested in the payments made during the first five years; that is, between the 1st payment and the 5*12=60th payment. ΣInt(1,60) gives us the answer: -$39095.73 (the negative sign simply indicates the direction of cash flow)

                                                                                                                                                                          Formulas

                                                                                                                                                                          ΣInt( is calculated in terms of ΣPrn(, for which a recurrence exists. Since the total amount paid during an interval is known (it's the payment size, multiplied by the number of payments), we can subtract ΣPrn( from this total to get ΣInt(:

                                                                                                                                                                          (1) \(\begin{align} \texttt{\Sigma Int}(n_1,n_2)=(n_2-n_1+1)\texttt{PMT}-\texttt{\Sigma Prn}(n_1,n_2) \end{align}\)

                                                                                                                                                                          Error Conditions

                                                                                                                                                                          • ERR:DOMAIN is thrown if either payment number is negative or a decimal.

                                                                                                                                                                          Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583.

                                                                                                                                                                          History

                                                                                                                                                                          Calculator OS Version Description
                                                                                                                                                                          TI-83 0.01013 Added
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                                                                                                                                                                          Hex Value $BB03
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                                                                                                                                                                          • FR: paSomPrinc(

                                                                                                                                                                          ΣPrn(

                                                                                                                                                                          Overview

                                                                                                                                                                          Computes the sum, rounded to roundvalue, of the principal amount between pmt1 and pmt2 for an amortization schedule.

                                                                                                                                                                          Availability: Token available everywhere.

                                                                                                                                                                          Syntax

                                                                                                                                                                          ΣPrn(pmt1,pmt2[,roundvalue])

                                                                                                                                                                          Arguments

                                                                                                                                                                          NameTypeOptional
                                                                                                                                                                          Σ
                                                                                                                                                                          pmt1
                                                                                                                                                                          pmt2Yes
                                                                                                                                                                          roundvalueYes

                                                                                                                                                                          Location

                                                                                                                                                                          apps, 1:Finance, CALC, 0:Prn(

                                                                                                                                                                          Description

                                                                                                                                                                          The ΣPrn( command calculates, for an amortization schedule, the principal amount over a range of payments: the portion of those payments that went toward paying off the principal. Its two required arguments are payment1 and payment2, which define the range of payments we're interested in. However, it also uses the values of the finance variables PV, PMT, and I% in its calculations.

                                                                                                                                                                          The optional argument, roundvalue, is the number of digits to which the calculator will round all internal calculations. Since this rounding affects further steps, this isn't the same as using round( to round the result of ΣPrn( to the same number of digits.

                                                                                                                                                                          Usually, you will know the values of N, PV, and I%, but not PMT. This means you'll have to use the finance solver to solve for PMT before calculating ΣPrn(; virtually always, FV will equal 0.

                                                                                                                                                                          Sample Problem

                                                                                                                                                                          Imagine that you have taken out a 30-year fixed-rate mortgage. The loan amount is $100000, and the annual interest rate (APR) is 8%. Payments will be made monthly. How much of the principal amount was paid in the first five years?

                                                                                                                                                                          We know the values of N, I%, and PV, though we still need to convert them to monthly values (since payments are made monthly). N is 30*12, and I% is 8/12. PV is just 100000.

                                                                                                                                                                          Now, we use the finance solver to solve for PMT. Since you intend to pay out the entire loan, FV is 0. Using either the interactive TVM solver, or the tvm_Pmt command, we get a value of about -$733.76 for PMT.

                                                                                                                                                                          We are ready to use ΣPrn(. We are interested in the payments made during the first five years; that is, between the 1st payment and the 5*12=60th payment. ΣPrn(1,60) gives us the answer: -$4930.14 (the negative sign simply indicates the direction of cash flow)

                                                                                                                                                                          Formulas

                                                                                                                                                                          The formula that the calculator uses for ΣPrn( is in terms of bal(:

                                                                                                                                                                          (1) \(\begin{align} \texttt{\Sigma Prn}(n_1,n_2)=\texttt{bal}(n_2)-\texttt{bal}(n_1) \end{align}\)

                                                                                                                                                                          When the roundvalue argument isn't given, we can substitute the explicit formula for bal( and simplify to get the following formula:

                                                                                                                                                                          (2) \(\begin{align} \texttt{\Sigma Prn}(n_1,n_2)=\left(\texttt{PV}-\frac{\texttt{PMT}}{I\%/100}\right)\left[\left(1-\frac{I\%}{100}\right)^{n_1}-\left(1-\frac{I\%}{100}\right)^{n_2}\right] \end{align}\)

                                                                                                                                                                          Error Conditions

                                                                                                                                                                          • ERR:DOMAIN is thrown if either payment number is negative or a decimal.

                                                                                                                                                                          Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, kg583.

                                                                                                                                                                          History

                                                                                                                                                                          Calculator OS Version Description
                                                                                                                                                                          TI-83 0.01013 Added
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                                                                                                                                                                          Hex Value $7E01
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                                                                                                                                                                          • FR: Simul

                                                                                                                                                                          Simul

                                                                                                                                                                          Overview

                                                                                                                                                                          Sets mode to graph functions simultaneously.

                                                                                                                                                                          Availability: Token only available from within the Basic editor.

                                                                                                                                                                          Syntax

                                                                                                                                                                          Simul

                                                                                                                                                                          Location

                                                                                                                                                                          mode, Simul

                                                                                                                                                                          Description

                                                                                                                                                                          Simul puts the calculator into simultaneous graphing mode. When multiple equations are enabled at the same time, simultaneous graphing mode graphs them at the same time (as opposed to Sequential mode, in which they will be graphed one after the other)

                                                                                                                                                                          If you use a list in an equation, as with Y1={1,2,3}X, this will graph several equations that will always graph separately, regardless of this setting, which only affects multiple functions in different equation variables.

                                                                                                                                                                          Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Myles_Zadok.

                                                                                                                                                                          History

                                                                                                                                                                          Calculator OS Version Description
                                                                                                                                                                          TI-82 1.0 Added
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                                                                                                                                                                          Hex Value $BB32
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                                                                                                                                                                          • FR: RegSin

                                                                                                                                                                          SinReg

                                                                                                                                                                          Overview

                                                                                                                                                                          Attempts iterations times to fit a sinusoidal regression model to Xlistname and Ylistname using a period guess, and stores the regression equation to regequ.

                                                                                                                                                                          Availability: Token available everywhere.

                                                                                                                                                                          Syntax

                                                                                                                                                                          SinReg [iterations,Xlistname,Ylistname,period,regequ]

                                                                                                                                                                          Arguments

                                                                                                                                                                          NameTypeOptional
                                                                                                                                                                          iterationsYes
                                                                                                                                                                          XlistnamelistYes
                                                                                                                                                                          YlistnamelistYes
                                                                                                                                                                          periodYes
                                                                                                                                                                          regequYes

                                                                                                                                                                          Location

                                                                                                                                                                          stat, CALC, C:SinReg

                                                                                                                                                                          Description

                                                                                                                                                                          SinReg tries to fit a sine wave to a given list of points. To use it, you must first store the points to two lists: one of the x-coordinates and one of the y-coordinates, ordered so that the ith element of one list matches up with the ith element of the other list (i.e. the first element of the x-list and the first element of the y-list make up an ordered pair). L₁ and L₂ are the default lists used, and the List Editor (STAT > Edit…) is a useful window for entering the points.

                                                                                                                                                                          SinReg requires that the lists contain at least 4 points. Also, if you do not provide two data points per cycle, the calculator may return a wrong answer. These conditions are an absolute minimum, and the command may fail to work even when they are met, and throw a ERR:SINGULAR MAT error. This is also likely to happen if the data are not actually periodic in nature.

                                                                                                                                                                          In addition, to use SinReg in its simplest form, the x-coordinates must be sorted in increasing order, and the difference between consecutive x-coordinates must be the same throughout (i.e., x𝑖+1-x𝑖 should be the same for all i). You can then call SinReg with no arguments, and it will attempt to fit a sine wave to the data in L₁ and L₂:

                                                                                                                                                                          :{1,2,3,4,5,6,7,8,9,10,11,12→L₁
:{21,24,34,46,58,67,72,70,61,50,40,27→L₂
:SinReg

                                                                                                                                                                          On the home screen, or as the last line of a program, this will display the equation of the curve: you'll be shown the format, y=a*sin(b__x+c)+d, and the values of a, b, c and d. It will also be stored in the RegEQ variable, but you will not be able to use this variable in a program - accessing it just pastes the equation wherever your cursor was. Finally, the statistical variables a, b, c, and d will be set to the values computed as well. There are no correlation statistics available for SinReg even if Diagnostic Mode is turned on (see DiagnosticOn and DiagnosticOff).

                                                                                                                                                                          A word of caution: the calculator assumes that Radian mode is enabled. If the calculator is set to Degree mode, the equation will still be in terms of radians: it will be correct, but values plugged in will give wrong answers. You will have to either switch to Radian mode, or multiply the values of b and c by 180/π.

                                                                                                                                                                          You do not have to do the regression on L₁ and L₂, in which case you'll have to enter the names of the lists after the command. For example:

                                                                                                                                                                          :{1,2,3,4,5,6,7,8,9,10,11,12→MONTH
:{21,24,34,46,58,67,72,70,61,50,40,27→TEMP
:SinReg ʟMONTH,ʟTEMP

                                                                                                                                                                          Unlike the other regression commands, SinReg does not allow you to use a frequency list for data. You can get around this by adding repeating coordinates multiple times.

                                                                                                                                                                          The optional argument iterations should come before the data lists, and if provided will change the amount of time and effort the calculator spends on the problem. The value should be an integer 1 to 16; larger numbers mean greater precision, but a longer calculation time. The default value is 3, and for good reason: with a high precision value, the calculation may take a minute to complete, or longer, depending on the complexity of the problem.

                                                                                                                                                                          The optional argument period should be given after the data lists - this is the length of a complete cycle in the data, if known. You might know the exact value of the period, for example, when the calculation involves time - a complete cycle could be a day, a month, or a year. Providing this argument is strongly recommended whenever it is available: this removes conditions on the x-coordinates' order and increment, and makes the calculation much faster and more accurate. If you have previously done a SinReg fit and desire a refined estimate, the value 2π_/b_ can be given as the period.

                                                                                                                                                                          Finally, you can enter an equation variable (such as Y₁) after the command, so that the curve's equation is stored to this variable automatically. This does not require you to supply the names of the lists, but if you do, the equation variable must come last. You can use polar, parametric, or sequential variables as well, but since the equation will be in terms of X anyway, this does not make much sense.

                                                                                                                                                                          An example of SinReg with all the optional arguments:

                                                                                                                                                                          :{1,2,3,4,5,6,7,8,9,10,11,12→MONTH
:{21,24,34,46,58,67,72,70,61,50,40,27→TEMP
:SinReg 16,ʟMONTH,ʟTEMP,12,Y₁

                                                                                                                                                                          The Levenberg-Marquardt nonlinear least-squares algorithm is used by SinReg.

                                                                                                                                                                          Error Conditions

                                                                                                                                                                          • ERR:SINGULAR MAT is thrown if you don't provide the calculator at least 4 points, or two data points per cycle.

                                                                                                                                                                          Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, thornahawk, Timothy Foster.___

                                                                                                                                                                          History

                                                                                                                                                                          Calculator OS Version Description
                                                                                                                                                                          TI-83 0.01013 Added
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                                                                                                                                                                          Hex Value $E3
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                                                                                                                                                                          • FR: Tricroi(

                                                                                                                                                                          SortA(

                                                                                                                                                                          Overview

                                                                                                                                                                          Sorts elements of listname in ascending order.

                                                                                                                                                                          Availability: Token available everywhere.

                                                                                                                                                                          Syntax

                                                                                                                                                                          SortA(listname)

                                                                                                                                                                          Arguments

                                                                                                                                                                          NameTypeOptional
                                                                                                                                                                          listnamelist

                                                                                                                                                                          Location

                                                                                                                                                                          2nd, list, OPS, 1:SortA(

                                                                                                                                                                          Overview

                                                                                                                                                                          Sorts elements of keylistname in ascending order, then sorts each dependlist as a dependent list.

                                                                                                                                                                          Availability: Token available everywhere.

                                                                                                                                                                          Syntax

                                                                                                                                                                          SortA(keylistname,dependlist1[,dependlist2,...,dependlist n])

                                                                                                                                                                          Arguments

                                                                                                                                                                          NameTypeOptional
                                                                                                                                                                          keylistnamelist
                                                                                                                                                                          dependlist1list
                                                                                                                                                                          dependlist2listYes
                                                                                                                                                                          dependlist nlistYes

                                                                                                                                                                          Location

                                                                                                                                                                          2nd, list, OPS, 1:SortA(

                                                                                                                                                                          Description

                                                                                                                                                                          The SortA( command sorts a list in ascending order. It does not return it, but instead edits the original list variable (so it takes only list variables as arguments).

                                                                                                                                                                          SortA( can also be passed multiple lists. In this case, it will sort the first list, and reorder the others so that elements which had the same indices initially will continue having the same indices. For example, suppose the X and Y coordinates of some points were stored in ʟX and ʟY, so that the Nth point had coordinates ʟX(N) and ʟY(N). Then SortA(ʟX,ʟY) would sort the points by their x-coordinates, still preserving the same points.

                                                                                                                                                                          However, SortA( is not stable: if several elements in the first list are equal, then the corresponding elements in the subsequent lists may still end up being in a different order than they were initially.

                                                                                                                                                                          Algorithm

                                                                                                                                                                          The algorithm used by SortA( and SortD( appears to be a modified selection sort. It is still O(n2) on all inputs, but for some reason takes twice as long on a list with all equal elements. It is not stable.

                                                                                                                                                                          Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan.

                                                                                                                                                                          History

                                                                                                                                                                          Calculator OS Version Description
                                                                                                                                                                          TI-82 1.0 Added
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                                                                                                                                                                          • FR: Tridécroi(

                                                                                                                                                                          SortD(

                                                                                                                                                                          Overview

                                                                                                                                                                          Sorts elements of listname in descending order.

                                                                                                                                                                          Availability: Token available everywhere.

                                                                                                                                                                          Syntax

                                                                                                                                                                          SortD(listname)

                                                                                                                                                                          Arguments

                                                                                                                                                                          NameTypeOptional
                                                                                                                                                                          listnamelist

                                                                                                                                                                          Location

                                                                                                                                                                          2nd, list, OPS, 2:SortD(

                                                                                                                                                                          Overview

                                                                                                                                                                          Sorts elements of keylistname in descending order, then sorts each dependlist as a dependent list.

                                                                                                                                                                          Availability: Token available everywhere.

                                                                                                                                                                          Syntax

                                                                                                                                                                          SortD(keylistname,dependlist1[,dependlist2,..., dependlist n])

                                                                                                                                                                          Arguments

                                                                                                                                                                          NameTypeOptional
                                                                                                                                                                          keylistnamelist
                                                                                                                                                                          dependlist1list
                                                                                                                                                                          dependlist2listYes
                                                                                                                                                                          dependlist nlistYes

                                                                                                                                                                          Location

                                                                                                                                                                          2nd, list, OPS, 2:SortD(

                                                                                                                                                                          Description

                                                                                                                                                                          The SortD( command sorts a list in descending order. It does not return it, but instead edits the original list variable (so it takes only list variables as arguments).

                                                                                                                                                                          SortD( can also be passed multiple lists. In this case, it will sort the first list, and reorder the others so that elements which had the same indices initially will continue having the same indices. For example, suppose the X and Y coordinates of some points were stored in ʟX and ʟY, so that the Nth point had coordinates ʟX(N) and ʟY(N). Then SortD(ʟX,ʟY) would sort the points by their x-coordinates, still preserving the same points.

                                                                                                                                                                          However, SortD( is not stable: if several elements in the first list are equal, then the corresponding elements in the subsequent lists may still end up being in a different order than they were initially.

                                                                                                                                                                          Algorithm

                                                                                                                                                                          The algorithm used by SortD( and SortA( appears to be a modified selection sort. It is still O(n2) on all inputs, but for some reason takes twice as long on a list with all equal elements. It is not stable.

                                                                                                                                                                          Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan.

                                                                                                                                                                          History

                                                                                                                                                                          Calculator OS Version Description
                                                                                                                                                                          TI-82 1.0 Added
                                                                                                                                                                          Property Value
                                                                                                                                                                          Hex Value $D9
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                                                                                                                                                                          • FR: Stop

                                                                                                                                                                          Stop

                                                                                                                                                                          Overview

                                                                                                                                                                          Ends program execution; returns to home screen.

                                                                                                                                                                          Availability: Token only available from within the Basic editor.

                                                                                                                                                                          Syntax

                                                                                                                                                                          Stop

                                                                                                                                                                          Location

                                                                                                                                                                          prgm, CTL, F:Stop

                                                                                                                                                                          Description

                                                                                                                                                                          When the Stop command is used in a program it exits the program (terminating the program execution) and returns you to the home screen. If it is encountered within loops, the loops will be stopped.

                                                                                                                                                                          There is some distinction when using Stop with subprograms: the Stop command will stop the program execution of the subprogram, as well as the calling program, and return you to the home screen; the program will stop completely. If this functionality is not desired, then you should use the Return command instead.

                                                                                                                                                                          Optimization

                                                                                                                                                                          You don't have to put a Stop command at the end of a program or subprogram if you can organize the program so that it just naturally quits. When the calculator reaches the end of a program, it will automatically stop executing as if it had encountered a Stop command (the Stop is implied).

                                                                                                                                                                          :ClrHome
:Input "Guess:",A
:Stop
Remove the Stop
:ClrHome
:Input "Guess:",A

                                                                                                                                                                          Error Conditions

                                                                                                                                                                          • ERR:INVALID occurs if this statement is used outside a program.

                                                                                                                                                                          See Also

                                                                                                                                                                          Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

                                                                                                                                                                          History

                                                                                                                                                                          Calculator OS Version Description
                                                                                                                                                                          TI-82 1.0 Added
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                                                                                                                                                                          Hex Value $9A
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                                                                                                                                                                          • FR: SauveBDG

                                                                                                                                                                          StoreGDB

                                                                                                                                                                          Overview

                                                                                                                                                                          Stores current graph in database GDBn.

                                                                                                                                                                          Availability: Token available everywhere.

                                                                                                                                                                          Syntax

                                                                                                                                                                          StoreGDB n

                                                                                                                                                                          Arguments

                                                                                                                                                                          NameTypeOptional
                                                                                                                                                                          n

                                                                                                                                                                          Location

                                                                                                                                                                          2nd, draw, STO, 3:StoreGDB

                                                                                                                                                                          Description

                                                                                                                                                                          The StoreGDB command stores all graph settings needed to reconstruct the current graph to a GDB (Graph DataBase) variable, one of GDB1, GDB2, …, GDB0 (as indicated by the argument). These settings can then be recalled using the RecallGDB command.

                                                                                                                                                                          The settings stored in a GDB include:

                                                                                                                                                                          • The graphing mode currently enabled.
                                                                                                                                                                          • All equations in the current graphing mode, but NOT other graphing modes.
                                                                                                                                                                          • All window variables applicable to the current graphing mode. This does not include zoom variables, table settings, or irrelevant variables such as Tmin when in function mode.
                                                                                                                                                                          • The menu settings relevant to graphing (everything in the 2nd FORMAT menu, as well as Connected/Dot and Sequential/Simul settings in the MODE menu)

                                                                                                                                                                          The number passed to StoreGDB must be one of 0 through 9. It has to be a number: StoreGDB X will not work, even if X contains a value 0 through 9.

                                                                                                                                                                          Advanced Uses

                                                                                                                                                                          The StoreGDB and RecallGDB variables are useful in cleaning up after a program finishes running, preserving the user's settings. If your program heavily relies on the graph screen, it may end up editing window size or other graph settings, which the user might want to be saved. This is easily done:

                                                                                                                                                                          Add StoreGDB 1 (or any other number) to the beginning of your program.

                                                                                                                                                                          Then, feel free to edit any graph settings you like.

                                                                                                                                                                          At the end of your program, add RecallGDB 1, followed by DelVar GDB1, to recall the graph settings stored at the beginning.

                                                                                                                                                                          GDBs can also be useful in adding extra string storage. You can store strings to the Yn variables, and back them up in a GDB; to retrieve them later, recall the GDB and use Equ►String( to store the equations to the strings again.

                                                                                                                                                                          Error Conditions

                                                                                                                                                                          • ERR:DATA TYPE is thrown if the argument is not a number 0 through 9.

                                                                                                                                                                          See Also

                                                                                                                                                                          Source: parts of this page were written by the following TI|BD contributors: DarkerLine, Electromagnet8, GoVegan.

                                                                                                                                                                          History

                                                                                                                                                                          Calculator OS Version Description
                                                                                                                                                                          TI-82 1.0 Added
                                                                                                                                                                          Property Value
                                                                                                                                                                          Hex Value $98
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                                                                                                                                                                          • FR: SauveImage

                                                                                                                                                                          StorePic

                                                                                                                                                                          Overview

                                                                                                                                                                          Stores current picture in picture Picn.

                                                                                                                                                                          Availability: Token available everywhere.

                                                                                                                                                                          Syntax

                                                                                                                                                                          StorePic n

                                                                                                                                                                          Arguments

                                                                                                                                                                          NameTypeOptional
                                                                                                                                                                          n

                                                                                                                                                                          Location

                                                                                                                                                                          2nd, draw, STO, 1:StorePic

                                                                                                                                                                          Description

                                                                                                                                                                          StorePic saves the graph screen to a picture (to recall it later, use RecallPic). Every detail of the graph screen will be stored as it appears, with the sole exception of X and Y labels on the axes (if they are shown).

                                                                                                                                                                          The number passed to StorePic must be one of 0 through 9. It has to be a number: StorePic X will not work, even if X contains a value 0 through 9.

                                                                                                                                                                          Advanced Uses

                                                                                                                                                                          A combination of StorePic and RecallPic can be used to maintain a background over which another sprite moves:

                                                                                                                                                                          First, draw the background, and save it to a picture file with StorePic.
                                                                                                                                                                          Next, draw the sprite to the screen.
                                                                                                                                                                          When you want to move the sprite, erase it, then use RecallPic to draw the background again.
                                                                                                                                                                          Then draw the sprite to its new location on the screen again (this can be done before or after using RecallPic).

                                                                                                                                                                          Also, if a screen in your program takes more than a second to draw, and is displayed several times, you might want to consider storing it to a picture the first time it's drawn, and then recalling it every next time you want to draw it.

                                                                                                                                                                          Error Conditions

                                                                                                                                                                          • ERR:DATA TYPE is thrown if the argument is not a number 0 through 9.

                                                                                                                                                                          Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, kg583.

                                                                                                                                                                          History

                                                                                                                                                                          Calculator OS Version Description
                                                                                                                                                                          TI-82 1.0 Added
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                                                                                                                                                                          Hex Value $AA09
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                                                                                                                                                                          • FR: Chaine0

                                                                                                                                                                          Str0

                                                                                                                                                                          Overview

                                                                                                                                                                          Availability: Token available everywhere.

                                                                                                                                                                          Syntax

                                                                                                                                                                          Str0

                                                                                                                                                                          Description

                                                                                                                                                                          Examples

                                                                                                                                                                          Explanation 1

                                                                                                                                                                          code 1

                                                                                                                                                                          Explanation 2

                                                                                                                                                                          code 2

                                                                                                                                                                          Error Conditions

                                                                                                                                                                          Advanced Notes

                                                                                                                                                                          History

                                                                                                                                                                          Calculator OS Version Description
                                                                                                                                                                          TI-83 0.01013 Added
                                                                                                                                                                          Property Value
                                                                                                                                                                          Hex Value $AA00
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                                                                                                                                                                          • FR: Chaine1

                                                                                                                                                                          Str1

                                                                                                                                                                          Overview

                                                                                                                                                                          Availability: Token available everywhere.

                                                                                                                                                                          Syntax

                                                                                                                                                                          Str1

                                                                                                                                                                          Description

                                                                                                                                                                          Examples

                                                                                                                                                                          Explanation 1

                                                                                                                                                                          code 1

                                                                                                                                                                          Explanation 2

                                                                                                                                                                          code 2

                                                                                                                                                                          Error Conditions

                                                                                                                                                                          Advanced Notes

                                                                                                                                                                          History

                                                                                                                                                                          Calculator OS Version Description
                                                                                                                                                                          TI-83 0.01013 Added
                                                                                                                                                                          Property Value
                                                                                                                                                                          Hex Value $AA01
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                                                                                                                                                                          • FR: Chaine2

                                                                                                                                                                          Str2

                                                                                                                                                                          Overview

                                                                                                                                                                          Availability: Token available everywhere.

                                                                                                                                                                          Syntax

                                                                                                                                                                          Str2

                                                                                                                                                                          Description

                                                                                                                                                                          Examples

                                                                                                                                                                          Explanation 1

                                                                                                                                                                          code 1

                                                                                                                                                                          Explanation 2

                                                                                                                                                                          code 2

                                                                                                                                                                          Error Conditions

                                                                                                                                                                          Advanced Notes

                                                                                                                                                                          History

                                                                                                                                                                          Calculator OS Version Description
                                                                                                                                                                          TI-83 0.01013 Added
                                                                                                                                                                          Property Value
                                                                                                                                                                          Hex Value $AA02
                                                                                                                                                                          Categories
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                                                                                                                                                                          • FR: Chaine3

                                                                                                                                                                          Str3

                                                                                                                                                                          Overview

                                                                                                                                                                          Availability: Token available everywhere.

                                                                                                                                                                          Syntax

                                                                                                                                                                          Str3

                                                                                                                                                                          Description

                                                                                                                                                                          Examples

                                                                                                                                                                          Explanation 1

                                                                                                                                                                          code 1

                                                                                                                                                                          Explanation 2

                                                                                                                                                                          code 2

                                                                                                                                                                          Error Conditions

                                                                                                                                                                          Advanced Notes

                                                                                                                                                                          History

                                                                                                                                                                          Calculator OS Version Description
                                                                                                                                                                          TI-83 0.01013 Added
                                                                                                                                                                          Property Value
                                                                                                                                                                          Hex Value $AA03
                                                                                                                                                                          Categories
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                                                                                                                                                                          • FR: Chaine4

                                                                                                                                                                          Str4

                                                                                                                                                                          Overview

                                                                                                                                                                          Availability: Token available everywhere.

                                                                                                                                                                          Syntax

                                                                                                                                                                          Str4

                                                                                                                                                                          Description

                                                                                                                                                                          Examples

                                                                                                                                                                          Explanation 1

                                                                                                                                                                          code 1

                                                                                                                                                                          Explanation 2

                                                                                                                                                                          code 2

                                                                                                                                                                          Error Conditions

                                                                                                                                                                          Advanced Notes

                                                                                                                                                                          History

                                                                                                                                                                          Calculator OS Version Description
                                                                                                                                                                          TI-83 0.01013 Added
                                                                                                                                                                          Property Value
                                                                                                                                                                          Hex Value $AA04
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                                                                                                                                                                          • FR: Chaine5

                                                                                                                                                                          Str5

                                                                                                                                                                          Overview

                                                                                                                                                                          Availability: Token available everywhere.

                                                                                                                                                                          Syntax

                                                                                                                                                                          Str5

                                                                                                                                                                          Description

                                                                                                                                                                          Examples

                                                                                                                                                                          Explanation 1

                                                                                                                                                                          code 1

                                                                                                                                                                          Explanation 2

                                                                                                                                                                          code 2

                                                                                                                                                                          Error Conditions

                                                                                                                                                                          Advanced Notes

                                                                                                                                                                          History

                                                                                                                                                                          Calculator OS Version Description
                                                                                                                                                                          TI-83 0.01013 Added
                                                                                                                                                                          Property Value
                                                                                                                                                                          Hex Value $AA05
                                                                                                                                                                          Categories
                                                                                                                                                                          Localizations
                                                                                                                                                                          • FR: Chaine6

                                                                                                                                                                          Str6

                                                                                                                                                                          Overview

                                                                                                                                                                          Availability: Token available everywhere.

                                                                                                                                                                          Syntax

                                                                                                                                                                          Str6

                                                                                                                                                                          Description

                                                                                                                                                                          Examples

                                                                                                                                                                          Explanation 1

                                                                                                                                                                          code 1

                                                                                                                                                                          Explanation 2

                                                                                                                                                                          code 2

                                                                                                                                                                          Error Conditions

                                                                                                                                                                          Advanced Notes

                                                                                                                                                                          History

                                                                                                                                                                          Calculator OS Version Description
                                                                                                                                                                          TI-83 0.01013 Added
                                                                                                                                                                          Property Value
                                                                                                                                                                          Hex Value $AA06
                                                                                                                                                                          Categories
                                                                                                                                                                          Localizations
                                                                                                                                                                          • FR: Chaine7

                                                                                                                                                                          Str7

                                                                                                                                                                          Overview

                                                                                                                                                                          Availability: Token available everywhere.

                                                                                                                                                                          Syntax

                                                                                                                                                                          Str7

                                                                                                                                                                          Description

                                                                                                                                                                          Examples

                                                                                                                                                                          Explanation 1

                                                                                                                                                                          code 1

                                                                                                                                                                          Explanation 2

                                                                                                                                                                          code 2

                                                                                                                                                                          Error Conditions

                                                                                                                                                                          Advanced Notes

                                                                                                                                                                          History

                                                                                                                                                                          Calculator OS Version Description
                                                                                                                                                                          TI-83 0.01013 Added
                                                                                                                                                                          Property Value
                                                                                                                                                                          Hex Value $AA07
                                                                                                                                                                          Categories
                                                                                                                                                                          Localizations
                                                                                                                                                                          • FR: Chaine8

                                                                                                                                                                          Str8

                                                                                                                                                                          Overview

                                                                                                                                                                          Availability: Token available everywhere.

                                                                                                                                                                          Syntax

                                                                                                                                                                          Str8

                                                                                                                                                                          Description

                                                                                                                                                                          Examples

                                                                                                                                                                          Explanation 1

                                                                                                                                                                          code 1

                                                                                                                                                                          Explanation 2

                                                                                                                                                                          code 2

                                                                                                                                                                          Error Conditions

                                                                                                                                                                          Advanced Notes

                                                                                                                                                                          History

                                                                                                                                                                          Calculator OS Version Description
                                                                                                                                                                          TI-83 0.01013 Added
                                                                                                                                                                          Property Value
                                                                                                                                                                          Hex Value $AA08
                                                                                                                                                                          Categories
                                                                                                                                                                          Localizations
                                                                                                                                                                          • FR: Chaine9

                                                                                                                                                                          Str9

                                                                                                                                                                          Overview

                                                                                                                                                                          Availability: Token available everywhere.

                                                                                                                                                                          Syntax

                                                                                                                                                                          Str9

                                                                                                                                                                          Description

                                                                                                                                                                          Examples

                                                                                                                                                                          Explanation 1

                                                                                                                                                                          code 1

                                                                                                                                                                          Explanation 2

                                                                                                                                                                          code 2

                                                                                                                                                                          Error Conditions

                                                                                                                                                                          Advanced Notes

                                                                                                                                                                          History

                                                                                                                                                                          Calculator OS Version Description
                                                                                                                                                                          TI-83 0.01013 Added
                                                                                                                                                                          Property Value
                                                                                                                                                                          Hex Value $BB56
                                                                                                                                                                          Categories
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                                                                                                                                                                          • FR: Chaine►Equ(

                                                                                                                                                                          String►Equ(

                                                                                                                                                                          Overview

                                                                                                                                                                          Converts string into an equation and stores it in Y= var.
                                                                                                                                                                          string can be a string or string variable.
                                                                                                                                                                          String►Equ( is the inverse of Equ►String(.

                                                                                                                                                                          Availability: Token only available from within the Basic editor.

                                                                                                                                                                          Syntax

                                                                                                                                                                          String►Equ(string,Y= var)

                                                                                                                                                                          Arguments

                                                                                                                                                                          NameTypeOptional
                                                                                                                                                                          stringstring
                                                                                                                                                                          var

                                                                                                                                                                          Location

                                                                                                                                                                          prgm, I/O, D:String>Equ(, F:String>Equ(

                                                                                                                                                                          Description

                                                                                                                                                                          This command stores the contents of a string to an equation variable (such as Y1 or X1T). This command can, in theory, be used whenever you need to set any equation variable.

                                                                                                                                                                          In practice, however, this command is useless. This is because the → (store) operation can be used for the same purpose:

                                                                                                                                                                          :String►Equ(Str1,Y1
can be
:Str1→Y1

                                                                                                                                                                          This replacement is universal, takes the same time to run (because it actually uses the same routines), is more convenient to type since you don't have to go through the command catalog, and is two bytes smaller.

                                                                                                                                                                          Advanced

                                                                                                                                                                          Unlike any normal use of the → (store) operation, this situation is different because it doesn't modify Ans. For example:

                                                                                                                                                                          :125
:"sin(X→Y1
:Disp Ans

                                                                                                                                                                          Because this use of → does not modify Ans, '125' will be displayed rather than 'sin(X'. However, if we were to replace Y1 with Str1, then the → operation would work normally, and 'sin(X' would be displayed.

                                                                                                                                                                          It's also important to realize the difference between the String►Equ( command and the related Equ►String(, aside from the fact that the latter is actually useful. The main difference is that while Equ►String('s arguments both have to be variables, String►Equ('s first argument can either be a variable (Str0 through Str9), a constant string (e.g., "sin(X)"), or an expression that returns a string (e.g., sub(Str1,1,5)). This applies to the → operation as well.

                                                                                                                                                                          Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Myles_Zadok, Timtech.

                                                                                                                                                                          History

                                                                                                                                                                          Calculator OS Version Description
                                                                                                                                                                          TI-83 0.01013 Added
                                                                                                                                                                          Property Value
                                                                                                                                                                          Hex Value $BB56
                                                                                                                                                                          Categories
                                                                                                                                                                          Localizations
                                                                                                                                                                          • FR: Chaine►Equ(

                                                                                                                                                                          String►Equ(

                                                                                                                                                                          Overview

                                                                                                                                                                          Converts string into an equation and stores it in Y= var.
                                                                                                                                                                          string can be a string or string variable.
                                                                                                                                                                          String►Equ( is the inverse of Equ►String(.

                                                                                                                                                                          Availability: Token only available from within the Basic editor.

                                                                                                                                                                          Syntax

                                                                                                                                                                          String►Equ(string,Y= var)

                                                                                                                                                                          Arguments

                                                                                                                                                                          NameTypeOptional
                                                                                                                                                                          stringstring
                                                                                                                                                                          var

                                                                                                                                                                          Location

                                                                                                                                                                          prgm, I/O, D:String>Equ(, F:String>Equ(

                                                                                                                                                                          Description

                                                                                                                                                                          This command stores the contents of a string to an equation variable (such as Y1 or X1T). This command can, in theory, be used whenever you need to set any equation variable.

                                                                                                                                                                          In practice, however, this command is useless. This is because the → (store) operation can be used for the same purpose:

                                                                                                                                                                          :String►Equ(Str1,Y1
can be
:Str1→Y1

                                                                                                                                                                          This replacement is universal, takes the same time to run (because it actually uses the same routines), is more convenient to type since you don't have to go through the command catalog, and is two bytes smaller.

                                                                                                                                                                          Advanced

                                                                                                                                                                          Unlike any normal use of the → (store) operation, this situation is different because it doesn't modify Ans. For example:

                                                                                                                                                                          :125
:"sin(X→Y1
:Disp Ans

                                                                                                                                                                          Because this use of → does not modify Ans, '125' will be displayed rather than 'sin(X'. However, if we were to replace Y1 with Str1, then the → operation would work normally, and 'sin(X' would be displayed.

                                                                                                                                                                          It's also important to realize the difference between the String►Equ( command and the related Equ►String(, aside from the fact that the latter is actually useful. The main difference is that while Equ►String('s arguments both have to be variables, String►Equ('s first argument can either be a variable (Str0 through Str9), a constant string (e.g., "sin(X)"), or an expression that returns a string (e.g., sub(Str1,1,5)). This applies to the → operation as well.

                                                                                                                                                                          Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Myles_Zadok, Timtech.

                                                                                                                                                                          History

                                                                                                                                                                          Calculator OS Version Description
                                                                                                                                                                          TI-83 0.01013 Added
                                                                                                                                                                          Property Value
                                                                                                                                                                          Hex Value $6231
                                                                                                                                                                          Categories
                                                                                                                                                                          Localizations
                                                                                                                                                                          • FR: Éctypxp

                                                                                                                                                                          Sxp

                                                                                                                                                                          Overview

                                                                                                                                                                          Syntax

                                                                                                                                                                          Sxp

                                                                                                                                                                          Description

                                                                                                                                                                          Examples

                                                                                                                                                                          Explanation 1

                                                                                                                                                                          code 1

                                                                                                                                                                          Explanation 2

                                                                                                                                                                          code 2

                                                                                                                                                                          Error Conditions

                                                                                                                                                                          Advanced Notes

                                                                                                                                                                          History

                                                                                                                                                                          Calculator OS Version Description
                                                                                                                                                                          TI-82 1.0 Added
                                                                                                                                                                          Property Value
                                                                                                                                                                          Hex Value $622C
                                                                                                                                                                          Categories
                                                                                                                                                                          Localizations
                                                                                                                                                                          • FR: Éctypx₁

                                                                                                                                                                          Sx₁

                                                                                                                                                                          Overview

                                                                                                                                                                          Syntax

                                                                                                                                                                          Sx₁

                                                                                                                                                                          Description

                                                                                                                                                                          Examples

                                                                                                                                                                          Explanation 1

                                                                                                                                                                          code 1

                                                                                                                                                                          Explanation 2

                                                                                                                                                                          code 2

                                                                                                                                                                          Error Conditions

                                                                                                                                                                          Advanced Notes

                                                                                                                                                                          History

                                                                                                                                                                          Calculator OS Version Description
                                                                                                                                                                          TI-82 1.0 Added
                                                                                                                                                                          Property Value
                                                                                                                                                                          Hex Value $622F
                                                                                                                                                                          Categories
                                                                                                                                                                          Localizations
                                                                                                                                                                          • FR: Éctypx₂

                                                                                                                                                                          Sx₂

                                                                                                                                                                          Overview

                                                                                                                                                                          Syntax

                                                                                                                                                                          Sx₂

                                                                                                                                                                          Description

                                                                                                                                                                          Examples

                                                                                                                                                                          Explanation 1

                                                                                                                                                                          code 1

                                                                                                                                                                          Explanation 2

                                                                                                                                                                          code 2

                                                                                                                                                                          Error Conditions

                                                                                                                                                                          Advanced Notes

                                                                                                                                                                          History

                                                                                                                                                                          Calculator OS Version Description
                                                                                                                                                                          TI-82 1.0 Added
                                                                                                                                                                          Property Value
                                                                                                                                                                          Hex Value $BB3C
                                                                                                                                                                          Categories
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                                                                                                                                                                          • FR: T-Test

                                                                                                                                                                          T-Test

                                                                                                                                                                          Overview

                                                                                                                                                                          Performs a t test with frequency freqlist. alternative=-1 is <; alternative=0 is ≠; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results.
                                                                                                                                                                          Color#: 10 - 24 or color name pasted from [vars] COLOR.

                                                                                                                                                                          Comment:Data list input

                                                                                                                                                                          Availability: Token only available from within the Basic editor.

                                                                                                                                                                          Syntax

                                                                                                                                                                          T-Test μ0[,listname,freqlist,alternative,drawflag,color#])

                                                                                                                                                                          Arguments

                                                                                                                                                                          NameTypeOptional
                                                                                                                                                                          μ
                                                                                                                                                                          0Yes
                                                                                                                                                                          listnamelistYes
                                                                                                                                                                          freqlistlistYes
                                                                                                                                                                          alternativeYes
                                                                                                                                                                          drawflagYes
                                                                                                                                                                          color#colorNumYes

                                                                                                                                                                          Location

                                                                                                                                                                          stat, TESTS, 2:T-Test

                                                                                                                                                                          Overview

                                                                                                                                                                          Performs a t test with frequency freqlist. alternative=-1 is < ; alternative=0 is ă; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results.
                                                                                                                                                                          Color#: 10 - 24 or color name pasted from [vars] COLOR.

                                                                                                                                                                          Availability: Token only available from within the Basic editor.

                                                                                                                                                                          Syntax

                                                                                                                                                                          T-Test μ0,x̄,Sx,n[,alternative,drawflag,color#])

                                                                                                                                                                          Arguments

                                                                                                                                                                          NameTypeOptional
                                                                                                                                                                          μ
                                                                                                                                                                          0
                                                                                                                                                                          x̄
                                                                                                                                                                          Sx
                                                                                                                                                                          nYes
                                                                                                                                                                          alternativeYes
                                                                                                                                                                          drawflagYes
                                                                                                                                                                          color#colorNumYes

                                                                                                                                                                          Location

                                                                                                                                                                          stat, TESTS, 2:T-Test

                                                                                                                                                                          Description

                                                                                                                                                                          T-Test performs a t significance test of a null hypothesis you supply. This test is valid for simple random samples from a population with an unknown standard deviation. In addition, either the population must be normally distributed, or the sample size has to be sufficiently large.

                                                                                                                                                                          The logic behind a T-Test is as follows: we want to test the hypothesis that the true mean of a population is a certain value (μ0). To do this, we assume that this "null hypothesis" is true, and calculate the probability that the variation from this mean occurred, under this assumption. If this probability is sufficiently low (usually, 5% is the cutoff point), we conclude that since it's so unlikely that the data could have occurred under the null hypothesis, the null hypothesis must be false, and therefore the true mean μ is not equal to μ0. If, on the other hand, the probability is not too low, we conclude that the data may well have occurred under the null hypothesis, and therefore there's no reason to reject it.

                                                                                                                                                                          In addition to the null hypothesis, we must have an alternative hypothesis as well - usually this is simply that the true mean is not μ0. However, in certain cases when we have reason to suspect the true mean is less than or greater than μ0, we might use a "one-sided" alternative hypothesis, which will state that the true mean μ<μ0 or that μ>μ0.

                                                                                                                                                                          As for the T-Test command itself, there are two ways of calling it: you may give it a list of all the sample data, or the necessary statistics about the list - its size, the mean, and the standard deviation. In either case, you can indicate what the alternate hypothesis is, by a value of 0, -1, or 1 for the alternative argument. 0 indicates a two-sided hypothesis of μ≠μ0, -1 indicates μ<μ0, and 1 indicates μ>μ0. (in fact, any negative argument will be treated as -1, and any positive argument as 1)

                                                                                                                                                                          Although you can access the T-Test command on the home screen, via the catalog, there's no need: the T-Test… interactive solver, found in the statistics menu, is much more intuitive to use - you don't have to memorize the syntax.

                                                                                                                                                                          In either case, it's important to understand the output of T-Test. Here are the meanings of each line:

                                                                                                                                                                          • The first line, involving μ, is the alternative hypothesis.
                                                                                                                                                                          • t is the test statistic, the standardized difference between the sample mean and μ0. If the null hypothesis is true, it should be close to 0.
                                                                                                                                                                          • p is the probability that the difference between the sample mean and μ0 would occur if the null hypothesis is true. When the value is sufficiently small, we reject the null hypothesis and conclude that the alternative hypothesis is true. You should have a cutoff value ready, such as 5% or 1%. If p is lower, you "reject the null hypothesis on a 5% (or 1%) level" in technical terms.
                                                                                                                                                                          • x-bar is the sample mean.
                                                                                                                                                                          • Sx is the sample standard deviation.
                                                                                                                                                                          • n is the sample size (not included, but also important, is df, the degrees of freedom, defined as n-1)

                                                                                                                                                                          Sample Problem

                                                                                                                                                                          According to M&M's advertising, each standard-size bag of M&M's contains an average of 10 blue M&M's. You think that this estimate is low, and that the true average is higher. You decide to test this hypothesis by buying thirty bags of M&M's. You count the number of blue M&M's in each, and store this number to L1.

                                                                                                                                                                          The value of μ0 is 10, because you want to test the null hypothesis that there are on average 10 blue M&M's per bag. We want to test the values in L1. Because we want to test if there's actually more than 10 blue M&M's per bag, we have a one-sided alternate hypothesis: μ>μ0, which corresponds to an argument of 1. To solve the problem, you'd use this code:

                                                                                                                                                                          :T-Test 10,L1,1

                                                                                                                                                                          Alternatively, you could calculate the mean, standard deviation, and size of your sample, and put those into the command instead. The sample size is 30; let's suppose that the mean was 11.2 and the standard deviation 1.3. The code you'd use is:

                                                                                                                                                                          :T-Test 10,11.2,1.3,30,1

                                                                                                                                                                          You will see the following output:

                                                                                                                                                                          T-Test
 μ>10
 z=5.055900531
 p=1.0857768e-5
 x=11.2
 Sx=1.3
 n=30

                                                                                                                                                                          The most important part of this output is "p=1.0857768e-5". This value of p is much smaller than 1% or 0.01; it's in fact around 0.00001. This is significant on the 1% level, so we reject the null hypothesis and conclude that the alternative hypothesis is true: μ>10, that is, the average number of blue M&M's in a bag is more than 10.

                                                                                                                                                                          Advanced Uses

                                                                                                                                                                          The final argument of T-Test, draw?, will display the results in a graphical manner if you put in "1" for it. The calculator will draw the Student's t distribution with the correct degrees of freedom, and shade the area of the graph beyond the t statistic. In addition, the value of t and the value of p will be displayed (the value of p corresponds to the shaded area). You would make your conclusions in the same way as for the regular output.

                                                                                                                                                                          As with most other statistical commands, you may use a frequency list in your input (when using the data list syntax).

                                                                                                                                                                          Optimization

                                                                                                                                                                          Most of the arguments of the T-Test command have default values, and the argument can be omitted if this value is accepted.

                                                                                                                                                                          • The draw? argument can be omitted if you don't want graphical output, although you could put "0" in as well.
                                                                                                                                                                          • If the draw? argument is omitted, you can omit the alternative argument to use a two-sided test (μ≠μ0). If you include the draw? argument, you have to include this - otherwise there will be confusion as to what the 5th argument means.
                                                                                                                                                                          • With data list input, you can always omit the frequency list if you won't be using it.
                                                                                                                                                                          • With data list input, if the draw? and alternative arguments are omitted, and your data is in L1, you may omit L1 as well. However, if alternative or draw? is present, you have to include it, or else the syntax may be confused with the syntax for summary stats input.

                                                                                                                                                                          The code in the sample problem above can't be optimized, because the alternative argument is 1:

                                                                                                                                                                          ::T-Test 10,L1,1

                                                                                                                                                                          However, if we were doing a two-sided test, we could omit the alternative and the list arguments (since we're testing L1):

                                                                                                                                                                          :T-Test 10,L1,0
can be
:T-Test 10

                                                                                                                                                                          Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

                                                                                                                                                                          History

                                                                                                                                                                          Calculator OS Version Description
                                                                                                                                                                          TI-83 0.01013 Added
                                                                                                                                                                          Property Value
                                                                                                                                                                          Hex Value $54
                                                                                                                                                                          Categories
                                                                                                                                                                          Localizations
                                                                                                                                                                          • FR: T

                                                                                                                                                                          T

                                                                                                                                                                          Overview

                                                                                                                                                                          Availability: Token available everywhere.

                                                                                                                                                                          Syntax

                                                                                                                                                                          T

                                                                                                                                                                          Description

                                                                                                                                                                          Examples

                                                                                                                                                                          Explanation 1

                                                                                                                                                                          code 1

                                                                                                                                                                          Explanation 2

                                                                                                                                                                          code 2

                                                                                                                                                                          Error Conditions

                                                                                                                                                                          Advanced Notes

                                                                                                                                                                          History

                                                                                                                                                                          Calculator OS Version Description
                                                                                                                                                                          TI-82 1.0 Added
                                                                                                                                                                          Property Value
                                                                                                                                                                          Hex Value $BB48
                                                                                                                                                                          Categories
                                                                                                                                                                          Localizations
                                                                                                                                                                          • FR: TintConf

                                                                                                                                                                          TInterval

                                                                                                                                                                          Overview

                                                                                                                                                                          Computes a t confidence interval.

                                                                                                                                                                          Comment:Data list input

                                                                                                                                                                          Availability: Token only available from within the Basic editor.

                                                                                                                                                                          Syntax

                                                                                                                                                                          TInterval [listname,freqlist,confidence level]

                                                                                                                                                                          Arguments

                                                                                                                                                                          NameTypeOptional
                                                                                                                                                                          listnamelistYes
                                                                                                                                                                          freqlistlistYes
                                                                                                                                                                          confidence levelYes

                                                                                                                                                                          Location

                                                                                                                                                                          stat, TESTS, 8:TInterval

                                                                                                                                                                          Overview

                                                                                                                                                                          Computes a t confidence interval.

                                                                                                                                                                          Comment:Summary stats input

                                                                                                                                                                          Availability: Token only available from within the Basic editor.

                                                                                                                                                                          Syntax

                                                                                                                                                                          TInterval x̄,Sx,n[,confidence level]

                                                                                                                                                                          Arguments

                                                                                                                                                                          NameTypeOptional
                                                                                                                                                                          x̄
                                                                                                                                                                          Sx
                                                                                                                                                                          nYes
                                                                                                                                                                          confidence levelYes

                                                                                                                                                                          Location

                                                                                                                                                                          stat, TESTS, 8:TInterval

                                                                                                                                                                          Description

                                                                                                                                                                          The TInterval command calculates a confidence interval for the mean value of a population, at a specific confidence level: for example, if the confidence level is 95%, you are 95% certain that the mean lies within the interval you get. Use TInterval when you have a single variable to analyze, and don't know the standard deviation. The TInterval assumes that your distribution is normal, but it will work for other distributions if the sample size is large enough.

                                                                                                                                                                          There are two ways to call the TInterval command: by supplying it with needed sample statistics (mean, sample standard deviation, and sample size), or by entering a list and letting the calculator work the statistics out.

                                                                                                                                                                          Sample Problem

                                                                                                                                                                          You want to know the average height of a student at your school. You haven't asked everyone, but you took a random sample of 30 people and found out their heights (and stored it to L1). You've decided to use a 95% confidence interval.

                                                                                                                                                                          Since the syntax for entering a data list is TInterval list, confidence level, here is your code:

                                                                                                                                                                          :TInterval L1,95
you can also use
:TInterval L1,.95

                                                                                                                                                                          Alternatively, you could calculate the mean, sample size, and standard deviation, and enter those instead. The sample size is 30; let's say the mean was 63 inches and the standard deviation was 6.2 inches.

                                                                                                                                                                          The syntax for entering statistics is TInterval mean, std. deviation, sample size, confidence level, so your code would look like:

                                                                                                                                                                          :TInterval 63,6.2,30,95
you can also use
:TInterval 63,6.2,30,.95

                                                                                                                                                                          Of course, the main use of the TInterval command is in a program. While you can enter the TInterval command on the home screen as well (just look in the catalog for it), it would probably be easier to select TInterval… from the STAT>TEST menu (see the sidebar).

                                                                                                                                                                          One thing to note about using TInterval in a program is that it will not display data if there are lines of code after it. Either the command is on the last line of code, or it will not display anything. The way to work around this is to display the lower and upper variables, as that is where TInterval stores the results.

                                                                                                                                                                          :TInterval //some statistical data
:Disp lower,upper

                                                                                                                                                                          Advanced Uses

                                                                                                                                                                          As with most other statistical commands, you can enter a second list after the data list, to add frequencies (only with the data list syntax, of course). The frequency list must contain non-negative integers, and can't be all 0.

                                                                                                                                                                          Optimization

                                                                                                                                                                          Using the data list syntax, all the arguments are optional: the calculator will assume you want to use L1 for your data unless another list is supplied, and that the confidence level you want is 95% unless you give another one. Using the summary stats syntax, the confidence level is also optional - again, the calculator will assume 95%. This means we can rewrite our code above in a simpler manner:

                                                                                                                                                                          :TInterval L1,95
can be just
:TInterval

                                                                                                                                                                          :TInterval 63,6.2,30,95
can be
:TInterval 63,6.2,30

                                                                                                                                                                          Error Conditions

                                                                                                                                                                          • ERR:DATA TYPE occurs if complex numbers are used (in some cases, ERR:ARGUMENT is thrown instead).
                                                                                                                                                                          • ERR:DIM MISMATCH occurs if the data and frequency lists aren't the same size.
                                                                                                                                                                          • ERR:DOMAIN occurs in any of the following cases:
                                                                                                                                                                            • The confidence level isn't in the range (0 .. 100).
                                                                                                                                                                            • The standard deviation isn't positive.
                                                                                                                                                                            • The sample size isn't an integer greater than 1.
                                                                                                                                                                          • ERR:STAT occurs if the frequency list's elements aren't integers.

                                                                                                                                                                          Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Myles_Zadok.

                                                                                                                                                                          History

                                                                                                                                                                          Calculator OS Version Description
                                                                                                                                                                          TI-83 0.01013 Added
                                                                                                                                                                          Property Value
                                                                                                                                                                          Hex Value $A7
                                                                                                                                                                          Categories
                                                                                                                                                                          Localizations
                                                                                                                                                                          • FR: Tangente(

                                                                                                                                                                          Tangent(

                                                                                                                                                                          Overview

                                                                                                                                                                          Draws a line tangent to expression at X=value with specified color #: 10-24 and line style linestyle #:1-2.
                                                                                                                                                                          Color#: 10 - 24 or color name pasted from [vars] COLOR.

                                                                                                                                                                          Availability: Token available everywhere.

                                                                                                                                                                          Syntax

                                                                                                                                                                          Tangent(expression,value[,color#,linestyle#])

                                                                                                                                                                          Arguments

                                                                                                                                                                          NameTypeOptional
                                                                                                                                                                          expressionexpression
                                                                                                                                                                          value
                                                                                                                                                                          color#colorNumYes
                                                                                                                                                                          linestyle#integerYes

                                                                                                                                                                          Location

                                                                                                                                                                          2nd, draw, DRAW, 5:Tangent(

                                                                                                                                                                          Description

                                                                                                                                                                          The Tangent( command draws a graph of an expression and then draws a line tangent to that expression, with the line touching the graph at the point of the specified value. You can either use a equation variable (such as Y1) or an expression in terms of X (such as X²). Though you can use equation variables from any graphing mode, they will be treated as functions in terms of X. Tangent( also ignores the graphing mode currently selected.

                                                                                                                                                                          Here is a simple example, where we are graphing the parabola X2 and then drawing a tangent line at the value X=2.

                                                                                                                                                                          :"X²→Y₁
:Tangent(Y₁,2

                                                                                                                                                                          or

                                                                                                                                                                          :Tangent(X²,2

                                                                                                                                                                          Advanced Uses

                                                                                                                                                                          Whether the graph shows up or not is dependent on the window dimensions of the graph screen, and you should use a friendly window to ensure it shows up as you intended.

                                                                                                                                                                          Tangent( will update X and Y for each coordinate drawn (like DrawF and DrawInv), and exit with the last coordinate still stored.

                                                                                                                                                                          When evaluating the expression using Tangent(, the calculator will ignore the following errors: ERR:DATA TYPE, ERR:DIVIDE BY 0, ERR:DOMAIN, ERR:INCREMENT, ERR:NONREAL ANS, ERR:OVERFLOW, and ERR:SINGULAR MAT. If one of these errors occurs, the data point will be omitted. However, the errors will still be thrown if they occur when evaluating the function at the point of tangency.

                                                                                                                                                                          Using Ans as an optimization for storing to an equation will not work. For example, the following code returns ERR:DATA TYPE because Ans is a string, not an equation variable.

                                                                                                                                                                          :"X²
:Tangent(Ans,2

                                                                                                                                                                          Of course, you can use Ans in the equation, if it's a real number, but that's usually not as useful.

                                                                                                                                                                          Error Conditions

                                                                                                                                                                          • ERR:INVALID is thrown if you try to use an equation variable that is undefined.

                                                                                                                                                                          Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

                                                                                                                                                                          History

                                                                                                                                                                          Calculator OS Version Description
                                                                                                                                                                          TI-82 1.0 Added
                                                                                                                                                                          Property Value
                                                                                                                                                                          Hex Value $632A
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                                                                                                                                                                          • FR: TblInput

                                                                                                                                                                          TblInput

                                                                                                                                                                          Overview

                                                                                                                                                                          Availability: Token available everywhere.

                                                                                                                                                                          Syntax

                                                                                                                                                                          TblInput

                                                                                                                                                                          Description

                                                                                                                                                                          Examples

                                                                                                                                                                          Explanation 1

                                                                                                                                                                          code 1

                                                                                                                                                                          Explanation 2

                                                                                                                                                                          code 2

                                                                                                                                                                          Error Conditions

                                                                                                                                                                          Advanced Notes

                                                                                                                                                                          History

                                                                                                                                                                          Calculator OS Version Description
                                                                                                                                                                          TI-82 1.0 Added
                                                                                                                                                                          Property Value
                                                                                                                                                                          Hex Value $631A
                                                                                                                                                                          Categories
                                                                                                                                                                          Localizations
                                                                                                                                                                          • FR: TblStart

                                                                                                                                                                          TblStart

                                                                                                                                                                          Overview

                                                                                                                                                                          Availability: Token available everywhere.

                                                                                                                                                                          Syntax

                                                                                                                                                                          TblStart

                                                                                                                                                                          Description

                                                                                                                                                                          Examples

                                                                                                                                                                          Explanation 1

                                                                                                                                                                          code 1

                                                                                                                                                                          Explanation 2

                                                                                                                                                                          code 2

                                                                                                                                                                          Error Conditions

                                                                                                                                                                          Advanced Notes

                                                                                                                                                                          History

                                                                                                                                                                          Calculator OS Version Description
                                                                                                                                                                          TI-82 1.0 Added
                                                                                                                                                                          Property Value
                                                                                                                                                                          Hex Value $93
                                                                                                                                                                          Categories
                                                                                                                                                                          Localizations
                                                                                                                                                                          • FR: Texte(

                                                                                                                                                                          Text(

                                                                                                                                                                          Overview

                                                                                                                                                                          Writes text on graph beginning at pixel (row,column), where 0 ≤ row ≤ 164 and 0 ≤ column ≤ 264.
                                                                                                                                                                          Full mode, row must be <=148; column must be 256
                                                                                                                                                                          Horiz mode, row must be row<=66 and column must be <=256
                                                                                                                                                                          G-T mode, row must be row <=126; column must be 176

                                                                                                                                                                          Availability: Token available everywhere.

                                                                                                                                                                          Syntax

                                                                                                                                                                          Text(row,column,text1,text2,...,text n)

                                                                                                                                                                          Arguments

                                                                                                                                                                          NameTypeOptional
                                                                                                                                                                          row
                                                                                                                                                                          column
                                                                                                                                                                          text1string
                                                                                                                                                                          text2string
                                                                                                                                                                          ...
                                                                                                                                                                          text nstring

                                                                                                                                                                          Location

                                                                                                                                                                          2nd, draw, DRAW, 0:Text(

                                                                                                                                                                          Description

                                                                                                                                                                          The Text( command allows you to display text on the graph screen, using the small font. It takes three arguments: the row, which can range from 0 to the number of pixels tall the screen is (62 on grayscale, 164 on color) at which you want to display something, the column, which can range from 0 to the number of pixels wide the screen is (94 on grayscale, 264 on color), and whatever it is you want to display. Like the Output( command, it is limited to numbers and strings. If part of what you want to display goes off the screen, it will not be displayed - the calculator will cut you off at the most characters that will fit on the screen entirely.

                                                                                                                                                                          Unlike the large text used on the home screen, the small font this command uses varies in width from 2 pixels to as many as 6 (counting the blank space at the end of each character, which is 1 pixel). All characters are 6 pixels tall, but the top row of pixels is used very rarely (only in international characters such as ä). On the TI-84+/SE/CSE/CE, the Text( command may also erase a single row of pixels underneath the text: whether this occurs or not depends on whether it was the menu screen or the table that was visited last, of the two.
                                                                                                                                                                          Without storing them to a special string, the Text( command cannot be used to display quotation marks (") and the STO (→) command. However, you can mimic these respectively by using two apostrophes (' ' ), and two subtract signs and a greater than sign (—>).

                                                                                                                                                                          Like many other drawing commands, if you're outside a program and on the graph screen, you can use this command directly, without going to the home screen. Just select Text( from the draw menu, and you will be able to type text at a cursor you control with arrow keys; press CLEAR or ENTER (among other things) to exit this mode.

                                                                                                                                                                          Advanced Uses

                                                                                                                                                                          On the TI-83/84/+/SE/CSE/CE, Text( has an alternate syntax: put a -1 before the row and column to display the text using the large font instead of the small font. With this syntax, Text( becomes like an Output( for the graph screen, but with more features: you don't have to display text exactly aligned to one of the home screen's rows and columns, and you can display more than one string or number at a time. Also, text still won't wrap like Output('s does.

                                                                                                                                                                          This feature may be helpful in making programs more appealing, but remember that it does not work on the regular TI-83. If you want to maintain compatibility, don't use this syntax, or make an alternate version of your program without it.

                                                                                                                                                                          The Text( command is also critical to the sprite technique known as text sprites. Although they have limitations, they allow pure Basic programs to have high-quality graphics without taking up lots of space. This effect is not as good on the color calculators.

                                                                                                                                                                          On the TI-84+ and TI-84+ SE, another compatibility issue occurs with Text(. On certain occasions, using Text( to display small text on the graph screen will erase a 1-pixel margin below the text itself. The cause is a system option which is turned on when accessing the new MODE menu, and turned off when accessing the table, matrix editor, or list editor. The 1-pixel margin may not seem like a big deal, but it's enough to stop certain games (such as Bryan Thomas's Contra) from working on the TI-84+/SE.

                                                                                                                                                                          The situation can be detected quite easily: turn on a pixel, display text 6 rows above it, and test if the pixel is still turned on. Fixing the situation is slightly more difficult:

                                                                                                                                                                          • The hex code AsmPrgmFDCB058EC9 will disable the option (but it requires having an additional subprogram).
                                                                                                                                                                          • DispTable will also do the trick, but of course it will display the table as well.
                                                                                                                                                                          • Switch the program to G-T while it's on the graphscreen. Before doing this it's useful to have a FnOff.
                                                                                                                                                                            • The above two don't work in resetting the flag on OSes 2.53 MP or higher, the hex code is required.
                                                                                                                                                                          • There's the option of telling users to access a certain screen before playing…

                                                                                                                                                                          You can also try to get around the situation by storing and recalling pictures, to prevent anything from being erased when you don't want it to be.

                                                                                                                                                                          Error Conditions

                                                                                                                                                                          • ERR:DOMAIN is thrown if the coordinates of Text( are not integers or are out of range. A few comments:
                                                                                                                                                                            • ERR:DATA TYPE can sometimes occur instead on the TI-83+ or higher because of confusion with the alternate syntax
                                                                                                                                                                            • Similarly, Text(-1,0,0) will cause no error and display nothing whatsoever on the TI-83+ or higher.
                                                                                                                                                                            • With Text(-1,… the upper bound on the row is one less of what it would be normally.
                                                                                                                                                                            • In Horiz mode the upper bound on the row is 25 rather than 57. In G-T mode the upper bound on the column is 46.
                                                                                                                                                                          • ERR:ARGUMENT is thrown if the number of arguments given to Text( is 256 or more or if one of the arguments contains an imaginary part. The latter restriction can be bypassed with clever programming. One such method is displayed here: <complex number>:Text(x,y,real(Ans),sub(“+-“,1+(imag(Ans)<0)),imag(Ans),”i

                                                                                                                                                                          Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, Edward H, GoVegan, iPhoenixOnTIBD, Ivoah, kg583, mattyjraps, Myles_Zadok, Timothy Foster, ztrumpet.

                                                                                                                                                                          History

                                                                                                                                                                          Calculator OS Version Description
                                                                                                                                                                          TI-82 1.0 Added
                                                                                                                                                                          Property Value
                                                                                                                                                                          Hex Value $EF67
                                                                                                                                                                          Categories
                                                                                                                                                                            Localizations
                                                                                                                                                                            • FR: CouleurTexte(

                                                                                                                                                                            TextColor(

                                                                                                                                                                            Overview

                                                                                                                                                                            Set text color prior to using the Text(command.
                                                                                                                                                                            Color#: 10 - 24 or color name pasted from [vars] COLOR.

                                                                                                                                                                            Availability: Token only available from within the Basic editor.

                                                                                                                                                                            Syntax

                                                                                                                                                                            TextColor([color#]

                                                                                                                                                                            Arguments

                                                                                                                                                                            NameTypeOptional
                                                                                                                                                                            color#colorNumYes

                                                                                                                                                                            Location

                                                                                                                                                                            2nd, draw, DRAW, A:TextColor(

                                                                                                                                                                            Description

                                                                                                                                                                            The TextColor( token is used to set the color for Text(. Although the default color is Blue, the calculator saves the color until it is changed again using TextColor( or when a memory reset occurs. When a memory reset occurs, the text color is reset back to blue.

                                                                                                                                                                            :TextColor(BLUE
:Text(0,0,"THIS TEXT IS BLUE
:TextColor(GRAY
:Text(12,0,"THIS TEXT IS GRAY
:Text(24,0,"THIS IS GRAY AS WELL
:TextColor(12
:Text(36,0,"THIS TEXT IS BLACK

                                                                                                                                                                            The following table are the colors associated with their numeric values.

                                                                                                                                                                            Color Token

                                                                                                                                                                            Numeric Value

                                                                                                                                                                            BLUE

                                                                                                                                                                            10

                                                                                                                                                                            RED

                                                                                                                                                                            11

                                                                                                                                                                            BLACK

                                                                                                                                                                            12

                                                                                                                                                                            MAGENTA

                                                                                                                                                                            13

                                                                                                                                                                            GREEN

                                                                                                                                                                            14

                                                                                                                                                                            ORANGE

                                                                                                                                                                            15

                                                                                                                                                                            BROWN

                                                                                                                                                                            16

                                                                                                                                                                            NAVY

                                                                                                                                                                            17

                                                                                                                                                                            LTBLUE

                                                                                                                                                                            18

                                                                                                                                                                            YELLOW

                                                                                                                                                                            19

                                                                                                                                                                            WHITE

                                                                                                                                                                            20

                                                                                                                                                                            LTGRAY

                                                                                                                                                                            21

                                                                                                                                                                            MEDGRAY

                                                                                                                                                                            22

                                                                                                                                                                            GRAY

                                                                                                                                                                            23

                                                                                                                                                                            DARKGRAY

                                                                                                                                                                            24

                                                                                                                                                                            Each color token is 2 bytes.
                                                                                                                                                                            The color tokens can be used in calculations. For example, LTBLUE/3 will equal 6.

                                                                                                                                                                            Background Colors

                                                                                                                                                                            When the calculator displays text on the graphscreen, it displays it on top of a predetermined background color. This background color is white for all colors of text, except for yellow, white, and light gray (LTGRAY), which have a background color of medium gray (MEDGRAY). If you want to display text in your game without the annoying text-background, you need to have the graphscreen background be white or medium gray so the text-background doesn't show. The only known alternative is to use Pxl-On to draw the text manually, so how you work around this issue depends almost entirely on how lazy you are. You can see how this works by looking at the image in the Command Summary sidebar.

                                                                                                                                                                            Error Conditions

                                                                                                                                                                            • ERR:DOMAIN is thrown if the argument specified is not an integer within the 10-24 range.

                                                                                                                                                                            Source: parts of this page were written by the following TI|BD contributors: Battlesquid, Electromagnet8, iPhoenixOnTIBD, Myles_Zadok.

                                                                                                                                                                            History

                                                                                                                                                                            Calculator OS Version Description
                                                                                                                                                                            TI-84+CSE 4.0 Added
                                                                                                                                                                            Property Value
                                                                                                                                                                            Hex Value $CF
                                                                                                                                                                            Categories
                                                                                                                                                                            Localizations
                                                                                                                                                                            • FR: Then

                                                                                                                                                                            Then

                                                                                                                                                                            Overview

                                                                                                                                                                            Availability: Token available everywhere.

                                                                                                                                                                            Syntax

                                                                                                                                                                            ThenSee If:Then

                                                                                                                                                                            Arguments

                                                                                                                                                                            NameTypeOptional
                                                                                                                                                                            See

                                                                                                                                                                            Location

                                                                                                                                                                            Then

                                                                                                                                                                            Description

                                                                                                                                                                            The If command is crucial to most programs. It allows you to execute code if and only if an expression is not equal to zero. Advanced uses of the If command allow you to execute a different block of code if the check turns out to be false. The simplest form of the command is quite easy to understand:

                                                                                                                                                                            :If (condition)
:statement

                                                                                                                                                                            When the calculator gets to that point in your program, it will check to see if the condition is nonzero. Most expressions you will use with If are called conditional expressions; that is, they return 1 if the condition is true and 0 if it is false. Examples include 2+2=4, A=5, and pxl-Test(R,C). Therefore, when the condition is true, the expression evaluates to 1 and the statement is run. When the condition is false, the expression evaluates to 0, and the statement is skipped.

                                                                                                                                                                            Using Then, Else, and End

                                                                                                                                                                            When you want more than one line of code to depend on the same condition, use an If-Then block.

                                                                                                                                                                            :If (condition)
:Then
code to execute if true
:End

                                                                                                                                                                            An If-Then block also has an optional Else clause, which is used to execute different code when the condition is false.

                                                                                                                                                                            :If (condition)
:Then
code to execute if true
:Else
code to execute if false
:End

                                                                                                                                                                            Advanced Uses

                                                                                                                                                                            If statements can execute and skip other If statements. This leads to odd yet effective constructs like these:

                                                                                                                                                                            :If A
:If B
//Executes if A is false or B is true

                                                                                                                                                                            If A:Then
//Executes if A is true
If B:Else
//Executes if A is false or B is false
End

                                                                                                                                                                            Memory Leaks

                                                                                                                                                                            Each time the program enters an If-Then block, the calculator uses 35+(size of the condition) bytes of memory to keep track of the block. This memory is given back to you as soon as the program reaches an End statement. This isn't really a problem unless you're low on RAM, or have a lot of nested If-Then statements. However, if you use Goto to jump out of such a statement, you lose those bytes for as long as the program is running — and if you keep doing this, you might easily run out of memory, resulting in ERR:MEMORY.

                                                                                                                                                                            Optimization

                                                                                                                                                                            As far as the TI-BASIC interpreter is concerned, a value of 0 is false, and any other value is true. We can use a numerical expression rather than a conditional one in the condition of the If statement in a case like the following:

                                                                                                                                                                            :If A≠0
:Disp "A IS NOT 0

can be
:If A
:Disp "A IS NOT 0

                                                                                                                                                                            When code in a single-line If statement simply changes a variable, it can often be replaced with an equivalent piecewise expression, which will be smaller and faster.

                                                                                                                                                                            :If A=B
:C+2→C

can be
:C+2(A=B→C

                                                                                                                                                                            Code Timings

                                                                                                                                                                            Single-line If statements are greatly slowed when they are the first line in For( loops without a closing parenthesis. For example,

                                                                                                                                                                            Very slow
:For(I,1,2000
:If 0:
:End

19 times faster (!)
:For(I,1,2000)
:If 0:
:End

                                                                                                                                                                            Error Conditions

                                                                                                                                                                            • ERR:DATA TYPE occurs if the parameter is complex, even if it's complex in a silly way like 0i.
                                                                                                                                                                            • ERR:INVALID occurs if this statement is used outside a program.
                                                                                                                                                                            • ERR:SYNTAX occurs if an If is the last statement in the program, or the last except for one empty line.

                                                                                                                                                                            Source: parts of this page were written by the following TI|BD contributors: burr, CloudVariable, DarkerLine, GoVegan, kg583, lirtosiast, Trenly.

                                                                                                                                                                            History

                                                                                                                                                                            Calculator OS Version Description
                                                                                                                                                                            TI-82 1.0 Added
                                                                                                                                                                            Property Value
                                                                                                                                                                            Hex Value $7E06
                                                                                                                                                                            Categories
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                                                                                                                                                                              • FR: Thick

                                                                                                                                                                              Thick

                                                                                                                                                                              Overview

                                                                                                                                                                              Resets all Y=editor line-style settings to Thick.

                                                                                                                                                                              Availability: Token only available from within the Basic editor.

                                                                                                                                                                              Syntax

                                                                                                                                                                              Thick

                                                                                                                                                                              Location

                                                                                                                                                                              zT, Thick

                                                                                                                                                                              Description

                                                                                                                                                                              The Thick command converts all lines in the current function type to be drawn using a 2-3 pixel wide line (hence "Thick"). This mode is the default line drawing mode. It can be called on the homescreen or in a program.

                                                                                                                                                                              :AxesOff
:GridOff
:Thick

                                                                                                                                                                              Error Conditions

                                                                                                                                                                              • ERR:SYNTAX is thrown if any character is included in the same line as the Thick command.

                                                                                                                                                                              Source: parts of this page were written by the following TI|BD contributors: Battlesquid, jonbush, kg583, MrWompWomp.

                                                                                                                                                                              History

                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                              TI-82 1.0 Connected added
                                                                                                                                                                              TI-84+CSE 4.0 Renamed Connected to Thick
                                                                                                                                                                              Property Value
                                                                                                                                                                              Hex Value $EF74
                                                                                                                                                                              Categories
                                                                                                                                                                                Localizations
                                                                                                                                                                                • FR: Fin

                                                                                                                                                                                Thin

                                                                                                                                                                                Overview

                                                                                                                                                                                Resets all Y=editor line-style settings to Thin.

                                                                                                                                                                                Availability: Token only available from within the Basic editor.

                                                                                                                                                                                Syntax

                                                                                                                                                                                Thin

                                                                                                                                                                                Location

                                                                                                                                                                                zT, Thin

                                                                                                                                                                                Description

                                                                                                                                                                                The Thin command will set all lines in the current function type to be only 1 pixel wide (hence "Thin"). The command can be run on the homescreen or within a program.

                                                                                                                                                                                :AxesOff
:GridOff
:Thin

                                                                                                                                                                                Error Conditions

                                                                                                                                                                                • ERR:SYNTAX is thrown if additional arguments are put on the command.

                                                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: Battlesquid, kg583, MrWompWomp.

                                                                                                                                                                                History

                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                TI-84+CSE 4.0 Added
                                                                                                                                                                                Property Value
                                                                                                                                                                                Hex Value $7E0F
                                                                                                                                                                                Categories
                                                                                                                                                                                Localizations
                                                                                                                                                                                • FR: f(n)

                                                                                                                                                                                Time

                                                                                                                                                                                Overview

                                                                                                                                                                                Sets sequence graphs to plot with respect to time.

                                                                                                                                                                                Availability: Token only available from within the Basic editor.

                                                                                                                                                                                Syntax

                                                                                                                                                                                Time

                                                                                                                                                                                Location

                                                                                                                                                                                2nd, format, Time

                                                                                                                                                                                Description

                                                                                                                                                                                NOTE: This article is about the Time setting for sequence graphing. If you're looking for the clock commands on the TI-84 Plus and TI-84 Plus SE, see Time and Date Commands.

                                                                                                                                                                                The Time command sets equations in sequence mode to graph as the points (n, u(n)) (for the u equation; (n, v(n)) and (n, w(n)) for the other two) - the default setting. In dot mode, only the points themselves will be plotted, but if you change the graphing style to connected line or thick line, the points will be connected.

                                                                                                                                                                                Essentially, this mode makes sequence graphs a limited version of function graphs, but with the possibility of recursion.

                                                                                                                                                                                See "Related Commands" for other possibilities of graphing sequences.

                                                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

                                                                                                                                                                                History

                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                TI-82 1.0 Added
                                                                                                                                                                                Property Value
                                                                                                                                                                                Hex Value $630F
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                                                                                                                                                                                • FR: Tmax

                                                                                                                                                                                Tmax

                                                                                                                                                                                Overview

                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                Syntax

                                                                                                                                                                                Tmax

                                                                                                                                                                                Description

                                                                                                                                                                                Examples

                                                                                                                                                                                Explanation 1

                                                                                                                                                                                code 1

                                                                                                                                                                                Explanation 2

                                                                                                                                                                                code 2

                                                                                                                                                                                Error Conditions

                                                                                                                                                                                Advanced Notes

                                                                                                                                                                                History

                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                TI-82 1.0 Added
                                                                                                                                                                                Property Value
                                                                                                                                                                                Hex Value $630E
                                                                                                                                                                                Categories
                                                                                                                                                                                Localizations
                                                                                                                                                                                • FR: Tmin

                                                                                                                                                                                Tmin

                                                                                                                                                                                Overview

                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                Syntax

                                                                                                                                                                                Tmin

                                                                                                                                                                                Description

                                                                                                                                                                                Examples

                                                                                                                                                                                Explanation 1

                                                                                                                                                                                code 1

                                                                                                                                                                                Explanation 2

                                                                                                                                                                                code 2

                                                                                                                                                                                Error Conditions

                                                                                                                                                                                Advanced Notes

                                                                                                                                                                                History

                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                TI-82 1.0 Added
                                                                                                                                                                                Property Value
                                                                                                                                                                                Hex Value $84
                                                                                                                                                                                Categories
                                                                                                                                                                                Localizations
                                                                                                                                                                                • FR: Trace

                                                                                                                                                                                Trace

                                                                                                                                                                                Overview

                                                                                                                                                                                Displays the graph and enters TRACE mode.

                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                Syntax

                                                                                                                                                                                Trace

                                                                                                                                                                                Location

                                                                                                                                                                                trace

                                                                                                                                                                                Description

                                                                                                                                                                                The Trace command displays the graph screen, and allows the user to trace any graphed equations or plots. It works in almost exactly the same way as pressing TRACE does outside a program. When the user presses ENTER, control returns to the program.

                                                                                                                                                                                When tracing, ExprOn and ExprOff affect how the currently-traced equation is displayed, and CoordOn and CoordOff affect whether the coordinates of the cursor are displayed (RectGC and PolarGC determine the type of coordinates).

                                                                                                                                                                                Since the ENTER key is already used for exiting, the Trace command lacks some of the functionality of pressing TRACE outside a program, where you can use ENTER to center the graphing window on the cursor. The independent variables X, T, θ, and n cannot by directly typed in, either - they can only be selected with the arrow buttons.

                                                                                                                                                                                Advanced Uses

                                                                                                                                                                                As a side effect, the coordinates of the last point traced are stored to X and Y (as well as R and θ, if you're in PolarGC mode, and T, θ and n depending on the graphing mode). Also, the window bounds may change if the user traces an equation past the edge of the screen.

                                                                                                                                                                                Error Conditions

                                                                                                                                                                                • ERR:INVALID is thrown if this command is used outside a program.

                                                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: b2jammer, DarkerLine, GoVegan.

                                                                                                                                                                                History

                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                TI-82 1.0 Added
                                                                                                                                                                                Property Value
                                                                                                                                                                                Hex Value $6338
                                                                                                                                                                                Categories
                                                                                                                                                                                Localizations
                                                                                                                                                                                • FR: TracePas

                                                                                                                                                                                TraceStep

                                                                                                                                                                                Overview

                                                                                                                                                                                Syntax

                                                                                                                                                                                TraceStep

                                                                                                                                                                                Description

                                                                                                                                                                                Examples

                                                                                                                                                                                Explanation 1

                                                                                                                                                                                code 1

                                                                                                                                                                                Explanation 2

                                                                                                                                                                                code 2

                                                                                                                                                                                Error Conditions

                                                                                                                                                                                Advanced Notes

                                                                                                                                                                                History

                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                TI-84+CSE 4.0 Added
                                                                                                                                                                                Property Value
                                                                                                                                                                                Hex Value $6322
                                                                                                                                                                                Categories
                                                                                                                                                                                Localizations
                                                                                                                                                                                • FR: Tstep

                                                                                                                                                                                Tstep

                                                                                                                                                                                Overview

                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                Syntax

                                                                                                                                                                                Tstep

                                                                                                                                                                                Description

                                                                                                                                                                                Examples

                                                                                                                                                                                Explanation 1

                                                                                                                                                                                code 1

                                                                                                                                                                                Explanation 2

                                                                                                                                                                                code 2

                                                                                                                                                                                Error Conditions

                                                                                                                                                                                Advanced Notes

                                                                                                                                                                                History

                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                TI-82 1.0 Added
                                                                                                                                                                                Property Value
                                                                                                                                                                                Hex Value $55
                                                                                                                                                                                Categories
                                                                                                                                                                                Localizations
                                                                                                                                                                                • FR: U

                                                                                                                                                                                U

                                                                                                                                                                                Overview

                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                Syntax

                                                                                                                                                                                U

                                                                                                                                                                                Description

                                                                                                                                                                                Examples

                                                                                                                                                                                Explanation 1

                                                                                                                                                                                code 1

                                                                                                                                                                                Explanation 2

                                                                                                                                                                                code 2

                                                                                                                                                                                Error Conditions

                                                                                                                                                                                Advanced Notes

                                                                                                                                                                                History

                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                TI-82 1.0 Added
                                                                                                                                                                                Property Value
                                                                                                                                                                                Hex Value $6306
                                                                                                                                                                                Categories
                                                                                                                                                                                Localizations
                                                                                                                                                                                • FR: U𝑛-₁

                                                                                                                                                                                U𝑛-₁

                                                                                                                                                                                Overview

                                                                                                                                                                                Syntax

                                                                                                                                                                                U𝑛-₁

                                                                                                                                                                                Description

                                                                                                                                                                                Examples

                                                                                                                                                                                Explanation 1

                                                                                                                                                                                code 1

                                                                                                                                                                                Explanation 2

                                                                                                                                                                                code 2

                                                                                                                                                                                Error Conditions

                                                                                                                                                                                Advanced Notes

                                                                                                                                                                                History

                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                TI-82 1.0 U𝑛-₁ added
                                                                                                                                                                                TI-83 0.01013 U𝑛-₁ removed
                                                                                                                                                                                TI-83 1.010 U𝑛-₁ added
                                                                                                                                                                                Property Value
                                                                                                                                                                                Hex Value $BB69
                                                                                                                                                                                Categories
                                                                                                                                                                                Localizations
                                                                                                                                                                                • FR: DésArchive

                                                                                                                                                                                UnArchive

                                                                                                                                                                                Overview

                                                                                                                                                                                Moves the specified variables from the user data archive memory to RAM.
                                                                                                                                                                                To archive variables, use Archive.

                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                Syntax

                                                                                                                                                                                UnArchive variable

                                                                                                                                                                                Arguments

                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                variable

                                                                                                                                                                                Location

                                                                                                                                                                                2nd, mem, 6:UnArchive

                                                                                                                                                                                Description

                                                                                                                                                                                The UnArchive command moves a variable from the archive (also known as ROM) to RAM. A quick synopsis of the difference between the two:

                                                                                                                                                                                • Data in the archive cannot be accessed, but it's protected from RAM clears (which may occur during battery removal if not done carefully); also, the archive can hold much more data.
                                                                                                                                                                                • Data in RAM can be accessed for calculations, but it can also be deleted during a RAM clear or accidentally overwritten by another program.

                                                                                                                                                                                It is, in general, not recommended to place real variables in the archive (since so many programs use them); also, some variables cannot be archived (see the Archive command for details). Although programs can be archived and unarchived, the Archive and UnArchive commands will not archive or unarchive programs from within a program. For the most part, lists are the only type of variable it makes sense to archive and unarchive in a program.

                                                                                                                                                                                The UnArchive command doesn't do anything if the variable in question is already in RAM. However, there is no way to test if a variable is in RAM or archive, short of trying to access it and potentially getting an error.

                                                                                                                                                                                Advanced Uses

                                                                                                                                                                                The Archive and UnArchive commands can be used in conjunction for saving data as a program exits.

                                                                                                                                                                                Optimization

                                                                                                                                                                                The SetUpEditor command is often used in place of the UnArchive command when dealing with lists, for several reasons:

                                                                                                                                                                                • using SetUpEditor will not prevent the program from working on a TI-83, like UnArchive will
                                                                                                                                                                                • SetUpEditor will create a list with length 0 if it doesn't exist; UnArchive will throw an error
                                                                                                                                                                                • SetUpEditor saves space in the program, since it can unarchive more than one list at a time, and doesn't require the little L in front

                                                                                                                                                                                Error Conditions

                                                                                                                                                                                • ERR:MEMORY is thrown if there isn't enough memory available in RAM for the variable.
                                                                                                                                                                                • ERR:VARIABLE is thrown when unarchiving a system variable or a application even if there is enough space.

                                                                                                                                                                                See Also

                                                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, nap386.

                                                                                                                                                                                History

                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                TI-83+ 0.103 Added
                                                                                                                                                                                Property Value
                                                                                                                                                                                Hex Value $EF2F
                                                                                                                                                                                Categories
                                                                                                                                                                                Localizations
                                                                                                                                                                                • FR: ᵤ

                                                                                                                                                                                ᵤ

                                                                                                                                                                                Overview

                                                                                                                                                                                Syntax

                                                                                                                                                                                ᵤ

                                                                                                                                                                                Description

                                                                                                                                                                                Examples

                                                                                                                                                                                Explanation 1

                                                                                                                                                                                code 1

                                                                                                                                                                                Explanation 2

                                                                                                                                                                                code 2

                                                                                                                                                                                Error Conditions

                                                                                                                                                                                Advanced Notes

                                                                                                                                                                                History

                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                TI-84+ 2.53 Added
                                                                                                                                                                                Property Value
                                                                                                                                                                                Hex Value $EF9F
                                                                                                                                                                                Categories
                                                                                                                                                                                Localizations
                                                                                                                                                                                • FR: Annuler effacer

                                                                                                                                                                                Undo Clear

                                                                                                                                                                                Overview

                                                                                                                                                                                Comment:CE OS 5.3+

                                                                                                                                                                                Syntax

                                                                                                                                                                                Undo Clear

                                                                                                                                                                                Description

                                                                                                                                                                                Examples

                                                                                                                                                                                Explanation 1

                                                                                                                                                                                code 1

                                                                                                                                                                                Explanation 2

                                                                                                                                                                                code 2

                                                                                                                                                                                Error Conditions

                                                                                                                                                                                Advanced Notes

                                                                                                                                                                                History

                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                TI-84+CE 5.3.0 Added
                                                                                                                                                                                Property Value
                                                                                                                                                                                Hex Value $EF3A
                                                                                                                                                                                Categories
                                                                                                                                                                                  Localizations
                                                                                                                                                                                  • FR: Un⁄d

                                                                                                                                                                                  Un⁄d

                                                                                                                                                                                  Overview

                                                                                                                                                                                  Displays results as a mixed number, if applicable.

                                                                                                                                                                                  Availability: Token available everywhere.

                                                                                                                                                                                  Syntax

                                                                                                                                                                                  Un/d

                                                                                                                                                                                  Location

                                                                                                                                                                                  math, NUMC: Un/d

                                                                                                                                                                                  Description

                                                                                                                                                                                  Un/d is a template that allows you to input a fraction with a whole number in front of it.
                                                                                                                                                                                  Un/d is accessible from most screens by pressing ALPHA and Y= then 2.
                                                                                                                                                                                  What this command does is that it adds the whole number to the fraction. It does not calculate a product but instead it calculates an addition.

                                                                                                                                                                                  Source: parts of this page were written by the following TI|BD contributors: burr, ccrh2009, DracoMhuuh.

                                                                                                                                                                                  History

                                                                                                                                                                                  Calculator OS Version Description
                                                                                                                                                                                  TI-84+ 2.53 Added
                                                                                                                                                                                  Property Value
                                                                                                                                                                                  Hex Value $6306
                                                                                                                                                                                  Categories
                                                                                                                                                                                  Localizations
                                                                                                                                                                                  • FR: U𝑛-₁

                                                                                                                                                                                  U𝑛-₁

                                                                                                                                                                                  Overview

                                                                                                                                                                                  Syntax

                                                                                                                                                                                  U𝑛-₁

                                                                                                                                                                                  Description

                                                                                                                                                                                  Examples

                                                                                                                                                                                  Explanation 1

                                                                                                                                                                                  code 1

                                                                                                                                                                                  Explanation 2

                                                                                                                                                                                  code 2

                                                                                                                                                                                  Error Conditions

                                                                                                                                                                                  Advanced Notes

                                                                                                                                                                                  History

                                                                                                                                                                                  Calculator OS Version Description
                                                                                                                                                                                  TI-82 1.0 U𝑛-₁ added
                                                                                                                                                                                  TI-83 0.01013 U𝑛-₁ removed
                                                                                                                                                                                  TI-83 1.010 U𝑛-₁ added
                                                                                                                                                                                  Property Value
                                                                                                                                                                                  Hex Value $56
                                                                                                                                                                                  Categories
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                                                                                                                                                                                  • FR: V

                                                                                                                                                                                  V

                                                                                                                                                                                  Overview

                                                                                                                                                                                  Availability: Token available everywhere.

                                                                                                                                                                                  Syntax

                                                                                                                                                                                  V

                                                                                                                                                                                  Description

                                                                                                                                                                                  Examples

                                                                                                                                                                                  Explanation 1

                                                                                                                                                                                  code 1

                                                                                                                                                                                  Explanation 2

                                                                                                                                                                                  code 2

                                                                                                                                                                                  Error Conditions

                                                                                                                                                                                  Advanced Notes

                                                                                                                                                                                  History

                                                                                                                                                                                  Calculator OS Version Description
                                                                                                                                                                                  TI-82 1.0 Added
                                                                                                                                                                                  Property Value
                                                                                                                                                                                  Hex Value $AA
                                                                                                                                                                                  Categories
                                                                                                                                                                                  Localizations
                                                                                                                                                                                  • FR: VARSTRING

                                                                                                                                                                                  VARSTRING

                                                                                                                                                                                  Overview

                                                                                                                                                                                  Syntax

                                                                                                                                                                                  VARSTRING

                                                                                                                                                                                  Description

                                                                                                                                                                                  Examples

                                                                                                                                                                                  Explanation 1

                                                                                                                                                                                  code 1

                                                                                                                                                                                  Explanation 2

                                                                                                                                                                                  code 2

                                                                                                                                                                                  Error Conditions

                                                                                                                                                                                  Advanced Notes

                                                                                                                                                                                  History

                                                                                                                                                                                  Calculator OS Version Description
                                                                                                                                                                                  Property Value
                                                                                                                                                                                  Hex Value $9D
                                                                                                                                                                                  Categories
                                                                                                                                                                                  Localizations
                                                                                                                                                                                  • FR: Verticale

                                                                                                                                                                                  Vertical

                                                                                                                                                                                  Overview

                                                                                                                                                                                  Draws a vertical line at xwith specified color and line style.
                                                                                                                                                                                  Color#: 10 - 24 or color name pasted from [vars] COLOR.
                                                                                                                                                                                  line style #: 1-4.

                                                                                                                                                                                  Availability: Token available everywhere.

                                                                                                                                                                                  Syntax

                                                                                                                                                                                  Vertical x[,color#,linestyle#]

                                                                                                                                                                                  Arguments

                                                                                                                                                                                  NameTypeOptional
                                                                                                                                                                                  x
                                                                                                                                                                                  color#colorNumYes
                                                                                                                                                                                  linestyle#integerYes

                                                                                                                                                                                  Location

                                                                                                                                                                                  2nd, draw, DRAW, 4:Vertical

                                                                                                                                                                                  Description

                                                                                                                                                                                  Vertical X draws a vertical line from the top of the graph screen to the bottom at X. Vertical is usually only used to replace a line that stretches the entire length of the graph screen, along with its counterpart Horizontal.

                                                                                                                                                                                  Vertical is affected by the window settings, unlike the Pxl- commands.

                                                                                                                                                                                  :Vertical 5

                                                                                                                                                                                  Uses on TI 84+C Version Calculators

                                                                                                                                                                                  The Vertical command takes an additional color argument for TI 84+C version calculators, as shown below:

                                                                                                                                                                                  Vertical 5,BLACK

                                                                                                                                                                                  Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583, Xphoenix.

                                                                                                                                                                                  History

                                                                                                                                                                                  Calculator OS Version Description
                                                                                                                                                                                  TI-82 1.0 Added
                                                                                                                                                                                  Property Value
                                                                                                                                                                                  Hex Value $6307
                                                                                                                                                                                  Categories
                                                                                                                                                                                  Localizations
                                                                                                                                                                                  • FR: V𝑛-₁

                                                                                                                                                                                  V𝑛-₁

                                                                                                                                                                                  Overview

                                                                                                                                                                                  Syntax

                                                                                                                                                                                  V𝑛-₁

                                                                                                                                                                                  Description

                                                                                                                                                                                  Examples

                                                                                                                                                                                  Explanation 1

                                                                                                                                                                                  code 1

                                                                                                                                                                                  Explanation 2

                                                                                                                                                                                  code 2

                                                                                                                                                                                  Error Conditions

                                                                                                                                                                                  Advanced Notes

                                                                                                                                                                                  History

                                                                                                                                                                                  Calculator OS Version Description
                                                                                                                                                                                  TI-82 1.0 V𝑛-₁ added
                                                                                                                                                                                  TI-83 0.01013 V𝑛-₁ removed
                                                                                                                                                                                  TI-83 1.010 V𝑛-₁ added
                                                                                                                                                                                  Property Value
                                                                                                                                                                                  Hex Value $6307
                                                                                                                                                                                  Categories
                                                                                                                                                                                  Localizations
                                                                                                                                                                                  • FR: V𝑛-₁

                                                                                                                                                                                  V𝑛-₁

                                                                                                                                                                                  Overview

                                                                                                                                                                                  Syntax

                                                                                                                                                                                  V𝑛-₁

                                                                                                                                                                                  Description

                                                                                                                                                                                  Examples

                                                                                                                                                                                  Explanation 1

                                                                                                                                                                                  code 1

                                                                                                                                                                                  Explanation 2

                                                                                                                                                                                  code 2

                                                                                                                                                                                  Error Conditions

                                                                                                                                                                                  Advanced Notes

                                                                                                                                                                                  History

                                                                                                                                                                                  Calculator OS Version Description
                                                                                                                                                                                  TI-82 1.0 V𝑛-₁ added
                                                                                                                                                                                  TI-83 0.01013 V𝑛-₁ removed
                                                                                                                                                                                  TI-83 1.010 V𝑛-₁ added
                                                                                                                                                                                  Property Value
                                                                                                                                                                                  Hex Value $57
                                                                                                                                                                                  Categories
                                                                                                                                                                                  Localizations
                                                                                                                                                                                  • FR: W

                                                                                                                                                                                  W

                                                                                                                                                                                  Overview

                                                                                                                                                                                  Availability: Token available everywhere.

                                                                                                                                                                                  Syntax

                                                                                                                                                                                  W

                                                                                                                                                                                  Description

                                                                                                                                                                                  Examples

                                                                                                                                                                                  Explanation 1

                                                                                                                                                                                  code 1

                                                                                                                                                                                  Explanation 2

                                                                                                                                                                                  code 2

                                                                                                                                                                                  Error Conditions

                                                                                                                                                                                  Advanced Notes

                                                                                                                                                                                  History

                                                                                                                                                                                  Calculator OS Version Description
                                                                                                                                                                                  TI-82 1.0 Added
                                                                                                                                                                                  Property Value
                                                                                                                                                                                  Hex Value $EF4B
                                                                                                                                                                                  Categories
                                                                                                                                                                                  Localizations
                                                                                                                                                                                  • FR: BLANC

                                                                                                                                                                                  WHITE

                                                                                                                                                                                  Overview

                                                                                                                                                                                  Availability: Token available everywhere.

                                                                                                                                                                                  Syntax

                                                                                                                                                                                  WHITE

                                                                                                                                                                                  Description

                                                                                                                                                                                  Examples

                                                                                                                                                                                  Explanation 1

                                                                                                                                                                                  code 1

                                                                                                                                                                                  Explanation 2

                                                                                                                                                                                  code 2

                                                                                                                                                                                  Error Conditions

                                                                                                                                                                                  Advanced Notes

                                                                                                                                                                                  History

                                                                                                                                                                                  Calculator OS Version Description
                                                                                                                                                                                  TI-84+CSE 4.0 Added
                                                                                                                                                                                  Property Value
                                                                                                                                                                                  Hex Value $EF96
                                                                                                                                                                                  Categories
                                                                                                                                                                                    Localizations
                                                                                                                                                                                    • FR: Wait

                                                                                                                                                                                    Wait

                                                                                                                                                                                    Overview

                                                                                                                                                                                    Suspends execution of a program for a given time. Maximum time is 100 seconds.

                                                                                                                                                                                    Comment:CE OS 5.2+

                                                                                                                                                                                    Availability: Token only available from within the Basic editor.

                                                                                                                                                                                    Syntax

                                                                                                                                                                                    Waittime

                                                                                                                                                                                    Arguments

                                                                                                                                                                                    NameTypeOptional
                                                                                                                                                                                    time

                                                                                                                                                                                    Location

                                                                                                                                                                                    prgm, A:Wait

                                                                                                                                                                                    Overview

                                                                                                                                                                                    Suspends execution of a program for a given time. Maximum time is 100 seconds.

                                                                                                                                                                                    Comment:CE OS 5.2+

                                                                                                                                                                                    Availability: Token only available from within the Basic editor.

                                                                                                                                                                                    Syntax

                                                                                                                                                                                    Waittime

                                                                                                                                                                                    Arguments

                                                                                                                                                                                    NameTypeOptional
                                                                                                                                                                                    time

                                                                                                                                                                                    Location

                                                                                                                                                                                    prgm, 4:Wait

                                                                                                                                                                                    Special Category

                                                                                                                                                                                    TI-Innovator™ Hub

                                                                                                                                                                                    Description

                                                                                                                                                                                    The Wait command was introduced in TI-OS 5.2 for the TI-84+CE. The Wait command tells the calculator to wait for a specified number of seconds before continuing. The specified amount of seconds can be a decimal, as it is not limited to whole numbers. This command can be useful for displaying information momentarily before proceeding in a program. The Wait command functions similarly to the Pause command, but without the extra arguments.

                                                                                                                                                                                    :Disp "WAIT FOR IT!
:Wait 4
:Disp "Surprise

                                                                                                                                                                                    Advanced Uses

                                                                                                                                                                                    The Wait command is useful for facilitating automatic linking within programs. Since the Get( and GetCalc( commands only work when the sending calculator is in a preemptible state, including a small Wait delay will allow the other calculator to receive data.

                                                                                                                                                                                    Because the Wait command is relatively new, it may be advisable to avoid using it to ensure compatibility with older operating systems. Similar functionality can be achieved with the second optional argument to the Pause command.

                                                                                                                                                                                    Optimization

                                                                                                                                                                                    Traditionally it was recommended to use either a For( loop or the rand( command to create a delay within a program. The For( loop takes more space, and the rand( command uses more memory during execution.

                                                                                                                                                                                    :rand(100
can be
:Wait 1

                                                                                                                                                                                    Error Conditions

                                                                                                                                                                                    • ERROR: INVALID is thrown if the Wait command is executed on the home screen.

                                                                                                                                                                                    Source: parts of this page were written by the following TI|BD contributors: Battlesquid, jonbush, Michael2_3B.

                                                                                                                                                                                    History

                                                                                                                                                                                    Calculator OS Version Description
                                                                                                                                                                                    TI-84+CE 5.2.0 Added
                                                                                                                                                                                    Property Value
                                                                                                                                                                                    Hex Value $7E0E
                                                                                                                                                                                    Categories
                                                                                                                                                                                    Localizations
                                                                                                                                                                                    • FR: Toile

                                                                                                                                                                                    Web

                                                                                                                                                                                    Overview

                                                                                                                                                                                    Sets sequence graphs to trace as webs.

                                                                                                                                                                                    Availability: Token only available from within the Basic editor.

                                                                                                                                                                                    Syntax

                                                                                                                                                                                    Web

                                                                                                                                                                                    Location

                                                                                                                                                                                    2nd, format, Web

                                                                                                                                                                                    Description

                                                                                                                                                                                    In Web mode, sequence equations are graphed as web diagrams. This is a way of visualizing iterations of a function (that is, the sequence n, f(n), f(f(n)), f(f(f(n))), … for some function f and starting value n). For this mode to properly work, each sequence equation should be in terms of its previous value only: u(n) should be a function of u(n-1). Referencing other sequence equations, or u(n-2), will yield ERR:INVALID; referencing the value n is allowed by the calculator, but makes the result meaningless so you should avoid it.

                                                                                                                                                                                    When you go to the graph screen, the associated function y=f(x) will be graphed. That is, if you define u(n) = cos(u(n-1)), the function y=cos(x) will be graphed. If you have AxesOn enabled, the line y=x will also be graphed. It's easy to see that the intersection points of the graphs y=f(x) and the line y=x represent the fixed points (points such that f(x)=x) of the function.

                                                                                                                                                                                    The web diagram itself will be drawn if you press TRACE or use the Trace command. First you will choose the equation (u, v, or w) to trace; then, by pressing RIGHT repeatedly, the web will be drawn, starting from the initial value _n_Min. In a web diagram, a point (n, f(n)) on the graph of y=f(x) is connected by a horizontal segment to the point (f(n), f(n)) on the graph of y=x, and then by a vertical segment to the point (f(n), f(f(n))) on the graph of y=f(x) again; this process is repeated. Each pair of a horizontal and vertical segment represents an added iteration of.

                                                                                                                                                                                    Web diagrams can be used to look at the attracting behavior of fixed points. For example:

                                                                                                                                                                                    1. Graph the equation u(n)=cos(u(n-1)), u(_n_Min)=1 in Web mode, with Xmin=0, Xmax=1, Ymin=0, Ymax=1 in the WINDOW menu. You'll see that it has a single fixed point. If you TRACE the graph, the line segments will spiral around into the fixed point, so appears to be attractive.

                                                                                                                                                                                    2. Graph the equation u(n)=π/2cos(u(n-1)), u(_n_Min)=1 in Web mode, with Xmin=0, Xmax=π/2, Ymin=0, Ymax=π/2 in the WINDOW menu. This equation looks a lot like the previous one, and also has a single fixed point. However, if you TRACE the graph, the line segments (which start out quite close to the fixed point) will spiral away from it. This intuitively shows that the fixed point of f(x)=π/2cos(x) is not attractive.

                                                                                                                                                                                    See "Related Commands" for other possibilities of graphing sequences.

                                                                                                                                                                                    Error Conditions

                                                                                                                                                                                    • ERR:INVALID is thrown if an equation being graphed references other sequence equations or the n-2 term.

                                                                                                                                                                                    Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

                                                                                                                                                                                    History

                                                                                                                                                                                    Calculator OS Version Description
                                                                                                                                                                                    TI-82 1.0 Added
                                                                                                                                                                                    Property Value
                                                                                                                                                                                    Hex Value $D1
                                                                                                                                                                                    Categories
                                                                                                                                                                                    Localizations
                                                                                                                                                                                    • FR: While

                                                                                                                                                                                    While

                                                                                                                                                                                    Overview

                                                                                                                                                                                    Executes commands while condition is true.

                                                                                                                                                                                    Availability: Token only available from within the Basic editor.

                                                                                                                                                                                    Syntax

                                                                                                                                                                                    :Whilecondition:commands :End:command

                                                                                                                                                                                    Arguments

                                                                                                                                                                                    NameTypeOptional
                                                                                                                                                                                    condition
                                                                                                                                                                                    commands
                                                                                                                                                                                    command

                                                                                                                                                                                    Location

                                                                                                                                                                                    prgm, CTL, 5:While

                                                                                                                                                                                    Description

                                                                                                                                                                                    A While loop executes a block of commands between the While and End commands as long as the specified condition is true. The condition is tested at the beginning of the loop (when the End command is encountered), so if the condition is initially false, the block of commands will never get executed. This distinguishes it from the Repeat command.

                                                                                                                                                                                    After each time the While loop is executed, the condition is checked to see if it is still true. If it is, the block of commands is executed again, otherwise the program resumes after the End statement.

                                                                                                                                                                                    Advanced Uses

                                                                                                                                                                                    When using While loops, you have to provide the code to break out of the loop (it isn't built into the loop). If there is no code that ends the loop, then you will have an infinite loop. An infinite loop just keeps executing, until you have to manually exit the loop (by pressing the ON key). In the case that you actually want an infinite loop, you can just use 1 as the condition. Because 1 is always true (based on Boolean logic), the way the calculator sees it, the condition will always be true, and the loop will never end.

                                                                                                                                                                                    :While 1
:statement(s)
:End

                                                                                                                                                                                    Each time the program enters an While block, the calculator uses 35+(size of the condition) bytes of memory to keep track of this. This memory is given back to you as soon as the program reaches End. This isn't really a problem unless you're low on RAM, or have a lot of nested While statements. However, if you use Goto to jump out of a While block, you lose those bytes for as long as the program is running — and if you keep doing this, you might easily run out of memory, resulting in ERR:MEMORY.

                                                                                                                                                                                    Optimization

                                                                                                                                                                                    Because the While and Repeat commands are so similar, either one can be used in the same situation, but using one usually results in simpler code than the other. To decide which to use, answer some simple questions about the purpose of the code.

                                                                                                                                                                                    1. Should the code inside the loop be executed at least once? (Alternatively, does the condition use some variable that we first use inside the loop?) If it should, use a Repeat loop. Otherwise, use a While loop.
                                                                                                                                                                                    2. (Only if the previous question doesn't help) Think of the condition based on which the loop keeps going. Is this condition best phrased as "run the loop as long as this is true?" If so, use a While loop. Or is it more like "run the loop until this is true?" If so, Repeat is best.

                                                                                                                                                                                    Example: we want the user to pick a number, but it has to be positive, so we'll keep asking until it is.

                                                                                                                                                                                    1. Yes, we should run the loop once. Otherwise, where will we get the number from? So, we should use the Repeat loop.
                                                                                                                                                                                    :Repeat N>0
:Prompt N
:End

                                                                                                                                                                                    Another example: we want to wait for the user to press a key.

                                                                                                                                                                                    1. We're not going to have any code in the loop, all that the loop will have is a condition. So the answer to question 1 is irrelevant.
                                                                                                                                                                                    2. We can phrase the problem as "run the loop until a key is pressed" or as "run the loop while no key is pressed." However, we have a good way of testing for the former (getKey), while the latter can only be checked with not(getKey). Therefore, it's better to use a Repeat command:
                                                                                                                                                                                    :Repeat getKey
:End

                                                                                                                                                                                    Command Timings

                                                                                                                                                                                    While and Repeat loops are identical regarding speed, so that shouldn't be a factor in deciding between them. However, For( loops are much faster at what they do, that is, at going through consecutive values for one variable. You should consider if a For( loop is more appropriate to your situation. If not, choose between a Repeat loop and a While loop.

                                                                                                                                                                                    Error Conditions

                                                                                                                                                                                    • ERR:INVALID occurs if this statement is used outside a program.

                                                                                                                                                                                    Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, eibmoz_, GoVegan, Weregoose.

                                                                                                                                                                                    History

                                                                                                                                                                                    Calculator OS Version Description
                                                                                                                                                                                    TI-82 1.0 Added
                                                                                                                                                                                    Property Value
                                                                                                                                                                                    Hex Value $58
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                                                                                                                                                                                    • FR: X

                                                                                                                                                                                    X

                                                                                                                                                                                    Overview

                                                                                                                                                                                    Availability: Token available everywhere.

                                                                                                                                                                                    Syntax

                                                                                                                                                                                    X

                                                                                                                                                                                    Description

                                                                                                                                                                                    Examples

                                                                                                                                                                                    Explanation 1

                                                                                                                                                                                    code 1

                                                                                                                                                                                    Explanation 2

                                                                                                                                                                                    code 2

                                                                                                                                                                                    Error Conditions

                                                                                                                                                                                    Advanced Notes

                                                                                                                                                                                    History

                                                                                                                                                                                    Calculator OS Version Description
                                                                                                                                                                                    TI-82 1.0 Added
                                                                                                                                                                                    Property Value
                                                                                                                                                                                    Hex Value $6328
                                                                                                                                                                                    Categories
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                                                                                                                                                                                    • FR: XFact

                                                                                                                                                                                    XFact

                                                                                                                                                                                    Overview

                                                                                                                                                                                    Syntax

                                                                                                                                                                                    XFact

                                                                                                                                                                                    Description

                                                                                                                                                                                    Examples

                                                                                                                                                                                    Explanation 1

                                                                                                                                                                                    code 1

                                                                                                                                                                                    Explanation 2

                                                                                                                                                                                    code 2

                                                                                                                                                                                    Error Conditions

                                                                                                                                                                                    Advanced Notes

                                                                                                                                                                                    History

                                                                                                                                                                                    Calculator OS Version Description
                                                                                                                                                                                    TI-82 1.0 Added
                                                                                                                                                                                    Property Value
                                                                                                                                                                                    Hex Value $630B
                                                                                                                                                                                    Categories
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                                                                                                                                                                                    • FR: Xmax

                                                                                                                                                                                    Xmax

                                                                                                                                                                                    Overview

                                                                                                                                                                                    Availability: Token available everywhere.

                                                                                                                                                                                    Syntax

                                                                                                                                                                                    Xmax

                                                                                                                                                                                    Description

                                                                                                                                                                                    Examples

                                                                                                                                                                                    Explanation 1

                                                                                                                                                                                    code 1

                                                                                                                                                                                    Explanation 2

                                                                                                                                                                                    code 2

                                                                                                                                                                                    Error Conditions

                                                                                                                                                                                    Advanced Notes

                                                                                                                                                                                    History

                                                                                                                                                                                    Calculator OS Version Description
                                                                                                                                                                                    TI-82 1.0 Added
                                                                                                                                                                                    Property Value
                                                                                                                                                                                    Hex Value $630A
                                                                                                                                                                                    Categories
                                                                                                                                                                                    Localizations
                                                                                                                                                                                    • FR: Xmin

                                                                                                                                                                                    Xmin

                                                                                                                                                                                    Overview

                                                                                                                                                                                    Availability: Token available everywhere.

                                                                                                                                                                                    Syntax

                                                                                                                                                                                    Xmin

                                                                                                                                                                                    Description

                                                                                                                                                                                    Examples

                                                                                                                                                                                    Explanation 1

                                                                                                                                                                                    code 1

                                                                                                                                                                                    Explanation 2

                                                                                                                                                                                    code 2

                                                                                                                                                                                    Error Conditions

                                                                                                                                                                                    Advanced Notes

                                                                                                                                                                                    History

                                                                                                                                                                                    Calculator OS Version Description
                                                                                                                                                                                    TI-82 1.0 Added
                                                                                                                                                                                    Property Value
                                                                                                                                                                                    Hex Value $6336
                                                                                                                                                                                    Categories
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                                                                                                                                                                                    • FR: Xres

                                                                                                                                                                                    Xres

                                                                                                                                                                                    Overview

                                                                                                                                                                                    Syntax

                                                                                                                                                                                    Xres

                                                                                                                                                                                    Description

                                                                                                                                                                                    Examples

                                                                                                                                                                                    Explanation 1

                                                                                                                                                                                    code 1

                                                                                                                                                                                    Explanation 2

                                                                                                                                                                                    code 2

                                                                                                                                                                                    Error Conditions

                                                                                                                                                                                    Advanced Notes

                                                                                                                                                                                    History

                                                                                                                                                                                    Calculator OS Version Description
                                                                                                                                                                                    TI-83 0.01013 Added
                                                                                                                                                                                    Property Value
                                                                                                                                                                                    Hex Value $6302
                                                                                                                                                                                    Categories
                                                                                                                                                                                    Localizations
                                                                                                                                                                                    • FR: Xscl

                                                                                                                                                                                    Xscl

                                                                                                                                                                                    Overview

                                                                                                                                                                                    Availability: Token available everywhere.

                                                                                                                                                                                    Syntax

                                                                                                                                                                                    Xscl

                                                                                                                                                                                    Description

                                                                                                                                                                                    Examples

                                                                                                                                                                                    Explanation 1

                                                                                                                                                                                    code 1

                                                                                                                                                                                    Explanation 2

                                                                                                                                                                                    code 2

                                                                                                                                                                                    Error Conditions

                                                                                                                                                                                    Advanced Notes

                                                                                                                                                                                    History

                                                                                                                                                                                    Calculator OS Version Description
                                                                                                                                                                                    TI-82 1.0 Added
                                                                                                                                                                                    Property Value
                                                                                                                                                                                    Hex Value $5E20
                                                                                                                                                                                    Categories
                                                                                                                                                                                    Localizations
                                                                                                                                                                                    • FR: X₁ᴛ

                                                                                                                                                                                    X₁ᴛ

                                                                                                                                                                                    Overview

                                                                                                                                                                                    Syntax

                                                                                                                                                                                    X₁ᴛ

                                                                                                                                                                                    Description

                                                                                                                                                                                    Examples

                                                                                                                                                                                    Explanation 1

                                                                                                                                                                                    code 1

                                                                                                                                                                                    Explanation 2

                                                                                                                                                                                    code 2

                                                                                                                                                                                    Error Conditions

                                                                                                                                                                                    Advanced Notes

                                                                                                                                                                                    History

                                                                                                                                                                                    Calculator OS Version Description
                                                                                                                                                                                    TI-82 1.0 Added
                                                                                                                                                                                    Property Value
                                                                                                                                                                                    Hex Value $5E22
                                                                                                                                                                                    Categories
                                                                                                                                                                                    Localizations
                                                                                                                                                                                    • FR: X₂ᴛ

                                                                                                                                                                                    X₂ᴛ

                                                                                                                                                                                    Overview

                                                                                                                                                                                    Syntax

                                                                                                                                                                                    X₂ᴛ

                                                                                                                                                                                    Description

                                                                                                                                                                                    Examples

                                                                                                                                                                                    Explanation 1

                                                                                                                                                                                    code 1

                                                                                                                                                                                    Explanation 2

                                                                                                                                                                                    code 2

                                                                                                                                                                                    Error Conditions

                                                                                                                                                                                    Advanced Notes

                                                                                                                                                                                    History

                                                                                                                                                                                    Calculator OS Version Description
                                                                                                                                                                                    TI-82 1.0 Added
                                                                                                                                                                                    Property Value
                                                                                                                                                                                    Hex Value $5E24
                                                                                                                                                                                    Categories
                                                                                                                                                                                    Localizations
                                                                                                                                                                                    • FR: X₃ᴛ

                                                                                                                                                                                    X₃ᴛ

                                                                                                                                                                                    Overview

                                                                                                                                                                                    Syntax

                                                                                                                                                                                    X₃ᴛ

                                                                                                                                                                                    Description

                                                                                                                                                                                    Examples

                                                                                                                                                                                    Explanation 1

                                                                                                                                                                                    code 1

                                                                                                                                                                                    Explanation 2

                                                                                                                                                                                    code 2

                                                                                                                                                                                    Error Conditions

                                                                                                                                                                                    Advanced Notes

                                                                                                                                                                                    History

                                                                                                                                                                                    Calculator OS Version Description
                                                                                                                                                                                    TI-82 1.0 Added
                                                                                                                                                                                    Property Value
                                                                                                                                                                                    Hex Value $5E26
                                                                                                                                                                                    Categories
                                                                                                                                                                                    Localizations
                                                                                                                                                                                    • FR: X₄ᴛ

                                                                                                                                                                                    X₄ᴛ

                                                                                                                                                                                    Overview

                                                                                                                                                                                    Syntax

                                                                                                                                                                                    X₄ᴛ

                                                                                                                                                                                    Description

                                                                                                                                                                                    Examples

                                                                                                                                                                                    Explanation 1

                                                                                                                                                                                    code 1

                                                                                                                                                                                    Explanation 2

                                                                                                                                                                                    code 2

                                                                                                                                                                                    Error Conditions

                                                                                                                                                                                    Advanced Notes

                                                                                                                                                                                    History

                                                                                                                                                                                    Calculator OS Version Description
                                                                                                                                                                                    TI-82 1.0 Added
                                                                                                                                                                                    Property Value
                                                                                                                                                                                    Hex Value $5E28
                                                                                                                                                                                    Categories
                                                                                                                                                                                    Localizations
                                                                                                                                                                                    • FR: X₅ᴛ

                                                                                                                                                                                    X₅ᴛ

                                                                                                                                                                                    Overview

                                                                                                                                                                                    Syntax

                                                                                                                                                                                    X₅ᴛ

                                                                                                                                                                                    Description

                                                                                                                                                                                    Examples

                                                                                                                                                                                    Explanation 1

                                                                                                                                                                                    code 1

                                                                                                                                                                                    Explanation 2

                                                                                                                                                                                    code 2

                                                                                                                                                                                    Error Conditions

                                                                                                                                                                                    Advanced Notes

                                                                                                                                                                                    History

                                                                                                                                                                                    Calculator OS Version Description
                                                                                                                                                                                    TI-82 1.0 Added
                                                                                                                                                                                    Property Value
                                                                                                                                                                                    Hex Value $5E2A
                                                                                                                                                                                    Categories
                                                                                                                                                                                    Localizations
                                                                                                                                                                                    • FR: X₆ᴛ

                                                                                                                                                                                    X₆ᴛ

                                                                                                                                                                                    Overview

                                                                                                                                                                                    Syntax

                                                                                                                                                                                    X₆ᴛ

                                                                                                                                                                                    Description

                                                                                                                                                                                    Examples

                                                                                                                                                                                    Explanation 1

                                                                                                                                                                                    code 1

                                                                                                                                                                                    Explanation 2

                                                                                                                                                                                    code 2

                                                                                                                                                                                    Error Conditions

                                                                                                                                                                                    Advanced Notes

                                                                                                                                                                                    History

                                                                                                                                                                                    Calculator OS Version Description
                                                                                                                                                                                    TI-82 1.0 Added
                                                                                                                                                                                    Property Value
                                                                                                                                                                                    Hex Value $59
                                                                                                                                                                                    Categories
                                                                                                                                                                                    Localizations
                                                                                                                                                                                    • FR: Y

                                                                                                                                                                                    Y

                                                                                                                                                                                    Overview

                                                                                                                                                                                    Availability: Token available everywhere.

                                                                                                                                                                                    Syntax

                                                                                                                                                                                    Y

                                                                                                                                                                                    Description

                                                                                                                                                                                    Examples

                                                                                                                                                                                    Explanation 1

                                                                                                                                                                                    code 1

                                                                                                                                                                                    Explanation 2

                                                                                                                                                                                    code 2

                                                                                                                                                                                    Error Conditions

                                                                                                                                                                                    Advanced Notes

                                                                                                                                                                                    History

                                                                                                                                                                                    Calculator OS Version Description
                                                                                                                                                                                    TI-82 1.0 Added
                                                                                                                                                                                    Property Value
                                                                                                                                                                                    Hex Value $EF4A
                                                                                                                                                                                    Categories
                                                                                                                                                                                    Localizations
                                                                                                                                                                                    • FR: JAUNE

                                                                                                                                                                                    YELLOW

                                                                                                                                                                                    Overview

                                                                                                                                                                                    Availability: Token available everywhere.

                                                                                                                                                                                    Syntax

                                                                                                                                                                                    YELLOW

                                                                                                                                                                                    Description

                                                                                                                                                                                    Examples

                                                                                                                                                                                    Explanation 1

                                                                                                                                                                                    code 1

                                                                                                                                                                                    Explanation 2

                                                                                                                                                                                    code 2

                                                                                                                                                                                    Error Conditions

                                                                                                                                                                                    Advanced Notes

                                                                                                                                                                                    History

                                                                                                                                                                                    Calculator OS Version Description
                                                                                                                                                                                    TI-84+CSE 4.0 Added
                                                                                                                                                                                    Property Value
                                                                                                                                                                                    Hex Value $6329
                                                                                                                                                                                    Categories
                                                                                                                                                                                    Localizations
                                                                                                                                                                                    • FR: YFact

                                                                                                                                                                                    YFact

                                                                                                                                                                                    Overview

                                                                                                                                                                                    Syntax

                                                                                                                                                                                    YFact

                                                                                                                                                                                    Description

                                                                                                                                                                                    Examples

                                                                                                                                                                                    Explanation 1

                                                                                                                                                                                    code 1

                                                                                                                                                                                    Explanation 2

                                                                                                                                                                                    code 2

                                                                                                                                                                                    Error Conditions

                                                                                                                                                                                    Advanced Notes

                                                                                                                                                                                    History

                                                                                                                                                                                    Calculator OS Version Description
                                                                                                                                                                                    TI-82 1.0 Added
                                                                                                                                                                                    Property Value
                                                                                                                                                                                    Hex Value $630D
                                                                                                                                                                                    Categories
                                                                                                                                                                                    Localizations
                                                                                                                                                                                    • FR: Ymax

                                                                                                                                                                                    Ymax

                                                                                                                                                                                    Overview

                                                                                                                                                                                    Availability: Token available everywhere.

                                                                                                                                                                                    Syntax

                                                                                                                                                                                    Ymax

                                                                                                                                                                                    Description

                                                                                                                                                                                    Examples

                                                                                                                                                                                    Explanation 1

                                                                                                                                                                                    code 1

                                                                                                                                                                                    Explanation 2

                                                                                                                                                                                    code 2

                                                                                                                                                                                    Error Conditions

                                                                                                                                                                                    Advanced Notes

                                                                                                                                                                                    History

                                                                                                                                                                                    Calculator OS Version Description
                                                                                                                                                                                    TI-82 1.0 Added
                                                                                                                                                                                    Property Value
                                                                                                                                                                                    Hex Value $630C
                                                                                                                                                                                    Categories
                                                                                                                                                                                    Localizations
                                                                                                                                                                                    • FR: Ymin

                                                                                                                                                                                    Ymin

                                                                                                                                                                                    Overview

                                                                                                                                                                                    Availability: Token available everywhere.

                                                                                                                                                                                    Syntax

                                                                                                                                                                                    Ymin

                                                                                                                                                                                    Description

                                                                                                                                                                                    Examples

                                                                                                                                                                                    Explanation 1

                                                                                                                                                                                    code 1

                                                                                                                                                                                    Explanation 2

                                                                                                                                                                                    code 2

                                                                                                                                                                                    Error Conditions

                                                                                                                                                                                    Advanced Notes

                                                                                                                                                                                    History

                                                                                                                                                                                    Calculator OS Version Description
                                                                                                                                                                                    TI-82 1.0 Added
                                                                                                                                                                                    Property Value
                                                                                                                                                                                    Hex Value $6303
                                                                                                                                                                                    Categories
                                                                                                                                                                                    Localizations
                                                                                                                                                                                    • FR: Yscl

                                                                                                                                                                                    Yscl

                                                                                                                                                                                    Overview

                                                                                                                                                                                    Availability: Token available everywhere.

                                                                                                                                                                                    Syntax

                                                                                                                                                                                    Yscl

                                                                                                                                                                                    Description

                                                                                                                                                                                    Examples

                                                                                                                                                                                    Explanation 1

                                                                                                                                                                                    code 1

                                                                                                                                                                                    Explanation 2

                                                                                                                                                                                    code 2

                                                                                                                                                                                    Error Conditions

                                                                                                                                                                                    Advanced Notes

                                                                                                                                                                                    History

                                                                                                                                                                                    Calculator OS Version Description
                                                                                                                                                                                    TI-82 1.0 Added
                                                                                                                                                                                    Property Value
                                                                                                                                                                                    Hex Value $5E19
                                                                                                                                                                                    Categories
                                                                                                                                                                                    Localizations
                                                                                                                                                                                    • FR: Y₀

                                                                                                                                                                                    Y₀

                                                                                                                                                                                    Overview

                                                                                                                                                                                    Syntax

                                                                                                                                                                                    Y₀

                                                                                                                                                                                    Description

                                                                                                                                                                                    Examples

                                                                                                                                                                                    Explanation 1

                                                                                                                                                                                    code 1

                                                                                                                                                                                    Explanation 2

                                                                                                                                                                                    code 2

                                                                                                                                                                                    Error Conditions

                                                                                                                                                                                    Advanced Notes

                                                                                                                                                                                    History

                                                                                                                                                                                    Calculator OS Version Description
                                                                                                                                                                                    TI-82 1.0 Added
                                                                                                                                                                                    Property Value
                                                                                                                                                                                    Hex Value $5E10
                                                                                                                                                                                    Categories
                                                                                                                                                                                    Localizations
                                                                                                                                                                                    • FR: Y₁

                                                                                                                                                                                    Y₁

                                                                                                                                                                                    Overview

                                                                                                                                                                                    Syntax

                                                                                                                                                                                    Y₁

                                                                                                                                                                                    Description

                                                                                                                                                                                    Examples

                                                                                                                                                                                    Explanation 1

                                                                                                                                                                                    code 1

                                                                                                                                                                                    Explanation 2

                                                                                                                                                                                    code 2

                                                                                                                                                                                    Error Conditions

                                                                                                                                                                                    Advanced Notes

                                                                                                                                                                                    History

                                                                                                                                                                                    Calculator OS Version Description
                                                                                                                                                                                    TI-82 1.0 Added
                                                                                                                                                                                    Property Value
                                                                                                                                                                                    Hex Value $5E21
                                                                                                                                                                                    Categories
                                                                                                                                                                                    Localizations
                                                                                                                                                                                    • FR: Y₁ᴛ

                                                                                                                                                                                    Y₁ᴛ

                                                                                                                                                                                    Overview

                                                                                                                                                                                    Syntax

                                                                                                                                                                                    Y₁ᴛ

                                                                                                                                                                                    Description

                                                                                                                                                                                    Examples

                                                                                                                                                                                    Explanation 1

                                                                                                                                                                                    code 1

                                                                                                                                                                                    Explanation 2

                                                                                                                                                                                    code 2

                                                                                                                                                                                    Error Conditions

                                                                                                                                                                                    Advanced Notes

                                                                                                                                                                                    History

                                                                                                                                                                                    Calculator OS Version Description
                                                                                                                                                                                    TI-82 1.0 Added
                                                                                                                                                                                    Property Value
                                                                                                                                                                                    Hex Value $5E11
                                                                                                                                                                                    Categories
                                                                                                                                                                                    Localizations
                                                                                                                                                                                    • FR: Y₂

                                                                                                                                                                                    Y₂

                                                                                                                                                                                    Overview

                                                                                                                                                                                    Syntax

                                                                                                                                                                                    Y₂

                                                                                                                                                                                    Description

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                                                                                                                                                                                    Explanation 1

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                                                                                                                                                                                    Explanation 2

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                                                                                                                                                                                    History

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                                                                                                                                                                                    • FR: Y₂ᴛ

                                                                                                                                                                                    Y₂ᴛ

                                                                                                                                                                                    Overview

                                                                                                                                                                                    Syntax

                                                                                                                                                                                    Y₂ᴛ

                                                                                                                                                                                    Description

                                                                                                                                                                                    Examples

                                                                                                                                                                                    Explanation 1

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                                                                                                                                                                                    Explanation 2

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                                                                                                                                                                                    Advanced Notes

                                                                                                                                                                                    History

                                                                                                                                                                                    Calculator OS Version Description
                                                                                                                                                                                    TI-82 1.0 Added
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                                                                                                                                                                                    • FR: Y₃

                                                                                                                                                                                    Y₃

                                                                                                                                                                                    Overview

                                                                                                                                                                                    Syntax

                                                                                                                                                                                    Y₃

                                                                                                                                                                                    Description

                                                                                                                                                                                    Examples

                                                                                                                                                                                    Explanation 1

                                                                                                                                                                                    code 1

                                                                                                                                                                                    Explanation 2

                                                                                                                                                                                    code 2

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                                                                                                                                                                                    Advanced Notes

                                                                                                                                                                                    History

                                                                                                                                                                                    Calculator OS Version Description
                                                                                                                                                                                    TI-82 1.0 Added
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                                                                                                                                                                                    • FR: Y₃ᴛ

                                                                                                                                                                                    Y₃ᴛ

                                                                                                                                                                                    Overview

                                                                                                                                                                                    Syntax

                                                                                                                                                                                    Y₃ᴛ

                                                                                                                                                                                    Description

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                                                                                                                                                                                    Explanation 1

                                                                                                                                                                                    code 1

                                                                                                                                                                                    Explanation 2

                                                                                                                                                                                    code 2

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                                                                                                                                                                                    History

                                                                                                                                                                                    Calculator OS Version Description
                                                                                                                                                                                    TI-82 1.0 Added
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                                                                                                                                                                                    • FR: Y₄

                                                                                                                                                                                    Y₄

                                                                                                                                                                                    Overview

                                                                                                                                                                                    Syntax

                                                                                                                                                                                    Y₄

                                                                                                                                                                                    Description

                                                                                                                                                                                    Examples

                                                                                                                                                                                    Explanation 1

                                                                                                                                                                                    code 1

                                                                                                                                                                                    Explanation 2

                                                                                                                                                                                    code 2

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                                                                                                                                                                                    Advanced Notes

                                                                                                                                                                                    History

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                                                                                                                                                                                    • FR: Y₄ᴛ

                                                                                                                                                                                    Y₄ᴛ

                                                                                                                                                                                    Overview

                                                                                                                                                                                    Syntax

                                                                                                                                                                                    Y₄ᴛ

                                                                                                                                                                                    Description

                                                                                                                                                                                    Examples

                                                                                                                                                                                    Explanation 1

                                                                                                                                                                                    code 1

                                                                                                                                                                                    Explanation 2

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                                                                                                                                                                                    Advanced Notes

                                                                                                                                                                                    History

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                                                                                                                                                                                    • FR: Y₅

                                                                                                                                                                                    Y₅

                                                                                                                                                                                    Overview

                                                                                                                                                                                    Syntax

                                                                                                                                                                                    Y₅

                                                                                                                                                                                    Description

                                                                                                                                                                                    Examples

                                                                                                                                                                                    Explanation 1

                                                                                                                                                                                    code 1

                                                                                                                                                                                    Explanation 2

                                                                                                                                                                                    code 2

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                                                                                                                                                                                    Advanced Notes

                                                                                                                                                                                    History

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                                                                                                                                                                                    • FR: Y₅ᴛ

                                                                                                                                                                                    Y₅ᴛ

                                                                                                                                                                                    Overview

                                                                                                                                                                                    Syntax

                                                                                                                                                                                    Y₅ᴛ

                                                                                                                                                                                    Description

                                                                                                                                                                                    Examples

                                                                                                                                                                                    Explanation 1

                                                                                                                                                                                    code 1

                                                                                                                                                                                    Explanation 2

                                                                                                                                                                                    code 2

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                                                                                                                                                                                    History

                                                                                                                                                                                    Calculator OS Version Description
                                                                                                                                                                                    TI-82 1.0 Added
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                                                                                                                                                                                    Hex Value $5E15
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                                                                                                                                                                                    • FR: Y₆

                                                                                                                                                                                    Y₆

                                                                                                                                                                                    Overview

                                                                                                                                                                                    Syntax

                                                                                                                                                                                    Y₆

                                                                                                                                                                                    Description

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                                                                                                                                                                                    Explanation 1

                                                                                                                                                                                    code 1

                                                                                                                                                                                    Explanation 2

                                                                                                                                                                                    code 2

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                                                                                                                                                                                    Advanced Notes

                                                                                                                                                                                    History

                                                                                                                                                                                    Calculator OS Version Description
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                                                                                                                                                                                    • FR: Y₆ᴛ

                                                                                                                                                                                    Y₆ᴛ

                                                                                                                                                                                    Overview

                                                                                                                                                                                    Syntax

                                                                                                                                                                                    Y₆ᴛ

                                                                                                                                                                                    Description

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                                                                                                                                                                                    Explanation 1

                                                                                                                                                                                    code 1

                                                                                                                                                                                    Explanation 2

                                                                                                                                                                                    code 2

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                                                                                                                                                                                    History

                                                                                                                                                                                    Calculator OS Version Description
                                                                                                                                                                                    TI-82 1.0 Added
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                                                                                                                                                                                    Hex Value $5E16
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                                                                                                                                                                                    • FR: Y₇

                                                                                                                                                                                    Y₇

                                                                                                                                                                                    Overview

                                                                                                                                                                                    Syntax

                                                                                                                                                                                    Y₇

                                                                                                                                                                                    Description

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                                                                                                                                                                                    Explanation 1

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                                                                                                                                                                                    Explanation 2

                                                                                                                                                                                    code 2

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                                                                                                                                                                                    Advanced Notes

                                                                                                                                                                                    History

                                                                                                                                                                                    Calculator OS Version Description
                                                                                                                                                                                    TI-82 1.0 Added
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                                                                                                                                                                                    Hex Value $5E17
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                                                                                                                                                                                    • FR: Y₈

                                                                                                                                                                                    Y₈

                                                                                                                                                                                    Overview

                                                                                                                                                                                    Syntax

                                                                                                                                                                                    Y₈

                                                                                                                                                                                    Description

                                                                                                                                                                                    Examples

                                                                                                                                                                                    Explanation 1

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                                                                                                                                                                                    Explanation 2

                                                                                                                                                                                    code 2

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                                                                                                                                                                                    History

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                                                                                                                                                                                    • FR: Y₉

                                                                                                                                                                                    Y₉

                                                                                                                                                                                    Overview

                                                                                                                                                                                    Syntax

                                                                                                                                                                                    Y₉

                                                                                                                                                                                    Description

                                                                                                                                                                                    Examples

                                                                                                                                                                                    Explanation 1

                                                                                                                                                                                    code 1

                                                                                                                                                                                    Explanation 2

                                                                                                                                                                                    code 2

                                                                                                                                                                                    Error Conditions

                                                                                                                                                                                    Advanced Notes

                                                                                                                                                                                    History

                                                                                                                                                                                    Calculator OS Version Description
                                                                                                                                                                                    TI-82 1.0 Added
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                                                                                                                                                                                    • FR: Z-Test(

                                                                                                                                                                                    Z-Test(

                                                                                                                                                                                    Overview

                                                                                                                                                                                    Performs a z test with frequency freqlist. alternative= -1 is <; alternative=0 is ≠; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results.
                                                                                                                                                                                    Color#: 10 - 24 or color name pasted from [vars] COLOR.

                                                                                                                                                                                    Comment:Data list input

                                                                                                                                                                                    Availability: Token only available from within the Basic editor.

                                                                                                                                                                                    Syntax

                                                                                                                                                                                    Z-Test(μ0,σ[,listname,freqlist,alternative,drawflag,color#])

                                                                                                                                                                                    Arguments

                                                                                                                                                                                    NameTypeOptional
                                                                                                                                                                                    μ
                                                                                                                                                                                    0
                                                                                                                                                                                    σ
                                                                                                                                                                                    listnamelist
                                                                                                                                                                                    freqlistlist
                                                                                                                                                                                    alternative
                                                                                                                                                                                    drawflag
                                                                                                                                                                                    color#colorNum

                                                                                                                                                                                    Location

                                                                                                                                                                                    stat, TESTS, 1:Z-Test(

                                                                                                                                                                                    Overview

                                                                                                                                                                                    Performs a z test. alternative=-1 is <; alternative=0 is ≠; alternative=1 is >. drawflag=1 draws results; drawflag=0 calculates results.
                                                                                                                                                                                    Color#: 10 - 24 or color name pasted from [vars] COLOR.

                                                                                                                                                                                    Comment:Summary stats input

                                                                                                                                                                                    Availability: Token only available from within the Basic editor.

                                                                                                                                                                                    Syntax

                                                                                                                                                                                    Z-Test(μ0,σ,x̄,n[,alternative,drawflag,color#])

                                                                                                                                                                                    Arguments

                                                                                                                                                                                    NameTypeOptional
                                                                                                                                                                                    μ
                                                                                                                                                                                    0
                                                                                                                                                                                    σ
                                                                                                                                                                                    x̄Yes
                                                                                                                                                                                    nYes
                                                                                                                                                                                    alternativeYes
                                                                                                                                                                                    drawflagYes
                                                                                                                                                                                    color#colorNumYes

                                                                                                                                                                                    Location

                                                                                                                                                                                    stat, TESTS, 1:Z-Test(

                                                                                                                                                                                    Description

                                                                                                                                                                                    Z-Test( performs a z significance test of a null hypothesis you supply. This test is valid for simple random samples from a population with a known standard deviation. In addition, either the population must be normally distributed, or the sample size has to be sufficiently large.

                                                                                                                                                                                    The logic behind a Z-Test is as follows: we want to test the hypothesis that the true mean of a population is a certain value (μ0). To do this, we assume that this "null hypothesis" is true, and calculate the probability that the variation from this mean occurred, under this assumption. If this probability is sufficiently low (usually, 5% is the cutoff point), we conclude that since it's so unlikely that the data could have occurred under the null hypothesis, the null hypothesis must be false, and therefore the true mean μ is not equal to μ0. If, on the other hand, the probability is not too low, we conclude that the data may well have occurred under the null hypothesis, and therefore there's no reason to reject it.

                                                                                                                                                                                    In addition to the null hypothesis, we must have an alternative hypothesis as well - usually this is simply that the true mean is not μ0. However, in certain cases when we have reason to suspect the true mean is less than or greater than μ0, we might use a "one-sided" alternative hypothesis, which will state that the true mean μ<μ0 or that μ>μ0.

                                                                                                                                                                                    As for the Z-Test( command itself, there are two ways of calling it: you may give it a list of all the sample data, or the necessary statistics about the list - its size, and the mean. In either case, you can indicate what the alternate hypothesis is, by a value of 0, -1, or 1 for the alternative argument. 0 indicates a two-sided hypothesis of μ≠μ0, -1 indicates μ<μ0, and 1 indicates μ>μ0.

                                                                                                                                                                                    Although you can access the Z-Test( command on the home screen, via the catalog, there's no need: the Z-Test… interactive solver, found in the statistics menu, is much more intuitive to use - you don't have to memorize the syntax.

                                                                                                                                                                                    In either case, it's important to understand the output of Z-Test. Here are the meanings of each line:

                                                                                                                                                                                    • The first line, involving μ, is the alternative hypothesis.
                                                                                                                                                                                    • z is the test statistic, the standardized difference between the sample mean and μ0. If the null hypothesis is true, it should be close to 0.
                                                                                                                                                                                    • p is the probability that the difference between the sample mean and μ0 would occur if the null hypothesis is true. When the value is sufficiently small, we reject the null hypothesis and conclude that the alternative hypothesis is true. You should have a cutoff value ready, such as 5% or 1%. If p is lower, you "reject the null hypothesis on a 5% (or 1%) level" in technical terms.
                                                                                                                                                                                    • x-bar is the sample mean.
                                                                                                                                                                                    • Sx is the sample standard deviation. This isn't actually used in any calculations, and will only be shown for data list input.
                                                                                                                                                                                    • n is the sample size.

                                                                                                                                                                                    Sample Problem

                                                                                                                                                                                    According to M&M's advertising, each standard-size bag of M&M's contains an average of 10 blue M&M's with a standard deviation of 2 M&M's. You think that this estimate is low, and that the true average is higher. You decide to test this hypothesis by buying thirty bags of M&M's. You count the number of blue M&M's in each, and store this number to L1.

                                                                                                                                                                                    The value of μ0 is 10, because you want to test the null hypothesis that there are on average 10 blue M&M's per bag. The value of σ is 2. We want to test the values in L1. Because we want to test if there's actually more than 10 blue M&M's per bag, we have a one-sided alternate hypothesis: μ>μ0, which corresponds to an argument of 1. To solve the problem, you'd use this code:

                                                                                                                                                                                    :Z-Test(10,2,L1,1

                                                                                                                                                                                    Alternatively, you could calculate the mean and sample size of your sample, and put those into the command instead. The sample size is 30; let's suppose that the mean was 11.2. The code you'd use is:

                                                                                                                                                                                    :Z-Test(10,2,11.2,30,1

                                                                                                                                                                                    You will see the following output:

                                                                                                                                                                                    Z-Test
 μ>10
 z=3.286335345
 p=5.0755973e-4
 x=11.2
 n=30

                                                                                                                                                                                    The most important part of this output is "p=5.0755973e-4". This value of p is much smaller than 1% or 0.01; it's in fact around 0.0005. This is significant on the 1% level, so we reject the null hypothesis and conclude that the alternative hypothesis is true: μ>10, that is, the average number of blue M&M's in a bag is more than 10.

                                                                                                                                                                                    Advanced Uses

                                                                                                                                                                                    The final argument of Z-Test(, draw?, will display the results in a graphical manner if you put in "1" for it. The calculator will draw the standard normal curve, and shade the area of the graph beyound the z statistic. In addition, the value of z and the value of p will be displayed (the value of p corresponds to the shaded area). You would make your conclusions in the same way as for the regular output.

                                                                                                                                                                                    As with most other statistical commands, you may use a frequency list in your input (when using the data list syntax).

                                                                                                                                                                                    Optimization

                                                                                                                                                                                    Most of the arguments of the Z-Test( command have default values, and the argument can be omitted if this value is accepted.

                                                                                                                                                                                    • The draw? argument can be omitted if you don't want graphical output, although you could put "0" in as well.
                                                                                                                                                                                    • If the draw? argument is omitted, you can omit the alternative argument to use a two-sided test (μ≠μ0). If you include the draw? argument, you have to include this - otherwise there will be confusion as to what the 5th argument means.
                                                                                                                                                                                    • With data list input, you can always omit the frequency list if you won't be using it.
                                                                                                                                                                                    • With data list input, if the draw? and alternative arguments are omitted, and your data is in L1, you may omit L1 as well. However, if alternative or draw? is present, you have to include it, or else the syntax may be confused with the syntax for summary stats input.

                                                                                                                                                                                    The code in the sample problem above can't be optimized, because the alternative argument is 1:

                                                                                                                                                                                    ::Z-Test(10,2,L1,1

                                                                                                                                                                                    However, if we were doing a two-sided test, we could omit the alternative and the list arguments (since we're testing L1):

                                                                                                                                                                                    :Z-Test(10,2,L1,0
can be
:Z-Test(10,2

                                                                                                                                                                                    Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

                                                                                                                                                                                    History

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                                                                                                                                                                                    • FR: Z

                                                                                                                                                                                    Z

                                                                                                                                                                                    Overview

                                                                                                                                                                                    Availability: Token available everywhere.

                                                                                                                                                                                    Syntax

                                                                                                                                                                                    Z

                                                                                                                                                                                    Description

                                                                                                                                                                                    Examples

                                                                                                                                                                                    Explanation 1

                                                                                                                                                                                    code 1

                                                                                                                                                                                    Explanation 2

                                                                                                                                                                                    code 2

                                                                                                                                                                                    Error Conditions

                                                                                                                                                                                    Advanced Notes

                                                                                                                                                                                    History

                                                                                                                                                                                    Calculator OS Version Description
                                                                                                                                                                                    TI-82 1.0 Added
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                                                                                                                                                                                    • FR: Zboîte

                                                                                                                                                                                    ZBox

                                                                                                                                                                                    Overview

                                                                                                                                                                                    Displays a graph, lets you draw a box that defines a new viewing window, and updates the window.

                                                                                                                                                                                    Availability: Token only available from within the Basic editor.

                                                                                                                                                                                    Syntax

                                                                                                                                                                                    ZBox

                                                                                                                                                                                    Location

                                                                                                                                                                                    zoom, ZOOM, 1:ZBox

                                                                                                                                                                                    Description

                                                                                                                                                                                    The ZBox command allows the user to select a smaller window within the current graphing window to zoom in to. To select the window, use the arrow keys and ENTER to select one corner of the window; then as you use the arrow keys and ENTER to select the other corner, a rectangle of the window's dimensions will be shown.

                                                                                                                                                                                    It's not recommended to use this in most programs, because entering an empty window (with no width or no height) will cause an error and exit the program without letting it clean up.

                                                                                                                                                                                    Error Conditions

                                                                                                                                                                                    • ERR:INVALID occurs if this command is used outside a program.
                                                                                                                                                                                    • ERR:ZOOM is thrown if an empty window is selected (with no width or no height)

                                                                                                                                                                                    Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan.

                                                                                                                                                                                    History

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                                                                                                                                                                                    • FR: Zdécimal

                                                                                                                                                                                    ZDecimal

                                                                                                                                                                                    Overview

                                                                                                                                                                                    Adjusts the viewing window so that TraceStep=0.1, ΔX=0.5 and ΔY=0.5, and displays the graph screen with the origin centered on the screen.

                                                                                                                                                                                    Availability: Token only available from within the Basic editor.

                                                                                                                                                                                    Syntax

                                                                                                                                                                                    ZDecimal

                                                                                                                                                                                    Location

                                                                                                                                                                                    zoom, ZOOM, 4:ZDecimal

                                                                                                                                                                                    Description

                                                                                                                                                                                    The ZDecimal command makes the following changes to the window variables:

                                                                                                                                                                                    • Xmin=-4.7
                                                                                                                                                                                    • Xmax=4.7
                                                                                                                                                                                    • Xscl=1
                                                                                                                                                                                    • Ymin=-3.1
                                                                                                                                                                                    • Ymax=3.1
                                                                                                                                                                                    • Yscl=1

                                                                                                                                                                                    If using a TI-84+CSE or CE, the window variables become:

                                                                                                                                                                                    • Xmin=-6.6
                                                                                                                                                                                    • Xmax=6.6
                                                                                                                                                                                    • Xscl=1
                                                                                                                                                                                    • Ymin=-4.1
                                                                                                                                                                                    • Ymax=4.1
                                                                                                                                                                                    • Yscl=1

                                                                                                                                                                                    Because of the dimensions of the graph screen, this has the useful effect that every pixel has round X- and Y-coordinates with at most one decimal digit. Also, the screen has correct proportions: a specific distance in the X direction is the same number of pixels in length as the same distance in the Y direction. This makes the window dimensions created by ZDecimal a friendly window (the ZInteger and ZSquare commands also have this effect, but in slightly different ways)

                                                                                                                                                                                    Advanced Uses

                                                                                                                                                                                    Using the ZDecimal command prevents gaps in certain graphs, and makes sure vertical asymptotes with integer coordinates are graphed correctly. Also, circles will be drawn as actual circles with this graphing window(unlike other windows, with which they might appear stretched).

                                                                                                                                                                                    The values given for Xmin, Xmax, etc. above are only correct for the Full mode setting (which is the default, and the most common setting). In Horiz and G-T modes, the values will be different, preserving the property that two pixels next to each other differ in coordinates by 0.1:

                                                                                                                                                                                    • Ymin= -1.5 and Ymax= 1.5 in Horiz mode (Xmin and Xmax are the same)
                                                                                                                                                                                    • Ymin= -2.5 and Ymax= 2.5 in G-T mode, while Xmin= -2.3 and Xmax= 2.3

                                                                                                                                                                                    Error Conditions

                                                                                                                                                                                    • ERR:INVALID occurs if this command is used outside a program.

                                                                                                                                                                                    See Also

                                                                                                                                                                                    Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, kg583.

                                                                                                                                                                                    History

                                                                                                                                                                                    Calculator OS Version Description
                                                                                                                                                                                    TI-82 1.0 Added
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                                                                                                                                                                                      • FR: ZFrac1⁄10

                                                                                                                                                                                      ZFrac1⁄10

                                                                                                                                                                                      Overview

                                                                                                                                                                                      Sets the window variables so that you can trace in increments of , if possible. Sets TraceStepto and ΔX and ΔYto .

                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                      Syntax

                                                                                                                                                                                      ZFrac1/10

                                                                                                                                                                                      Location

                                                                                                                                                                                      zoom, ZOOM, G:ZFrac1/10

                                                                                                                                                                                      Description

                                                                                                                                                                                      ZFrac_X_ refers to a collection of Zoom commands in for the OS 2.53MP and up. The calculator boasts six such commands, each replacing X with a fraction of some sort. The commands all essentially operate in the same manner, so they are all covered here on this page.

                                                                                                                                                                                      This command centers the origin of the graph and makes each pixel X units tall and wide where "X" refers to the suffix of the command. For example, ZFrac1/3 makes each pixel a length of and height of 1/3, which means that each square unit would be a 3x3 square of pixels. It also sets Xscale and Yscale to 1.

                                                                                                                                                                                      It is useful when the users wants each pixel to be a uniform length and height, though other commands such as ZSquare, ZDecimal, and ZInteger also create a friendly window, and being more compatible, they would be more useful in programming across calculators.

                                                                                                                                                                                      The following is a list of the available ZFrac_X_ commands:

                                                                                                                                                                                      • ZFrac1/2
                                                                                                                                                                                      • ZFrac1/3
                                                                                                                                                                                      • ZFrac1/4
                                                                                                                                                                                      • ZFrac1/5
                                                                                                                                                                                      • ZFrac1/8
                                                                                                                                                                                      • ZFrac1/10

                                                                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: Timothy Foster, Xeda Elnara.

                                                                                                                                                                                      History

                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                      TI-84+ 2.53 Added
                                                                                                                                                                                      Property Value
                                                                                                                                                                                      Hex Value $EF18
                                                                                                                                                                                      Categories
                                                                                                                                                                                        Localizations
                                                                                                                                                                                        • FR: ZFrac1⁄2

                                                                                                                                                                                        ZFrac1⁄2

                                                                                                                                                                                        Overview

                                                                                                                                                                                        Sets the window variables so that you can trace in increments of , if possible. Sets TraceStepto and ΔX and ΔYto .

                                                                                                                                                                                        Availability: Token available everywhere.

                                                                                                                                                                                        Syntax

                                                                                                                                                                                        ZFrac1/2

                                                                                                                                                                                        Location

                                                                                                                                                                                        zoom, ZOOM, B:ZFrac1/2

                                                                                                                                                                                        Description

                                                                                                                                                                                        ZFrac_X_ refers to a collection of Zoom commands in for the OS 2.53MP and up. The calculator boasts six such commands, each replacing X with a fraction of some sort. The commands all essentially operate in the same manner, so they are all covered here on this page.

                                                                                                                                                                                        This command centers the origin of the graph and makes each pixel X units tall and wide where "X" refers to the suffix of the command. For example, ZFrac1/3 makes each pixel a length of and height of 1/3, which means that each square unit would be a 3x3 square of pixels. It also sets Xscale and Yscale to 1.

                                                                                                                                                                                        It is useful when the users wants each pixel to be a uniform length and height, though other commands such as ZSquare, ZDecimal, and ZInteger also create a friendly window, and being more compatible, they would be more useful in programming across calculators.

                                                                                                                                                                                        The following is a list of the available ZFrac_X_ commands:

                                                                                                                                                                                        • ZFrac1/2
                                                                                                                                                                                        • ZFrac1/3
                                                                                                                                                                                        • ZFrac1/4
                                                                                                                                                                                        • ZFrac1/5
                                                                                                                                                                                        • ZFrac1/8
                                                                                                                                                                                        • ZFrac1/10

                                                                                                                                                                                        Source: parts of this page were written by the following TI|BD contributors: Timothy Foster, Xeda Elnara.

                                                                                                                                                                                        History

                                                                                                                                                                                        Calculator OS Version Description
                                                                                                                                                                                        TI-84+ 2.53 Added
                                                                                                                                                                                        Property Value
                                                                                                                                                                                        Hex Value $EF19
                                                                                                                                                                                        Categories
                                                                                                                                                                                          Localizations
                                                                                                                                                                                          • FR: ZFrac1⁄3

                                                                                                                                                                                          ZFrac1⁄3

                                                                                                                                                                                          Overview

                                                                                                                                                                                          Sets the window variables so that you can trace in increments of , if possible. Sets TraceStepto and ΔX and ΔYto .

                                                                                                                                                                                          Availability: Token available everywhere.

                                                                                                                                                                                          Syntax

                                                                                                                                                                                          ZFrac1/3

                                                                                                                                                                                          Location

                                                                                                                                                                                          zoom, ZOOM, C:ZFrac1/3

                                                                                                                                                                                          Description

                                                                                                                                                                                          ZFrac_X_ refers to a collection of Zoom commands in for the OS 2.53MP and up. The calculator boasts six such commands, each replacing X with a fraction of some sort. The commands all essentially operate in the same manner, so they are all covered here on this page.

                                                                                                                                                                                          This command centers the origin of the graph and makes each pixel X units tall and wide where "X" refers to the suffix of the command. For example, ZFrac1/3 makes each pixel a length of and height of 1/3, which means that each square unit would be a 3x3 square of pixels. It also sets Xscale and Yscale to 1.

                                                                                                                                                                                          It is useful when the users wants each pixel to be a uniform length and height, though other commands such as ZSquare, ZDecimal, and ZInteger also create a friendly window, and being more compatible, they would be more useful in programming across calculators.

                                                                                                                                                                                          The following is a list of the available ZFrac_X_ commands:

                                                                                                                                                                                          • ZFrac1/2
                                                                                                                                                                                          • ZFrac1/3
                                                                                                                                                                                          • ZFrac1/4
                                                                                                                                                                                          • ZFrac1/5
                                                                                                                                                                                          • ZFrac1/8
                                                                                                                                                                                          • ZFrac1/10

                                                                                                                                                                                          Source: parts of this page were written by the following TI|BD contributors: Timothy Foster, Xeda Elnara.

                                                                                                                                                                                          History

                                                                                                                                                                                          Calculator OS Version Description
                                                                                                                                                                                          TI-84+ 2.53 Added
                                                                                                                                                                                          Property Value
                                                                                                                                                                                          Hex Value $EF1A
                                                                                                                                                                                          Categories
                                                                                                                                                                                            Localizations
                                                                                                                                                                                            • FR: ZFrac1⁄4

                                                                                                                                                                                            ZFrac1⁄4

                                                                                                                                                                                            Overview

                                                                                                                                                                                            Sets the window variables so that you can trace in increments of , if possible. Sets TraceStepto and ΔX and ΔYto .

                                                                                                                                                                                            Availability: Token available everywhere.

                                                                                                                                                                                            Syntax

                                                                                                                                                                                            ZFrac1/4

                                                                                                                                                                                            Location

                                                                                                                                                                                            zoom, ZOOM, D:ZFrac1/4

                                                                                                                                                                                            Description

                                                                                                                                                                                            ZFrac_X_ refers to a collection of Zoom commands in for the OS 2.53MP and up. The calculator boasts six such commands, each replacing X with a fraction of some sort. The commands all essentially operate in the same manner, so they are all covered here on this page.

                                                                                                                                                                                            This command centers the origin of the graph and makes each pixel X units tall and wide where "X" refers to the suffix of the command. For example, ZFrac1/3 makes each pixel a length of and height of 1/3, which means that each square unit would be a 3x3 square of pixels. It also sets Xscale and Yscale to 1.

                                                                                                                                                                                            It is useful when the users wants each pixel to be a uniform length and height, though other commands such as ZSquare, ZDecimal, and ZInteger also create a friendly window, and being more compatible, they would be more useful in programming across calculators.

                                                                                                                                                                                            The following is a list of the available ZFrac_X_ commands:

                                                                                                                                                                                            • ZFrac1/2
                                                                                                                                                                                            • ZFrac1/3
                                                                                                                                                                                            • ZFrac1/4
                                                                                                                                                                                            • ZFrac1/5
                                                                                                                                                                                            • ZFrac1/8
                                                                                                                                                                                            • ZFrac1/10

                                                                                                                                                                                            Source: parts of this page were written by the following TI|BD contributors: Timothy Foster, Xeda Elnara.

                                                                                                                                                                                            History

                                                                                                                                                                                            Calculator OS Version Description
                                                                                                                                                                                            TI-84+ 2.53 Added
                                                                                                                                                                                            Property Value
                                                                                                                                                                                            Hex Value $EF1B
                                                                                                                                                                                            Categories
                                                                                                                                                                                              Localizations
                                                                                                                                                                                              • FR: ZFrac1⁄5

                                                                                                                                                                                              ZFrac1⁄5

                                                                                                                                                                                              Overview

                                                                                                                                                                                              Sets the window variables so that you can trace in increments of , if possible. Sets TraceStepto and ΔX and ΔYto .

                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                              Syntax

                                                                                                                                                                                              ZFrac1/5

                                                                                                                                                                                              Location

                                                                                                                                                                                              zoom, ZOOM, E:ZFrac1/5

                                                                                                                                                                                              Description

                                                                                                                                                                                              ZFrac_X_ refers to a collection of Zoom commands in for the OS 2.53MP and up. The calculator boasts six such commands, each replacing X with a fraction of some sort. The commands all essentially operate in the same manner, so they are all covered here on this page.

                                                                                                                                                                                              This command centers the origin of the graph and makes each pixel X units tall and wide where "X" refers to the suffix of the command. For example, ZFrac1/3 makes each pixel a length of and height of 1/3, which means that each square unit would be a 3x3 square of pixels. It also sets Xscale and Yscale to 1.

                                                                                                                                                                                              It is useful when the users wants each pixel to be a uniform length and height, though other commands such as ZSquare, ZDecimal, and ZInteger also create a friendly window, and being more compatible, they would be more useful in programming across calculators.

                                                                                                                                                                                              The following is a list of the available ZFrac_X_ commands:

                                                                                                                                                                                              • ZFrac1/2
                                                                                                                                                                                              • ZFrac1/3
                                                                                                                                                                                              • ZFrac1/4
                                                                                                                                                                                              • ZFrac1/5
                                                                                                                                                                                              • ZFrac1/8
                                                                                                                                                                                              • ZFrac1/10

                                                                                                                                                                                              Source: parts of this page were written by the following TI|BD contributors: Timothy Foster, Xeda Elnara.

                                                                                                                                                                                              History

                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                              TI-84+ 2.53 Added
                                                                                                                                                                                              Property Value
                                                                                                                                                                                              Hex Value $EF1C
                                                                                                                                                                                              Categories
                                                                                                                                                                                                Localizations
                                                                                                                                                                                                • FR: ZFrac1⁄8

                                                                                                                                                                                                ZFrac1⁄8

                                                                                                                                                                                                Overview

                                                                                                                                                                                                Sets the window variables so that you can trace in increments of , if possible. Sets TraceStepto and ΔX and ΔYto .

                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                Syntax

                                                                                                                                                                                                ZFrac1/8

                                                                                                                                                                                                Location

                                                                                                                                                                                                zoom, ZOOM, F:ZFrac1/8

                                                                                                                                                                                                Description

                                                                                                                                                                                                ZFrac_X_ refers to a collection of Zoom commands in for the OS 2.53MP and up. The calculator boasts six such commands, each replacing X with a fraction of some sort. The commands all essentially operate in the same manner, so they are all covered here on this page.

                                                                                                                                                                                                This command centers the origin of the graph and makes each pixel X units tall and wide where "X" refers to the suffix of the command. For example, ZFrac1/3 makes each pixel a length of and height of 1/3, which means that each square unit would be a 3x3 square of pixels. It also sets Xscale and Yscale to 1.

                                                                                                                                                                                                It is useful when the users wants each pixel to be a uniform length and height, though other commands such as ZSquare, ZDecimal, and ZInteger also create a friendly window, and being more compatible, they would be more useful in programming across calculators.

                                                                                                                                                                                                The following is a list of the available ZFrac_X_ commands:

                                                                                                                                                                                                • ZFrac1/2
                                                                                                                                                                                                • ZFrac1/3
                                                                                                                                                                                                • ZFrac1/4
                                                                                                                                                                                                • ZFrac1/5
                                                                                                                                                                                                • ZFrac1/8
                                                                                                                                                                                                • ZFrac1/10

                                                                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: Timothy Foster, Xeda Elnara.

                                                                                                                                                                                                History

                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                TI-84+ 2.53 Added
                                                                                                                                                                                                Property Value
                                                                                                                                                                                                Hex Value $EF1D
                                                                                                                                                                                                Categories
                                                                                                                                                                                                  Localizations
                                                                                                                                                                                                  • FR: ZFrac1⁄10

                                                                                                                                                                                                  ZFrac1⁄10

                                                                                                                                                                                                  Overview

                                                                                                                                                                                                  Sets the window variables so that you can trace in increments of , if possible. Sets TraceStepto and ΔX and ΔYto .

                                                                                                                                                                                                  Availability: Token available everywhere.

                                                                                                                                                                                                  Syntax

                                                                                                                                                                                                  ZFrac1/10

                                                                                                                                                                                                  Location

                                                                                                                                                                                                  zoom, ZOOM, G:ZFrac1/10

                                                                                                                                                                                                  Description

                                                                                                                                                                                                  ZFrac_X_ refers to a collection of Zoom commands in for the OS 2.53MP and up. The calculator boasts six such commands, each replacing X with a fraction of some sort. The commands all essentially operate in the same manner, so they are all covered here on this page.

                                                                                                                                                                                                  This command centers the origin of the graph and makes each pixel X units tall and wide where "X" refers to the suffix of the command. For example, ZFrac1/3 makes each pixel a length of and height of 1/3, which means that each square unit would be a 3x3 square of pixels. It also sets Xscale and Yscale to 1.

                                                                                                                                                                                                  It is useful when the users wants each pixel to be a uniform length and height, though other commands such as ZSquare, ZDecimal, and ZInteger also create a friendly window, and being more compatible, they would be more useful in programming across calculators.

                                                                                                                                                                                                  The following is a list of the available ZFrac_X_ commands:

                                                                                                                                                                                                  • ZFrac1/2
                                                                                                                                                                                                  • ZFrac1/3
                                                                                                                                                                                                  • ZFrac1/4
                                                                                                                                                                                                  • ZFrac1/5
                                                                                                                                                                                                  • ZFrac1/8
                                                                                                                                                                                                  • ZFrac1/10

                                                                                                                                                                                                  Source: parts of this page were written by the following TI|BD contributors: Timothy Foster, Xeda Elnara.

                                                                                                                                                                                                  History

                                                                                                                                                                                                  Calculator OS Version Description
                                                                                                                                                                                                  TI-84+ 2.53 Added
                                                                                                                                                                                                  Property Value
                                                                                                                                                                                                  Hex Value $EF18
                                                                                                                                                                                                  Categories
                                                                                                                                                                                                    Localizations
                                                                                                                                                                                                    • FR: ZFrac1⁄2

                                                                                                                                                                                                    ZFrac1⁄2

                                                                                                                                                                                                    Overview

                                                                                                                                                                                                    Sets the window variables so that you can trace in increments of , if possible. Sets TraceStepto and ΔX and ΔYto .

                                                                                                                                                                                                    Availability: Token available everywhere.

                                                                                                                                                                                                    Syntax

                                                                                                                                                                                                    ZFrac1/2

                                                                                                                                                                                                    Location

                                                                                                                                                                                                    zoom, ZOOM, B:ZFrac1/2

                                                                                                                                                                                                    Description

                                                                                                                                                                                                    ZFrac_X_ refers to a collection of Zoom commands in for the OS 2.53MP and up. The calculator boasts six such commands, each replacing X with a fraction of some sort. The commands all essentially operate in the same manner, so they are all covered here on this page.

                                                                                                                                                                                                    This command centers the origin of the graph and makes each pixel X units tall and wide where "X" refers to the suffix of the command. For example, ZFrac1/3 makes each pixel a length of and height of 1/3, which means that each square unit would be a 3x3 square of pixels. It also sets Xscale and Yscale to 1.

                                                                                                                                                                                                    It is useful when the users wants each pixel to be a uniform length and height, though other commands such as ZSquare, ZDecimal, and ZInteger also create a friendly window, and being more compatible, they would be more useful in programming across calculators.

                                                                                                                                                                                                    The following is a list of the available ZFrac_X_ commands:

                                                                                                                                                                                                    • ZFrac1/2
                                                                                                                                                                                                    • ZFrac1/3
                                                                                                                                                                                                    • ZFrac1/4
                                                                                                                                                                                                    • ZFrac1/5
                                                                                                                                                                                                    • ZFrac1/8
                                                                                                                                                                                                    • ZFrac1/10

                                                                                                                                                                                                    Source: parts of this page were written by the following TI|BD contributors: Timothy Foster, Xeda Elnara.

                                                                                                                                                                                                    History

                                                                                                                                                                                                    Calculator OS Version Description
                                                                                                                                                                                                    TI-84+ 2.53 Added
                                                                                                                                                                                                    Property Value
                                                                                                                                                                                                    Hex Value $EF19
                                                                                                                                                                                                    Categories
                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                      • FR: ZFrac1⁄3

                                                                                                                                                                                                      ZFrac1⁄3

                                                                                                                                                                                                      Overview

                                                                                                                                                                                                      Sets the window variables so that you can trace in increments of , if possible. Sets TraceStepto and ΔX and ΔYto .

                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                      ZFrac1/3

                                                                                                                                                                                                      Location

                                                                                                                                                                                                      zoom, ZOOM, C:ZFrac1/3

                                                                                                                                                                                                      Description

                                                                                                                                                                                                      ZFrac_X_ refers to a collection of Zoom commands in for the OS 2.53MP and up. The calculator boasts six such commands, each replacing X with a fraction of some sort. The commands all essentially operate in the same manner, so they are all covered here on this page.

                                                                                                                                                                                                      This command centers the origin of the graph and makes each pixel X units tall and wide where "X" refers to the suffix of the command. For example, ZFrac1/3 makes each pixel a length of and height of 1/3, which means that each square unit would be a 3x3 square of pixels. It also sets Xscale and Yscale to 1.

                                                                                                                                                                                                      It is useful when the users wants each pixel to be a uniform length and height, though other commands such as ZSquare, ZDecimal, and ZInteger also create a friendly window, and being more compatible, they would be more useful in programming across calculators.

                                                                                                                                                                                                      The following is a list of the available ZFrac_X_ commands:

                                                                                                                                                                                                      • ZFrac1/2
                                                                                                                                                                                                      • ZFrac1/3
                                                                                                                                                                                                      • ZFrac1/4
                                                                                                                                                                                                      • ZFrac1/5
                                                                                                                                                                                                      • ZFrac1/8
                                                                                                                                                                                                      • ZFrac1/10

                                                                                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: Timothy Foster, Xeda Elnara.

                                                                                                                                                                                                      History

                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                      TI-84+ 2.53 Added
                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                      Hex Value $EF1A
                                                                                                                                                                                                      Categories
                                                                                                                                                                                                        Localizations
                                                                                                                                                                                                        • FR: ZFrac1⁄4

                                                                                                                                                                                                        ZFrac1⁄4

                                                                                                                                                                                                        Overview

                                                                                                                                                                                                        Sets the window variables so that you can trace in increments of , if possible. Sets TraceStepto and ΔX and ΔYto .

                                                                                                                                                                                                        Availability: Token available everywhere.

                                                                                                                                                                                                        Syntax

                                                                                                                                                                                                        ZFrac1/4

                                                                                                                                                                                                        Location

                                                                                                                                                                                                        zoom, ZOOM, D:ZFrac1/4

                                                                                                                                                                                                        Description

                                                                                                                                                                                                        ZFrac_X_ refers to a collection of Zoom commands in for the OS 2.53MP and up. The calculator boasts six such commands, each replacing X with a fraction of some sort. The commands all essentially operate in the same manner, so they are all covered here on this page.

                                                                                                                                                                                                        This command centers the origin of the graph and makes each pixel X units tall and wide where "X" refers to the suffix of the command. For example, ZFrac1/3 makes each pixel a length of and height of 1/3, which means that each square unit would be a 3x3 square of pixels. It also sets Xscale and Yscale to 1.

                                                                                                                                                                                                        It is useful when the users wants each pixel to be a uniform length and height, though other commands such as ZSquare, ZDecimal, and ZInteger also create a friendly window, and being more compatible, they would be more useful in programming across calculators.

                                                                                                                                                                                                        The following is a list of the available ZFrac_X_ commands:

                                                                                                                                                                                                        • ZFrac1/2
                                                                                                                                                                                                        • ZFrac1/3
                                                                                                                                                                                                        • ZFrac1/4
                                                                                                                                                                                                        • ZFrac1/5
                                                                                                                                                                                                        • ZFrac1/8
                                                                                                                                                                                                        • ZFrac1/10

                                                                                                                                                                                                        Source: parts of this page were written by the following TI|BD contributors: Timothy Foster, Xeda Elnara.

                                                                                                                                                                                                        History

                                                                                                                                                                                                        Calculator OS Version Description
                                                                                                                                                                                                        TI-84+ 2.53 Added
                                                                                                                                                                                                        Property Value
                                                                                                                                                                                                        Hex Value $EF1B
                                                                                                                                                                                                        Categories
                                                                                                                                                                                                          Localizations
                                                                                                                                                                                                          • FR: ZFrac1⁄5

                                                                                                                                                                                                          ZFrac1⁄5

                                                                                                                                                                                                          Overview

                                                                                                                                                                                                          Sets the window variables so that you can trace in increments of , if possible. Sets TraceStepto and ΔX and ΔYto .

                                                                                                                                                                                                          Availability: Token available everywhere.

                                                                                                                                                                                                          Syntax

                                                                                                                                                                                                          ZFrac1/5

                                                                                                                                                                                                          Location

                                                                                                                                                                                                          zoom, ZOOM, E:ZFrac1/5

                                                                                                                                                                                                          Description

                                                                                                                                                                                                          ZFrac_X_ refers to a collection of Zoom commands in for the OS 2.53MP and up. The calculator boasts six such commands, each replacing X with a fraction of some sort. The commands all essentially operate in the same manner, so they are all covered here on this page.

                                                                                                                                                                                                          This command centers the origin of the graph and makes each pixel X units tall and wide where "X" refers to the suffix of the command. For example, ZFrac1/3 makes each pixel a length of and height of 1/3, which means that each square unit would be a 3x3 square of pixels. It also sets Xscale and Yscale to 1.

                                                                                                                                                                                                          It is useful when the users wants each pixel to be a uniform length and height, though other commands such as ZSquare, ZDecimal, and ZInteger also create a friendly window, and being more compatible, they would be more useful in programming across calculators.

                                                                                                                                                                                                          The following is a list of the available ZFrac_X_ commands:

                                                                                                                                                                                                          • ZFrac1/2
                                                                                                                                                                                                          • ZFrac1/3
                                                                                                                                                                                                          • ZFrac1/4
                                                                                                                                                                                                          • ZFrac1/5
                                                                                                                                                                                                          • ZFrac1/8
                                                                                                                                                                                                          • ZFrac1/10

                                                                                                                                                                                                          Source: parts of this page were written by the following TI|BD contributors: Timothy Foster, Xeda Elnara.

                                                                                                                                                                                                          History

                                                                                                                                                                                                          Calculator OS Version Description
                                                                                                                                                                                                          TI-84+ 2.53 Added
                                                                                                                                                                                                          Property Value
                                                                                                                                                                                                          Hex Value $EF1C
                                                                                                                                                                                                          Categories
                                                                                                                                                                                                            Localizations
                                                                                                                                                                                                            • FR: ZFrac1⁄8

                                                                                                                                                                                                            ZFrac1⁄8

                                                                                                                                                                                                            Overview

                                                                                                                                                                                                            Sets the window variables so that you can trace in increments of , if possible. Sets TraceStepto and ΔX and ΔYto .

                                                                                                                                                                                                            Availability: Token available everywhere.

                                                                                                                                                                                                            Syntax

                                                                                                                                                                                                            ZFrac1/8

                                                                                                                                                                                                            Location

                                                                                                                                                                                                            zoom, ZOOM, F:ZFrac1/8

                                                                                                                                                                                                            Description

                                                                                                                                                                                                            ZFrac_X_ refers to a collection of Zoom commands in for the OS 2.53MP and up. The calculator boasts six such commands, each replacing X with a fraction of some sort. The commands all essentially operate in the same manner, so they are all covered here on this page.

                                                                                                                                                                                                            This command centers the origin of the graph and makes each pixel X units tall and wide where "X" refers to the suffix of the command. For example, ZFrac1/3 makes each pixel a length of and height of 1/3, which means that each square unit would be a 3x3 square of pixels. It also sets Xscale and Yscale to 1.

                                                                                                                                                                                                            It is useful when the users wants each pixel to be a uniform length and height, though other commands such as ZSquare, ZDecimal, and ZInteger also create a friendly window, and being more compatible, they would be more useful in programming across calculators.

                                                                                                                                                                                                            The following is a list of the available ZFrac_X_ commands:

                                                                                                                                                                                                            • ZFrac1/2
                                                                                                                                                                                                            • ZFrac1/3
                                                                                                                                                                                                            • ZFrac1/4
                                                                                                                                                                                                            • ZFrac1/5
                                                                                                                                                                                                            • ZFrac1/8
                                                                                                                                                                                                            • ZFrac1/10

                                                                                                                                                                                                            Source: parts of this page were written by the following TI|BD contributors: Timothy Foster, Xeda Elnara.

                                                                                                                                                                                                            History

                                                                                                                                                                                                            Calculator OS Version Description
                                                                                                                                                                                                            TI-84+ 2.53 Added
                                                                                                                                                                                                            Property Value
                                                                                                                                                                                                            Hex Value $8C
                                                                                                                                                                                                            Categories
                                                                                                                                                                                                            Localizations
                                                                                                                                                                                                            • FR: ZintConf

                                                                                                                                                                                                            ZInteger

                                                                                                                                                                                                            Overview

                                                                                                                                                                                                            Redefines the viewing window using the following dimensions: TraceStep=1,ΔX=0.5, Xscl=10,ΔY=1, Yscl=10.

                                                                                                                                                                                                            Availability: Token only available from within the Basic editor.

                                                                                                                                                                                                            Syntax

                                                                                                                                                                                                            ZInteger

                                                                                                                                                                                                            Location

                                                                                                                                                                                                            zoom, ZOOM, 8:ZInteger

                                                                                                                                                                                                            Description

                                                                                                                                                                                                            When ZInteger is chosen as a menu option outside a program, it asks for a point on the graph screen. This point's coordinates are rounded to the nearest integer point. Then the window variables are changed so the window is centered at this point, and so that the coordinates of every pixel are integers. ΔX and ΔY, the distances between two pixels next to each other, are both 1.

                                                                                                                                                                                                            The above process modifies Xmin, Xmax, Ymin, and Ymax. Xscl and Yscl are also modified: both are set to 10. No other variables are modified (unless you count ΔX and ΔY, which are affected as they are defined).

                                                                                                                                                                                                            The ZInteger command (usable in a program only) has a slightly different effect: instead of allowing you to choose a point, it automatically uses the point that is the current center.

                                                                                                                                                                                                            Advanced Uses

                                                                                                                                                                                                            A graph window commonly used in programming can be created by using the ZStandard and ZInteger commands:

                                                                                                                                                                                                            :ZStandard
:ZInteger

                                                                                                                                                                                                            Error Conditions

                                                                                                                                                                                                            • ERR:INVALID occurs if this command is used outside a program.

                                                                                                                                                                                                            See Also

                                                                                                                                                                                                            Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, seb83.

                                                                                                                                                                                                            History

                                                                                                                                                                                                            Calculator OS Version Description
                                                                                                                                                                                                            TI-82 1.0 Added
                                                                                                                                                                                                            Property Value
                                                                                                                                                                                                            Hex Value $BB41
                                                                                                                                                                                                            Categories
                                                                                                                                                                                                            Localizations
                                                                                                                                                                                                            • FR: ZintConf

                                                                                                                                                                                                            ZInterval

                                                                                                                                                                                                            Overview

                                                                                                                                                                                                            Computes a z confidence interval.

                                                                                                                                                                                                            Comment:Data list input

                                                                                                                                                                                                            Availability: Token only available from within the Basic editor.

                                                                                                                                                                                                            Syntax

                                                                                                                                                                                                            ZIntervalσ[,listname,freqlist,confidence level]

                                                                                                                                                                                                            Arguments

                                                                                                                                                                                                            NameTypeOptional
                                                                                                                                                                                                            σ
                                                                                                                                                                                                            listnamelist
                                                                                                                                                                                                            freqlistlist
                                                                                                                                                                                                            confidence level

                                                                                                                                                                                                            Location

                                                                                                                                                                                                            stat, TESTS, 7:ZInterval

                                                                                                                                                                                                            Overview

                                                                                                                                                                                                            Computes a z confidence interval.

                                                                                                                                                                                                            Comment:Summary stats input

                                                                                                                                                                                                            Availability: Token only available from within the Basic editor.

                                                                                                                                                                                                            Syntax

                                                                                                                                                                                                            ZIntervalσ,x̄,n[,confidence level]

                                                                                                                                                                                                            Arguments

                                                                                                                                                                                                            NameTypeOptional
                                                                                                                                                                                                            σ
                                                                                                                                                                                                            x̄
                                                                                                                                                                                                            nYes
                                                                                                                                                                                                            confidence levelYes

                                                                                                                                                                                                            Location

                                                                                                                                                                                                            stat, TESTS, 7:ZInterval

                                                                                                                                                                                                            Description

                                                                                                                                                                                                            The ZInterval command calculates a confidence interval for the mean value of a population, at a specific confidence level: for example, if the confidence level is 95%, you are 95% certain that the mean lies within the interval you get. Use ZInterval when you have a single variable to analyze, and you already know the standard deviation. The ZInterval assumes that your distribution is normal, but it will work for other distributions if the sample size is large enough.

                                                                                                                                                                                                            There are two ways to call the ZInterval command: by supplying it with needed sample statistics (mean and sample size), or by entering a list and letting the calculator work the statistics out. In either case, you will need to enter the standard deviation and desired confidence level as well.

                                                                                                                                                                                                            Sample Problem

                                                                                                                                                                                                            You want to know the average height of a student at your school. You haven't asked everyone, but you took a random sample of 30 people and found out their height (and stored it to L1). You've read in your textbook that the standard deviation of teenagers' heights is usually 6 inches. You've decided to use a 95% confidence interval.

                                                                                                                                                                                                            Since the syntax for entering a data list is ZInterval std. deviation, list, confidence level, the code would look like:

                                                                                                                                                                                                            :ZInterval 6,L1,95
you can also use
:ZInterval 6,L1,.95

                                                                                                                                                                                                            Alternatively, you could calculate the mean and sample size and enter those instead. The sample size in this case is 30; let's say the mean was 63 inches. The syntax for entering statistics is ZInterval std. deviation, mean, sample size, confidence level, so your code would look like:

                                                                                                                                                                                                            :ZInterval 6,63,30,95
you can also use
:ZInterval 6,63,30,.95

                                                                                                                                                                                                            Of course, the main use of the ZInterval command is in a program. While you can enter the ZInterval command on the home screen as well (just look in the catalog for it), it would probably be easier to select ZInterval… from the STAT>TEST menu (see the sidebar).

                                                                                                                                                                                                            Advanced Uses

                                                                                                                                                                                                            As with most other statistical commands, you can enter a second list after the data list, to add frequencies (only with the data list syntax, of course). The frequency list must contain non-negative real numbers, and can't be all 0.

                                                                                                                                                                                                            Optimization

                                                                                                                                                                                                            Using the data list syntax, all items but the standard deviation are optional: the calculator will assume you want to use L1 for your data unless another list is supplied, and that the confidence level you want is 95% unless you give another one. Using the summary stats syntax, the confidence level is also optional - again, the calculator will assume 95%. This means we can rewrite our code above in a simpler manner:

                                                                                                                                                                                                            :ZInterval 6,L1,95
can be
:ZInterval 6

                                                                                                                                                                                                            :ZInterval 6,63,30,95
can be
:ZInterval 6,63,30

                                                                                                                                                                                                            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

                                                                                                                                                                                                            History

                                                                                                                                                                                                            Calculator OS Version Description
                                                                                                                                                                                                            TI-83 0.01013 Added
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                                                                                                                                                                                                            • FR: ZPlotStart

                                                                                                                                                                                                            ZPlotStart

                                                                                                                                                                                                            Overview

                                                                                                                                                                                                            Syntax

                                                                                                                                                                                                            ZPlotStart

                                                                                                                                                                                                            Description

                                                                                                                                                                                                            Examples

                                                                                                                                                                                                            Explanation 1

                                                                                                                                                                                                            code 1

                                                                                                                                                                                                            Explanation 2

                                                                                                                                                                                                            code 2

                                                                                                                                                                                                            Error Conditions

                                                                                                                                                                                                            Advanced Notes

                                                                                                                                                                                                            History

                                                                                                                                                                                                            Calculator OS Version Description
                                                                                                                                                                                                            TI-82 1.0 Added
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                                                                                                                                                                                                            • FR: ZGraphPas

                                                                                                                                                                                                            ZPlotStep

                                                                                                                                                                                                            Overview

                                                                                                                                                                                                            Syntax

                                                                                                                                                                                                            ZPlotStep

                                                                                                                                                                                                            Description

                                                                                                                                                                                                            Examples

                                                                                                                                                                                                            Explanation 1

                                                                                                                                                                                                            code 1

                                                                                                                                                                                                            Explanation 2

                                                                                                                                                                                                            code 2

                                                                                                                                                                                                            Error Conditions

                                                                                                                                                                                                            Advanced Notes

                                                                                                                                                                                                            History

                                                                                                                                                                                                            Calculator OS Version Description
                                                                                                                                                                                                            TI-83 0.01013 Added
                                                                                                                                                                                                            Property Value
                                                                                                                                                                                                            Hex Value $8D
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                                                                                                                                                                                                            • FR: Zprécédent

                                                                                                                                                                                                            ZPrevious

                                                                                                                                                                                                            Overview

                                                                                                                                                                                                            Replots the graph using the window variables of the graph that was displayed before you executed the last ZOOM instruction.

                                                                                                                                                                                                            Availability: Token only available from within the Basic editor.

                                                                                                                                                                                                            Syntax

                                                                                                                                                                                                            ZPrevious

                                                                                                                                                                                                            Location

                                                                                                                                                                                                            zoom, MEMORY, 1:ZPrevious

                                                                                                                                                                                                            Description

                                                                                                                                                                                                            The ZPrevious command (and menu option) restore the window variables Xmin, Xmax, Xscl, Ymin, Ymax, and Yscl to the values they had before the last zoom command. This means, of course, that using ZPrevious a second time will cancel its effects.

                                                                                                                                                                                                            Since no variables that are specific to the current graphing mode are changed, ZPrevious doesn't always achieve the effect of reversing the previous zoom command. For example, in Polar graphing mode, ZStandard will set θmin and θmax to 0 and 2π respectively. However, even if they were different before ZStandard, ZPrevious will not restore these settings. Also, ZPrevious doesn't notice if you change the window settings directly (by storing to the window variables).

                                                                                                                                                                                                            Unlike ZoomSto and ZoomRcl, the values that ZPrevious uses aren't made available in any sort of variable.

                                                                                                                                                                                                            Optimization

                                                                                                                                                                                                            Using StoreGDB and RecallGDB is an excellent way to back up graph settings so a program doesn't modify them. However, if all you're doing is changing the window variables with one Zoom command, you can simply use ZPrevious at the end of the program instead.

                                                                                                                                                                                                            Error Conditions

                                                                                                                                                                                                            • ERR:INVALID occurs if this command is used outside a program (but not if the menu option is used, of course).

                                                                                                                                                                                                            Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, HJTP.

                                                                                                                                                                                                            History

                                                                                                                                                                                                            Calculator OS Version Description
                                                                                                                                                                                                            TI-82 1.0 Added
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                                                                                                                                                                                                              • FR: ZQuadrant1

                                                                                                                                                                                                              ZQuadrant1

                                                                                                                                                                                                              Overview

                                                                                                                                                                                                              Displays the portion of the graph that is in quadrant 1.

                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                              ZQuadrant1

                                                                                                                                                                                                              Location

                                                                                                                                                                                                              zoom, ZOOM, A:ZQuadrant1

                                                                                                                                                                                                              Description

                                                                                                                                                                                                              ZQuadrant1 was introduced in OS 2.53MP. As it's name might imply, it puts Quadrant I in the viewing window (the upper-left quadrant). Here are the window settings it affects:

                                                                                                                                                                                                              • Xmin is set to 0 and Xmax is set to 9.4 making each pixel .1 units.
                                                                                                                                                                                                              • Ymin is set to 0 and Ymax is set to 9.4 (each pixel is 47/310 units)
                                                                                                                                                                                                              • Xscl and Yscl are set to 1
                                                                                                                                                                                                              • ΔX is set to .1
                                                                                                                                                                                                              • ΔY is set to 47/310
                                                                                                                                                                                                              • Xres is set to 1

                                                                                                                                                                                                              This command does not seem to work in programs.

                                                                                                                                                                                                              Source: parts of this page were written by the following TI|BD contributors: burr, Xeda Elnara.

                                                                                                                                                                                                              History

                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                              TI-84+ 0.01 Added
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                                                                                                                                                                                                              • FR: Zorthonormal

                                                                                                                                                                                                              ZSquare

                                                                                                                                                                                                              Overview

                                                                                                                                                                                                              Adjusts the X or Y window settings so that each pixel represents an equal width and height in the coordinate system, and updates the viewing window.

                                                                                                                                                                                                              Availability: Token only available from within the Basic editor.

                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                              ZSquare

                                                                                                                                                                                                              Location

                                                                                                                                                                                                              zoom, ZOOM, 5:ZSquare

                                                                                                                                                                                                              Description

                                                                                                                                                                                                              The ZSquare command changes the window variables Xmin and Xmax, or Ymin and Ymax, so that ΔX=ΔY, preserving all other settings and the coordinate of the center of the screen. This ensures that a numerical distance on the graphscreen has the same physical length on the calculator display, no matter if it's vertical, horizontal, or diagonal. Probably the most obvious effect of this change is that circles (whether graphed with an equation or drawn with the Circle( command) are actually circles and not ovals.

                                                                                                                                                                                                              When determining which of Xmin and Xmax or Ymin and Ymax to change, the command picks the ones that would be increased, and not decreased. This way, the window can never get smaller.

                                                                                                                                                                                                              Note that ZDecimal, ZInteger, and to an extent ZTrig already have the same proportions, and don't require a ZSquare command to follow them.

                                                                                                                                                                                                              Advanced Uses

                                                                                                                                                                                                              ZSquare can be useful in setting up a friendly window.

                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                              • ERR:INVALID occurs if this command is used outside a program.

                                                                                                                                                                                                              See Also

                                                                                                                                                                                                              Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, HJTP.

                                                                                                                                                                                                              History

                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                              TI-82 1.0 Added
                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                              Hex Value $86
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                                                                                                                                                                                                              • FR: ZStandard

                                                                                                                                                                                                              ZStandard

                                                                                                                                                                                                              Overview

                                                                                                                                                                                                              Replots the functions immediately, updating the window variables to the default values.

                                                                                                                                                                                                              Availability: Token only available from within the Basic editor.

                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                              ZStandard

                                                                                                                                                                                                              Location

                                                                                                                                                                                                              zoom, ZOOM, 6:ZStandard

                                                                                                                                                                                                              Description

                                                                                                                                                                                                              The ZStandard command resets all window variables found in the Window screen to their default values. This means that, unlike the other zoom commands, ZStandard can affect variables other than Xmin, Xmax, Ymin, and Ymax. However, it will only affect variables that have a purpose in the current graphing mode. Here are the default values set by ZStandard:

                                                                                                                                                                                                              In all modes:

                                                                                                                                                                                                              • Xmin=-10
                                                                                                                                                                                                              • Xmax=10
                                                                                                                                                                                                              • Xscl=1
                                                                                                                                                                                                              • Ymin=-10
                                                                                                                                                                                                              • Ymax=10
                                                                                                                                                                                                              • Yscl=1

                                                                                                                                                                                                              Only in Func mode:

                                                                                                                                                                                                              • Xres=1

                                                                                                                                                                                                              Only in Param mode:

                                                                                                                                                                                                              • Tmin=0
                                                                                                                                                                                                              • Tmax=2π (in Radian mode) or 360 (in Degree mode)
                                                                                                                                                                                                              • Tstep=π/24 (in Radian mode) or 7.5 (in Degree mode)

                                                                                                                                                                                                              Only in Polar mode:

                                                                                                                                                                                                              • θmin=0
                                                                                                                                                                                                              • θmax=2π (in Radian mode) or 360 (in Degree mode)
                                                                                                                                                                                                              • θstep=π/24 (in Radian mode) or 7.5 (in Degree mode)

                                                                                                                                                                                                              Only in Seq mode:

                                                                                                                                                                                                              • _n_Min=1
                                                                                                                                                                                                              • _n_Max=10
                                                                                                                                                                                                              • PlotStart=1
                                                                                                                                                                                                              • PlotStep=1

                                                                                                                                                                                                              These settings are often useful as a "lowest common denominator" that will work fairly well for all graphs.

                                                                                                                                                                                                              Advanced Uses

                                                                                                                                                                                                              ZStandard is often used before commands such as ZSquare or ZInteger in programs. This serves two purposes: it makes sure that the center of the screen for ZSquare and ZInteger is (0,0), and it ensures that the graph screen is cleared without having to resort to ClrDraw (because with two different zooms in a row, the window settings have to change at least once, which means the graph will have to be regraphed)

                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                              • ERR:INVALID occurs if this command is used outside a program.

                                                                                                                                                                                                              Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan.

                                                                                                                                                                                                              History

                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                              TI-82 1.0 Added
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                                                                                                                                                                                                              • FR: ZTmax

                                                                                                                                                                                                              ZTmax

                                                                                                                                                                                                              Overview

                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                              ZTmax

                                                                                                                                                                                                              Description

                                                                                                                                                                                                              Examples

                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                              code 1

                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                              code 2

                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                              History

                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                              TI-82 1.0 Added
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                                                                                                                                                                                                              • FR: ZTmin

                                                                                                                                                                                                              ZTmin

                                                                                                                                                                                                              Overview

                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                              ZTmin

                                                                                                                                                                                                              Description

                                                                                                                                                                                                              Examples

                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                              code 1

                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                              code 2

                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                              History

                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                              TI-82 1.0 Added
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                                                                                                                                                                                                              • FR: ZTrig

                                                                                                                                                                                                              ZTrig

                                                                                                                                                                                                              Overview

                                                                                                                                                                                                              Replots the functions immediately, updating the window variables to preset values for plotting trig functions.

                                                                                                                                                                                                              Availability: Token only available from within the Basic editor.

                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                              ZTrig

                                                                                                                                                                                                              Location

                                                                                                                                                                                                              zoom, ZOOM, 7:ZTrig

                                                                                                                                                                                                              Description

                                                                                                                                                                                                              The ZTrig command sets the screen to a special friendly window useful for trigonometric calculations. Unlike the ZDecimal and ZInteger commands, for which the distance between two pixels is a short decimal or integer, ZTrig sets the horizontal distance between two pixels to be π/24 (in Radian mode) or 7.5 (in Degree mode) . The specific changes ZTrig makes are:

                                                                                                                                                                                                              • Xmin=-352.5° or -47/24πʳ
                                                                                                                                                                                                              • Xmax=352.5° or 47/24πr
                                                                                                                                                                                                              • Xscl=90° or π/2r
                                                                                                                                                                                                              • Ymin=-4
                                                                                                                                                                                                              • Ymax=4
                                                                                                                                                                                                              • Yscl=1

                                                                                                                                                                                                              Although this window is not quite square (and therefore, distances in the X and Y direction are not exactly equally proportioned), it is quite close, when in Radian mode. In a square window (such as the output of ZSquare), Ymax would have to be 31/24π, which is approximately 4.05789. As you can see, the value of 4 that ZTrig uses is not too far off.

                                                                                                                                                                                                              Advanced Uses

                                                                                                                                                                                                              In theory, ZTrig should be quite useful in graphing trigonometric functions, since the calculated points would fall exactly on important angles; for example, it would graph the asymptotes of Y=tan(X) correctly. This is actually only true when in Degree mode. In Radian mode, due to round-off error, the pixels far away from the origin do not exactly correspond to rational multiples of π. For example, the pixel which was supposed to correspond to π/2 actually has a value of .5000000001*π, which is enough to make this command mostly useless.

                                                                                                                                                                                                              However, in G-T mode, the size that the graph takes up on the screen is different, and ZTrig uses the same values, unlike ZDecimal.

                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                              • ERR:INVALID occurs if this command is used outside a program (but not if the menu option is used, of course).

                                                                                                                                                                                                              See Also

                                                                                                                                                                                                              Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Myles_Zadok.

                                                                                                                                                                                                              History

                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                              TI-82 1.0 Added
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                                                                                                                                                                                                              • FR: ZTstep

                                                                                                                                                                                                              ZTstep

                                                                                                                                                                                                              Overview

                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                              ZTstep

                                                                                                                                                                                                              Description

                                                                                                                                                                                                              Examples

                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                              code 1

                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                              code 2

                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                              History

                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                              TI-82 1.0 Added
                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                              Hex Value $6313
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                                                                                                                                                                                                              • FR: ZXmax

                                                                                                                                                                                                              ZXmax

                                                                                                                                                                                                              Overview

                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                              ZXmax

                                                                                                                                                                                                              Description

                                                                                                                                                                                                              Examples

                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                              code 1

                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                              code 2

                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                              History

                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                              TI-82 1.0 Added
                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                              Hex Value $6312
                                                                                                                                                                                                              Categories
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                                                                                                                                                                                                              • FR: ZXmin

                                                                                                                                                                                                              ZXmin

                                                                                                                                                                                                              Overview

                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                              ZXmin

                                                                                                                                                                                                              Description

                                                                                                                                                                                                              Examples

                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                              code 1

                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                              code 2

                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                              History

                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                              TI-82 1.0 Added
                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                              Hex Value $6337
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                                                                                                                                                                                                              • FR: ZXres

                                                                                                                                                                                                              ZXres

                                                                                                                                                                                                              Overview

                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                              ZXres

                                                                                                                                                                                                              Description

                                                                                                                                                                                                              Examples

                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                              code 1

                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                              code 2

                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                              History

                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                              TI-83 0.01013 Added
                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                              Hex Value $6300
                                                                                                                                                                                                              Categories
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                                                                                                                                                                                                              • FR: ZXscl

                                                                                                                                                                                                              ZXscl

                                                                                                                                                                                                              Overview

                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                              ZXscl

                                                                                                                                                                                                              Description

                                                                                                                                                                                                              Examples

                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                              code 1

                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                              code 2

                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                              History

                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                              TI-82 1.0 Added
                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                              Hex Value $6315
                                                                                                                                                                                                              Categories
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                                                                                                                                                                                                              • FR: ZYmax

                                                                                                                                                                                                              ZYmax

                                                                                                                                                                                                              Overview

                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                              ZYmax

                                                                                                                                                                                                              Description

                                                                                                                                                                                                              Examples

                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                              code 1

                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                              code 2

                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                              History

                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                              TI-82 1.0 Added
                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                              Hex Value $6314
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                                                                                                                                                                                                              • FR: ZYmin

                                                                                                                                                                                                              ZYmin

                                                                                                                                                                                                              Overview

                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                              ZYmin

                                                                                                                                                                                                              Description

                                                                                                                                                                                                              Examples

                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                              code 1

                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                              code 2

                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                              History

                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                              TI-82 1.0 Added
                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                              Hex Value $6301
                                                                                                                                                                                                              Categories
                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                              • FR: ZYscl

                                                                                                                                                                                                              ZYscl

                                                                                                                                                                                                              Overview

                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                              ZYscl

                                                                                                                                                                                                              Description

                                                                                                                                                                                                              Examples

                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                              code 1

                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                              code 2

                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                              History

                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                              TI-82 1.0 Added
                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                              Hex Value $631E
                                                                                                                                                                                                              Categories
                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                              • FR: Z𝑛Max

                                                                                                                                                                                                              Z𝑛Max

                                                                                                                                                                                                              Overview

                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                              Z𝑛Max

                                                                                                                                                                                                              Description

                                                                                                                                                                                                              Examples

                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                              code 1

                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                              code 2

                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                              History

                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                              TI-82 1.0 Added
                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                              Hex Value $6320
                                                                                                                                                                                                              Categories
                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                              • FR: Z𝑛Min

                                                                                                                                                                                                              Z𝑛Min

                                                                                                                                                                                                              Overview

                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                              Z𝑛Min

                                                                                                                                                                                                              Description

                                                                                                                                                                                                              Examples

                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                              code 1

                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                              code 2

                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                              History

                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                              TI-82 1.0 Added
                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                              Hex Value $89
                                                                                                                                                                                                              Categories
                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                              • FR: Zoom +

                                                                                                                                                                                                              Zoom In

                                                                                                                                                                                                              Overview

                                                                                                                                                                                                              Magnifies the part of the graph that surrounds the cursor location.

                                                                                                                                                                                                              Availability: Token only available from within the Basic editor.

                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                              Zoom In

                                                                                                                                                                                                              Location

                                                                                                                                                                                                              zoom, ZOOM, 2:Zoom In

                                                                                                                                                                                                              Description

                                                                                                                                                                                                              Outside a program, the Zoom In tool allows you to pick a point on the graph screen and change the graphing window to a smaller one centered at that point. The Zoom In command, used in a program, also changes the graphing window to a smaller one, but doesn't let you pick a point — it uses the center of the screen.

                                                                                                                                                                                                              The variables XFact and YFact are used to determine how much the graphing window changes: the total width of the screen, Xmax-Xmin, is divided by XFact, and the total height, Ymax-Ymin, is divided by YFact. Because you can't store a value less than 1 to either of these variables, the screen is guaranteed to get no larger.

                                                                                                                                                                                                              Aside from Xmin, Xmax, Ymin, and Ymax, no window variables are modified by this command (although ΔX and ΔY change as they are defined).

                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                              • ERR:INVALID occurs if this command is used outside a program.
                                                                                                                                                                                                              • ERR:WINDOW RANGE is thrown if the window is zoomed in beyond the level of the calculator's precision.

                                                                                                                                                                                                              Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan.

                                                                                                                                                                                                              History

                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                              TI-82 1.0 Added
                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                              Hex Value $8A
                                                                                                                                                                                                              Categories
                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                              • FR: Zoom -

                                                                                                                                                                                                              Zoom Out

                                                                                                                                                                                                              Overview

                                                                                                                                                                                                              Displays a greater portion of the graph, centered on the cursor location.

                                                                                                                                                                                                              Availability: Token only available from within the Basic editor.

                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                              Zoom Out

                                                                                                                                                                                                              Location

                                                                                                                                                                                                              zoom, ZOOM, 3:Zoom Out

                                                                                                                                                                                                              Description

                                                                                                                                                                                                              Outside a program, the Zoom Out tool allows you to pick a point on the graph screen and change the graphing window to a larger one centered at that point. The Zoom Out command, used in a program, also changes the graphing window to a larger one, but doesn't let you pick a point — it uses the center of the screen.

                                                                                                                                                                                                              The variables XFact and YFact are used to determine how much the graphing window changes: the total width of the screen, Xmax-Xmin, is multiplied by XFact, and the total height, Ymax-Ymin, is multiplied by YFact. Because you can't store a value less than 1 to either of these variables, the screen is guaranteed to get no smaller.

                                                                                                                                                                                                              Aside from Xmin, Xmax, Ymin, and Ymax, no window variables are modified by this command (although ΔX and ΔY change as they are defined).

                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                              • ERR:INVALID occurs if this command is used outside a program.
                                                                                                                                                                                                              • ERR:ZOOM is thrown if an overflow occurs calculating the new window dimensions (the window is too big)

                                                                                                                                                                                                              Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan.

                                                                                                                                                                                                              History

                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                              TI-82 1.0 Added
                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                              Hex Value $BB65
                                                                                                                                                                                                              Categories
                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                              • FR: ZminMax

                                                                                                                                                                                                              ZoomFit

                                                                                                                                                                                                              Overview

                                                                                                                                                                                                              Recalculates Ymin and Ymax to include the minimum and maximum Y values, between Xmin and Xmax, of the selected functions and replots the functions.

                                                                                                                                                                                                              Availability: Token only available from within the Basic editor.

                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                              ZoomFit

                                                                                                                                                                                                              Location

                                                                                                                                                                                                              zoom, ZOOM, 0:ZoomFit

                                                                                                                                                                                                              Description

                                                                                                                                                                                                              The ZoomFit zooms to the smallest window that contains all points of the currently graphed equations. In Func mode, this means that it calculates the minimum and maximum Y-value for the current Xmin to Xmax range, and sets Ymin and Ymax to those values (Xmin and Xmax remain unchanged). In other graphing modes, this process is done for both X and Y over the range of T, θ, or n.

                                                                                                                                                                                                              Optimization

                                                                                                                                                                                                              When graphing an equation with ZoomFit, the calculator will first calculate all points to find the minimum and maximum, then calculate all the points again to graph it. This can be time consuming if the equation is very complicated, and in that case doing part of the process manually might be faster if you reuse the points.

                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                              • ERR:INVALID is thrown if this command is using outside a program (although the menu option, of course, is fine).
                                                                                                                                                                                                              • ERR:WINDOW RANGE is thrown when the window ends up being empty (if the function is constant, for example)

                                                                                                                                                                                                              Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, HJTP.

                                                                                                                                                                                                              History

                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                              TI-83 1.010 Added
                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                              Hex Value $90
                                                                                                                                                                                                              Categories
                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                              • FR: ZoomRpl

                                                                                                                                                                                                              ZoomRcl

                                                                                                                                                                                                              Overview

                                                                                                                                                                                                              Graphs the selected functions in a user-defined viewing window.

                                                                                                                                                                                                              Availability: Token only available from within the Basic editor.

                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                              ZoomRcl

                                                                                                                                                                                                              Location

                                                                                                                                                                                                              zoom, MEMORY, 3:ZoomRcl

                                                                                                                                                                                                              Description

                                                                                                                                                                                                              The ZoomRcl command restores a backup of the window settings previously saved by ZoomSto — this backup is stored in special variables found in the VARS>Zoom… menu, which are distinguished by a Z in front of their name. For example, Xmin is restored from ZXmin, PlotStart is restored from ZPlotStart, etc.

                                                                                                                                                                                                              Only those settings are restored that apply to the current graphing mode (that is, those that you can see in the window screen). And if no backup had been made, then the default settings are restored to (see ZStandard).

                                                                                                                                                                                                              One source of confusion with this command can be the fact that ZoomSto and ZoomRcl only deal with the current graphing mode (and don't touch settings from other graphing modes), but some window variables are shared by graphing modes. So some saved zoom variables only applicable to one mode, such as ZTmin, can be from older saves than those applicable to all modes, such as ZXmin.

                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                              • ERR:INVALID occurs if this command is used outside a program (but not if the menu option is used, of course).

                                                                                                                                                                                                              Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Kydapoot.

                                                                                                                                                                                                              History

                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                              TI-82 1.0 Added
                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                              Hex Value $8F
                                                                                                                                                                                                              Categories
                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                              • FR: ZoomStat

                                                                                                                                                                                                              ZoomStat

                                                                                                                                                                                                              Overview

                                                                                                                                                                                                              Redefines the viewing window so that all statistical data points are displayed.

                                                                                                                                                                                                              Availability: Token only available from within the Basic editor.

                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                              ZoomStat

                                                                                                                                                                                                              Location

                                                                                                                                                                                                              zoom, ZOOM, 9:ZoomStat

                                                                                                                                                                                                              Description

                                                                                                                                                                                                              The ZoomStat command command zooms to a graphing window that accurately represents all the currently defined stat plots (see the PlotN( commands). You can think of it as ZoomFit, but for plots rather than equations.

                                                                                                                                                                                                              The specific function of the command is as follows: first, the minimum and maximum X and Y coordinates that stat plots will be using are calculated. Xmin, Xmax, Ymin, and Ymax are calculated to fit all these coordinates plus a padding on either side. The padding is 10% of the unpadded range on the left and right (for Xmin and Xmax), and 17% of the unpadded range on the top and bottom (for Ymin and Ymax).

                                                                                                                                                                                                              Of course, the exact function varies slightly with the type of plot defined. For example, Ymin and Ymax will not be affected by Boxplot and Modboxplot plots, since they ignore Y-coordinates when graphing. Also, Histogram fitting is a bit trickier than others. Xscl and Yscl also are changed for histograms, though not for the other plots.

                                                                                                                                                                                                              For all plots except Histogram, ZoomStat will create a window with Xmin=Xmax (or Ymin=Ymax) if the X range (or Y range) of the data is 0. This will throw an ERR:WINDOW RANGE. If a Histogram causes this error, though, ERR:STAT is thrown, and then when you access the graphscreen ERR:WINDOW RANGE will occur.

                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                              • ERR:INVALID is thrown if this command is using outside a program (although the menu option, of course, is fine).
                                                                                                                                                                                                              • ERR:STAT is thrown when trying to ZoomFit to a Histogram with only one distinct number in the data list.
                                                                                                                                                                                                              • ERR:WINDOW RANGE is thrown when the window ends up being empty.

                                                                                                                                                                                                              Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, seb83, Zaphod Beeblebrox.

                                                                                                                                                                                                              History

                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                              TI-82 1.0 Added
                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                              Hex Value $92
                                                                                                                                                                                                              Categories
                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                              • FR: SauveFen

                                                                                                                                                                                                              ZoomSto

                                                                                                                                                                                                              Overview

                                                                                                                                                                                                              Immediately stores the current viewing window.

                                                                                                                                                                                                              Availability: Token only available from within the Basic editor.

                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                              ZoomSto

                                                                                                                                                                                                              Location

                                                                                                                                                                                                              zoom, MEMORY, 2:ZoomSto

                                                                                                                                                                                                              Description

                                                                                                                                                                                                              The ZoomSto command backs up all window settings applicable to the current graphing mode (those that are shown in the WINDOW menu) to backup variables used specifically for this command. These backup variables are found in the VARS>Zoom… menu, and are distinguished by a Z in front of their name. For example, Xmin is backed up to ZXmin, PlotStart is backed up to ZPlotStart, etc.

                                                                                                                                                                                                              Using ZoomRcl, these backup variables can be used to overwrite the current window settings, recalling the saved window.

                                                                                                                                                                                                              One source of confusion with this command can be the fact that ZoomSto and ZoomRcl only deal with the current graphing mode (and don't touch settings from other graphing modes), but some window variables are shared by graphing modes. So some saved zoom variables only applicable to one mode, such as ZTmin, can be from older saves than those applicable to all modes, such as ZXmin.

                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                              • ERR:INVALID occurs if this command is used outside a program (but not if the menu option is used, of course).

                                                                                                                                                                                                              Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Kydapoot.

                                                                                                                                                                                                              History

                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                              TI-82 1.0 Added
                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                              Hex Value $6317
                                                                                                                                                                                                              Categories
                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                              • FR: Zθmax

                                                                                                                                                                                                              Zθmax

                                                                                                                                                                                                              Overview

                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                              Zθmax

                                                                                                                                                                                                              Description

                                                                                                                                                                                                              Examples

                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                              code 1

                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                              code 2

                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                              History

                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                              TI-82 1.0 Added
                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                              Hex Value $6316
                                                                                                                                                                                                              Categories
                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                              • FR: Zθmin

                                                                                                                                                                                                              Zθmin

                                                                                                                                                                                                              Overview

                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                              Zθmin

                                                                                                                                                                                                              Description

                                                                                                                                                                                                              Examples

                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                              code 1

                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                              code 2

                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                              History

                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                              TI-82 1.0 Added
                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                              Hex Value $6325
                                                                                                                                                                                                              Categories
                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                              • FR: Zθstep

                                                                                                                                                                                                              Zθstep

                                                                                                                                                                                                              Overview

                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                              Zθstep

                                                                                                                                                                                                              Description

                                                                                                                                                                                                              Examples

                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                              code 1

                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                              code 2

                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                              History

                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                              TI-82 1.0 Added
                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                              Hex Value $6308
                                                                                                                                                                                                              Categories
                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                              • FR: Zu(𝑛Min)

                                                                                                                                                                                                              Zu(𝑛Min)

                                                                                                                                                                                                              Overview

                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                              Zu(𝑛Min)

                                                                                                                                                                                                              Description

                                                                                                                                                                                                              Examples

                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                              code 1

                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                              code 2

                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                              History

                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                              TI-82 1.0 ZUnStart added
                                                                                                                                                                                                              TI-83 0.01013 Renamed ZUnStart to Zu(𝑛Min)
                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                              Hex Value $6308
                                                                                                                                                                                                              Categories
                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                              • FR: Zu(𝑛Min)

                                                                                                                                                                                                              Zu(𝑛Min)

                                                                                                                                                                                                              Overview

                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                              Zu(𝑛Min)

                                                                                                                                                                                                              Description

                                                                                                                                                                                                              Examples

                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                              code 1

                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                              code 2

                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                              History

                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                              TI-82 1.0 ZUnStart added
                                                                                                                                                                                                              TI-83 0.01013 Renamed ZUnStart to Zu(𝑛Min)
                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                              Hex Value $6309
                                                                                                                                                                                                              Categories
                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                              • FR: Zv(𝑛Min)

                                                                                                                                                                                                              Zv(𝑛Min)

                                                                                                                                                                                                              Overview

                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                              Zv(𝑛Min)

                                                                                                                                                                                                              Description

                                                                                                                                                                                                              Examples

                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                              code 1

                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                              code 2

                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                              History

                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                              TI-82 1.0 ZVnStart added
                                                                                                                                                                                                              TI-83 0.01013 Renamed ZVnStart to Zv(𝑛Min)
                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                              Hex Value $6309
                                                                                                                                                                                                              Categories
                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                              • FR: Zv(𝑛Min)

                                                                                                                                                                                                              Zv(𝑛Min)

                                                                                                                                                                                                              Overview

                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                              Zv(𝑛Min)

                                                                                                                                                                                                              Description

                                                                                                                                                                                                              Examples

                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                              code 1

                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                              code 2

                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                              History

                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                              TI-82 1.0 ZVnStart added
                                                                                                                                                                                                              TI-83 0.01013 Renamed ZVnStart to Zv(𝑛Min)
                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                              Hex Value $6333
                                                                                                                                                                                                              Categories
                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                              • FR: Zw(𝑛Min)

                                                                                                                                                                                                              Zw(𝑛Min)

                                                                                                                                                                                                              Overview

                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                              Zw(𝑛Min)

                                                                                                                                                                                                              Description

                                                                                                                                                                                                              Examples

                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                              code 1

                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                              code 2

                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                              History

                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                              TI-83 0.01013 Added
                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                              Hex Value $6333
                                                                                                                                                                                                              Categories
                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                              • FR: Zw(𝑛Min)

                                                                                                                                                                                                              Zw(𝑛Min)

                                                                                                                                                                                                              Overview

                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                              Zw(𝑛Min)

                                                                                                                                                                                                              Description

                                                                                                                                                                                                              Examples

                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                              code 1

                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                              code 2

                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                              History

                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                              TI-83 0.01013 Added
                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                              Hex Value $6317
                                                                                                                                                                                                              Categories
                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                              • FR: Zθmax

                                                                                                                                                                                                              Zθmax

                                                                                                                                                                                                              Overview

                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                              Zθmax

                                                                                                                                                                                                              Description

                                                                                                                                                                                                              Examples

                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                              code 1

                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                              code 2

                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                              History

                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                              TI-82 1.0 Added
                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                              Hex Value $6316
                                                                                                                                                                                                              Categories
                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                              • FR: Zθmin

                                                                                                                                                                                                              Zθmin

                                                                                                                                                                                                              Overview

                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                              Zθmin

                                                                                                                                                                                                              Description

                                                                                                                                                                                                              Examples

                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                              code 1

                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                              code 2

                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                              History

                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                              TI-82 1.0 Added
                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                              Hex Value $6325
                                                                                                                                                                                                              Categories
                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                              • FR: Zθstep

                                                                                                                                                                                                              Zθstep

                                                                                                                                                                                                              Overview

                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                              Zθstep

                                                                                                                                                                                                              Description

                                                                                                                                                                                                              Examples

                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                              code 1

                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                              code 2

                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                              History

                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                              TI-82 1.0 Added
                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                              Hex Value $631E
                                                                                                                                                                                                              Categories
                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                              • FR: Z𝑛Max

                                                                                                                                                                                                              Z𝑛Max

                                                                                                                                                                                                              Overview

                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                              Z𝑛Max

                                                                                                                                                                                                              Description

                                                                                                                                                                                                              Examples

                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                              code 1

                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                              code 2

                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                              History

                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                              TI-82 1.0 Added
                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                              Hex Value $6320
                                                                                                                                                                                                              Categories
                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                              • FR: Z𝑛Min

                                                                                                                                                                                                              Z𝑛Min

                                                                                                                                                                                                              Overview

                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                              Z𝑛Min

                                                                                                                                                                                                              Description

                                                                                                                                                                                                              Examples

                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                              code 1

                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                              code 2

                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                              History

                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                              TI-82 1.0 Added
                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                              Hex Value $06
                                                                                                                                                                                                              Categories
                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                              • FR: [

                                                                                                                                                                                                              [

                                                                                                                                                                                                              Overview

                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                              [

                                                                                                                                                                                                              Description

                                                                                                                                                                                                              Examples

                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                              code 1

                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                              code 2

                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                              History

                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                              TI-82 1.0 Added
                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                              Hex Value $EF3B
                                                                                                                                                                                                              Categories
                                                                                                                                                                                                                Localizations
                                                                                                                                                                                                                • FR: AUTO

                                                                                                                                                                                                                AUTO

                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                Displays answers in a similar format as the input.

                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                AUTO

                                                                                                                                                                                                                Location

                                                                                                                                                                                                                mode, Answers: AUTO

                                                                                                                                                                                                                Description

                                                                                                                                                                                                                Examples

                                                                                                                                                                                                                Explanation 1

                                                                                                                                                                                                                code 1

                                                                                                                                                                                                                Explanation 2

                                                                                                                                                                                                                code 2

                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                Advanced Notes

                                                                                                                                                                                                                History

                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                TI-84+ 2.53 Added
                                                                                                                                                                                                                Property Value
                                                                                                                                                                                                                Hex Value $5C00
                                                                                                                                                                                                                Categories
                                                                                                                                                                                                                Localizations
                                                                                                                                                                                                                • FR: [A]

                                                                                                                                                                                                                [A]

                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                [A]

                                                                                                                                                                                                                Description

                                                                                                                                                                                                                Examples

                                                                                                                                                                                                                Explanation 1

                                                                                                                                                                                                                code 1

                                                                                                                                                                                                                Explanation 2

                                                                                                                                                                                                                code 2

                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                Advanced Notes

                                                                                                                                                                                                                History

                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                TI-82 1.0 Added
                                                                                                                                                                                                                Property Value
                                                                                                                                                                                                                Hex Value $5C01
                                                                                                                                                                                                                Categories
                                                                                                                                                                                                                Localizations
                                                                                                                                                                                                                • FR: [B]

                                                                                                                                                                                                                [B]

                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                [B]

                                                                                                                                                                                                                Description

                                                                                                                                                                                                                Examples

                                                                                                                                                                                                                Explanation 1

                                                                                                                                                                                                                code 1

                                                                                                                                                                                                                Explanation 2

                                                                                                                                                                                                                code 2

                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                Advanced Notes

                                                                                                                                                                                                                History

                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                TI-82 1.0 Added
                                                                                                                                                                                                                Property Value
                                                                                                                                                                                                                Hex Value $EF38
                                                                                                                                                                                                                Categories
                                                                                                                                                                                                                  Localizations
                                                                                                                                                                                                                  • FR: CLASSIC

                                                                                                                                                                                                                  CLASSIC

                                                                                                                                                                                                                  Overview

                                                                                                                                                                                                                  Displays inputs and outputs on a single line, such as 1/2+3/4.

                                                                                                                                                                                                                  Availability: Token available everywhere.

                                                                                                                                                                                                                  Syntax

                                                                                                                                                                                                                  CLASSIC

                                                                                                                                                                                                                  Location

                                                                                                                                                                                                                  mode, CLASSIC

                                                                                                                                                                                                                  Description

                                                                                                                                                                                                                  CLASSIC will put the calculator into Classic mode as opposed to MathPrint mode. The Classic mode will make the calculator display everything as pre-MathPrint OS would, including input. For instance, rather than superscripting exponents as MathPrint mode would, Classic mode uses the simple caret syntax (^).

                                                                                                                                                                                                                  MathPrint mode:
                                                                                                                                                                                                                  24
                                                                                                                                                                                                                       16

                                                                                                                                                                                                                  Classic mode:
                                                                                                                                                                                                                  2^4
                                                                                                                                                                                                                       16

                                                                                                                                                                                                                  Advanced Uses

                                                                                                                                                                                                                  When in Classic mode, text and numbers are displayed much faster on the home screen and the function menus load faster. This can be useful in games that use the home screen, or just with calculations in general.

                                                                                                                                                                                                                  Source: parts of this page were written by the following TI|BD contributors: ccrh2009, jonbush, Kydapoot, lirtosiast, Myles_Zadok, Timothy Foster.

                                                                                                                                                                                                                  History

                                                                                                                                                                                                                  Calculator OS Version Description
                                                                                                                                                                                                                  TI-84+ 2.53 Added
                                                                                                                                                                                                                  Property Value
                                                                                                                                                                                                                  Hex Value $5C02
                                                                                                                                                                                                                  Categories
                                                                                                                                                                                                                  Localizations
                                                                                                                                                                                                                  • FR: [C]

                                                                                                                                                                                                                  [C]

                                                                                                                                                                                                                  Overview

                                                                                                                                                                                                                  Syntax

                                                                                                                                                                                                                  [C]

                                                                                                                                                                                                                  Description

                                                                                                                                                                                                                  Examples

                                                                                                                                                                                                                  Explanation 1

                                                                                                                                                                                                                  code 1

                                                                                                                                                                                                                  Explanation 2

                                                                                                                                                                                                                  code 2

                                                                                                                                                                                                                  Error Conditions

                                                                                                                                                                                                                  Advanced Notes

                                                                                                                                                                                                                  History

                                                                                                                                                                                                                  Calculator OS Version Description
                                                                                                                                                                                                                  TI-82 1.0 Added
                                                                                                                                                                                                                  Property Value
                                                                                                                                                                                                                  Hex Value $BB6D
                                                                                                                                                                                                                  Categories
                                                                                                                                                                                                                  Localizations
                                                                                                                                                                                                                  • FR: [CompiledAsm83P]

                                                                                                                                                                                                                  [CompiledAsm83P]

                                                                                                                                                                                                                  Overview

                                                                                                                                                                                                                  Syntax

                                                                                                                                                                                                                  [CompiledAsm83P]

                                                                                                                                                                                                                  Description

                                                                                                                                                                                                                  Examples

                                                                                                                                                                                                                  Explanation 1

                                                                                                                                                                                                                  code 1

                                                                                                                                                                                                                  Explanation 2

                                                                                                                                                                                                                  code 2

                                                                                                                                                                                                                  Error Conditions

                                                                                                                                                                                                                  Advanced Notes

                                                                                                                                                                                                                  History

                                                                                                                                                                                                                  Calculator OS Version Description
                                                                                                                                                                                                                  Property Value
                                                                                                                                                                                                                  Hex Value $EF69
                                                                                                                                                                                                                  Categories
                                                                                                                                                                                                                  Localizations
                                                                                                                                                                                                                  • FR: [CompiledAsm84C]

                                                                                                                                                                                                                  [CompiledAsm84C]

                                                                                                                                                                                                                  Overview

                                                                                                                                                                                                                  Syntax

                                                                                                                                                                                                                  [CompiledAsm84C]

                                                                                                                                                                                                                  Description

                                                                                                                                                                                                                  Examples

                                                                                                                                                                                                                  Explanation 1

                                                                                                                                                                                                                  code 1

                                                                                                                                                                                                                  Explanation 2

                                                                                                                                                                                                                  code 2

                                                                                                                                                                                                                  Error Conditions

                                                                                                                                                                                                                  Advanced Notes

                                                                                                                                                                                                                  History

                                                                                                                                                                                                                  Calculator OS Version Description
                                                                                                                                                                                                                  Property Value
                                                                                                                                                                                                                  Hex Value $EF7B
                                                                                                                                                                                                                  Categories
                                                                                                                                                                                                                  Localizations
                                                                                                                                                                                                                  • FR: [CompiledAsmCE]

                                                                                                                                                                                                                  [CompiledAsmCE]

                                                                                                                                                                                                                  Overview

                                                                                                                                                                                                                  Syntax

                                                                                                                                                                                                                  [CompiledAsmCE]

                                                                                                                                                                                                                  Description

                                                                                                                                                                                                                  Examples

                                                                                                                                                                                                                  Explanation 1

                                                                                                                                                                                                                  code 1

                                                                                                                                                                                                                  Explanation 2

                                                                                                                                                                                                                  code 2

                                                                                                                                                                                                                  Error Conditions

                                                                                                                                                                                                                  Advanced Notes

                                                                                                                                                                                                                  History

                                                                                                                                                                                                                  Calculator OS Version Description
                                                                                                                                                                                                                  Property Value
                                                                                                                                                                                                                  Hex Value $EF3C
                                                                                                                                                                                                                  Categories
                                                                                                                                                                                                                    Localizations
                                                                                                                                                                                                                    • FR: DEC

                                                                                                                                                                                                                    DEC

                                                                                                                                                                                                                    Overview

                                                                                                                                                                                                                    Displays answers as integers or decimal numbers.

                                                                                                                                                                                                                    Availability: Token available everywhere.

                                                                                                                                                                                                                    Syntax

                                                                                                                                                                                                                    DEC

                                                                                                                                                                                                                    Location

                                                                                                                                                                                                                    mode, Answers: DEC

                                                                                                                                                                                                                    Description

                                                                                                                                                                                                                    Examples

                                                                                                                                                                                                                    Explanation 1

                                                                                                                                                                                                                    code 1

                                                                                                                                                                                                                    Explanation 2

                                                                                                                                                                                                                    code 2

                                                                                                                                                                                                                    Error Conditions

                                                                                                                                                                                                                    Advanced Notes

                                                                                                                                                                                                                    History

                                                                                                                                                                                                                    Calculator OS Version Description
                                                                                                                                                                                                                    TI-84+ 2.53 Added
                                                                                                                                                                                                                    Property Value
                                                                                                                                                                                                                    Hex Value $5C03
                                                                                                                                                                                                                    Categories
                                                                                                                                                                                                                    Localizations
                                                                                                                                                                                                                    • FR: [D]

                                                                                                                                                                                                                    [D]

                                                                                                                                                                                                                    Overview

                                                                                                                                                                                                                    Syntax

                                                                                                                                                                                                                    [D]

                                                                                                                                                                                                                    Description

                                                                                                                                                                                                                    Examples

                                                                                                                                                                                                                    Explanation 1

                                                                                                                                                                                                                    code 1

                                                                                                                                                                                                                    Explanation 2

                                                                                                                                                                                                                    code 2

                                                                                                                                                                                                                    Error Conditions

                                                                                                                                                                                                                    Advanced Notes

                                                                                                                                                                                                                    History

                                                                                                                                                                                                                    Calculator OS Version Description
                                                                                                                                                                                                                    TI-82 1.0 Added
                                                                                                                                                                                                                    Property Value
                                                                                                                                                                                                                    Hex Value $BB31
                                                                                                                                                                                                                    Categories
                                                                                                                                                                                                                    Localizations
                                                                                                                                                                                                                    • FR: 𝑒

                                                                                                                                                                                                                    𝑒

                                                                                                                                                                                                                    Overview

                                                                                                                                                                                                                    Returns decimal approximation of the constant 𝑒.

                                                                                                                                                                                                                    Availability: Token available everywhere.

                                                                                                                                                                                                                    Syntax

                                                                                                                                                                                                                    𝑒

                                                                                                                                                                                                                    Location

                                                                                                                                                                                                                    2nd, e

                                                                                                                                                                                                                    Description

                                                                                                                                                                                                                    e is a constant on the TI-83 series calculators. The constant holds the approximate value of Euler's number, fairly important in calculus and other higher-level mathematics.

                                                                                                                                                                                                                    The approximate value, to as many digits as stored in the calculator, is 2.718281828459…

                                                                                                                                                                                                                    The main use of e is as the base of the exponential function 𝑒^( (which is also a separate function on the calculator), and its inverse, the natural logarithm ln(. From these functions, others such as the trigonometric functions (e.g. sin() and the hyperbolic functions (e.g. sinh() can be defined. In r𝑒^θ𝑖 mode, e is used in an alternate form of expressing complex numbers.

                                                                                                                                                                                                                    Important as the number e is, nine times out of ten you won't need the constant itself when using your calculator, but rather the 𝑒^( and ln( functions.

                                                                                                                                                                                                                    Source: parts of this page were written by the following TI|BD contributors: alexrudd, burr, DarkerLine, GoVegan, Myles_Zadok, simplethinker, Timothy Foster.

                                                                                                                                                                                                                    History

                                                                                                                                                                                                                    Calculator OS Version Description
                                                                                                                                                                                                                    TI-83 0.01013 Added
                                                                                                                                                                                                                    Property Value
                                                                                                                                                                                                                    Hex Value $5C04
                                                                                                                                                                                                                    Categories
                                                                                                                                                                                                                    Localizations
                                                                                                                                                                                                                    • FR: [E]

                                                                                                                                                                                                                    [E]

                                                                                                                                                                                                                    Overview

                                                                                                                                                                                                                    Syntax

                                                                                                                                                                                                                    [E]

                                                                                                                                                                                                                    Description

                                                                                                                                                                                                                    Examples

                                                                                                                                                                                                                    Explanation 1

                                                                                                                                                                                                                    code 1

                                                                                                                                                                                                                    Explanation 2

                                                                                                                                                                                                                    code 2

                                                                                                                                                                                                                    Error Conditions

                                                                                                                                                                                                                    Advanced Notes

                                                                                                                                                                                                                    History

                                                                                                                                                                                                                    Calculator OS Version Description
                                                                                                                                                                                                                    TI-82 1.0 Added
                                                                                                                                                                                                                    Property Value
                                                                                                                                                                                                                    Hex Value $EF3D
                                                                                                                                                                                                                    Categories
                                                                                                                                                                                                                    Localizations
                                                                                                                                                                                                                    • FR: FRAC-APPROX

                                                                                                                                                                                                                    FRAC-APPROX

                                                                                                                                                                                                                    Overview

                                                                                                                                                                                                                    Syntax

                                                                                                                                                                                                                    FRAC-APPROX

                                                                                                                                                                                                                    Description

                                                                                                                                                                                                                    Examples

                                                                                                                                                                                                                    Explanation 1

                                                                                                                                                                                                                    code 1

                                                                                                                                                                                                                    Explanation 2

                                                                                                                                                                                                                    code 2

                                                                                                                                                                                                                    Error Conditions

                                                                                                                                                                                                                    Advanced Notes

                                                                                                                                                                                                                    History

                                                                                                                                                                                                                    Calculator OS Version Description
                                                                                                                                                                                                                    TI-84+ 2.53 FRAC added
                                                                                                                                                                                                                    TI-84+CSE 4.0 Renamed FRAC to FRAC-APPROX
                                                                                                                                                                                                                    Property Value
                                                                                                                                                                                                                    Hex Value $5C05
                                                                                                                                                                                                                    Categories
                                                                                                                                                                                                                    Localizations
                                                                                                                                                                                                                    • FR: [F]

                                                                                                                                                                                                                    [F]

                                                                                                                                                                                                                    Overview

                                                                                                                                                                                                                    Syntax

                                                                                                                                                                                                                    [F]

                                                                                                                                                                                                                    Description

                                                                                                                                                                                                                    Examples

                                                                                                                                                                                                                    Explanation 1

                                                                                                                                                                                                                    code 1

                                                                                                                                                                                                                    Explanation 2

                                                                                                                                                                                                                    code 2

                                                                                                                                                                                                                    Error Conditions

                                                                                                                                                                                                                    Advanced Notes

                                                                                                                                                                                                                    History

                                                                                                                                                                                                                    Calculator OS Version Description
                                                                                                                                                                                                                    TI-83 0.01013 Added
                                                                                                                                                                                                                    Property Value
                                                                                                                                                                                                                    Hex Value $5C06
                                                                                                                                                                                                                    Categories
                                                                                                                                                                                                                    Localizations
                                                                                                                                                                                                                    • FR: [G]

                                                                                                                                                                                                                    [G]

                                                                                                                                                                                                                    Overview

                                                                                                                                                                                                                    Syntax

                                                                                                                                                                                                                    [G]

                                                                                                                                                                                                                    Description

                                                                                                                                                                                                                    Examples

                                                                                                                                                                                                                    Explanation 1

                                                                                                                                                                                                                    code 1

                                                                                                                                                                                                                    Explanation 2

                                                                                                                                                                                                                    code 2

                                                                                                                                                                                                                    Error Conditions

                                                                                                                                                                                                                    Advanced Notes

                                                                                                                                                                                                                    History

                                                                                                                                                                                                                    Calculator OS Version Description
                                                                                                                                                                                                                    TI-83 0.01013 Added
                                                                                                                                                                                                                    Property Value
                                                                                                                                                                                                                    Hex Value $5C07
                                                                                                                                                                                                                    Categories
                                                                                                                                                                                                                    Localizations
                                                                                                                                                                                                                    • FR: [H]
                                                                                                                                                                                                                    [H]

                                                                                                                                                                                                                    Overview

                                                                                                                                                                                                                    Syntax

                                                                                                                                                                                                                    [H]

                                                                                                                                                                                                                    Description

                                                                                                                                                                                                                    Examples

                                                                                                                                                                                                                    Explanation 1

                                                                                                                                                                                                                    code 1

                                                                                                                                                                                                                    Explanation 2

                                                                                                                                                                                                                    code 2

                                                                                                                                                                                                                    Error Conditions

                                                                                                                                                                                                                    Advanced Notes

                                                                                                                                                                                                                    History

                                                                                                                                                                                                                    Calculator OS Version Description
                                                                                                                                                                                                                    TI-83 0.01013 Added
                                                                                                                                                                                                                    Property Value
                                                                                                                                                                                                                    Hex Value $2C
                                                                                                                                                                                                                    Categories
                                                                                                                                                                                                                    Localizations
                                                                                                                                                                                                                    • FR: 𝑖

                                                                                                                                                                                                                    𝑖

                                                                                                                                                                                                                    Overview

                                                                                                                                                                                                                    Returns the complex number i.

                                                                                                                                                                                                                    Comment:Complex i

                                                                                                                                                                                                                    Availability: Token available everywhere.

                                                                                                                                                                                                                    Syntax

                                                                                                                                                                                                                    i

                                                                                                                                                                                                                    Location

                                                                                                                                                                                                                    2nd, 𝑖

                                                                                                                                                                                                                    Description

                                                                                                                                                                                                                    The 𝑖 symbol is short for √(-1), and is used for complex numbers in algebra and complex analysis. On the calculator, entering 𝑖 will not cause an error, even in Real mode, but operations that result in a complex number (such as taking the square root of a negative number) will. If you're dealing with complex numbers, then, it's best to switch to a+b𝑖 or r𝑒^θ𝑖 mode.

                                                                                                                                                                                                                    Advanced Uses

                                                                                                                                                                                                                    By using 𝑖 in a calculation, the calculator switches to complex number mode to do it, even if in Real mode. So √(-1) will throw an ERR:NONREAL ANS, but √(0𝑖-1) will not (even though it's the same number). This can be used to force calculations to be done using complex numbers regardless of the mode setting — usually by adding or subtracting 0𝑖, although more clever ways can be found.

                                                                                                                                                                                                                    A good example of this technique is our Quadratic Formula routine.

                                                                                                                                                                                                                    See Also

                                                                                                                                                                                                                    Source: parts of this page were written by the following TI|BD contributors: burr, CloudVariable, DarkerLine, GoVegan.

                                                                                                                                                                                                                    History

                                                                                                                                                                                                                    Calculator OS Version Description
                                                                                                                                                                                                                    TI-82 1.0 Added
                                                                                                                                                                                                                    Property Value
                                                                                                                                                                                                                    Hex Value $5C08
                                                                                                                                                                                                                    Categories
                                                                                                                                                                                                                    Localizations
                                                                                                                                                                                                                    • FR: [I]

                                                                                                                                                                                                                    [I]

                                                                                                                                                                                                                    Overview

                                                                                                                                                                                                                    Syntax

                                                                                                                                                                                                                    [I]

                                                                                                                                                                                                                    Description

                                                                                                                                                                                                                    Examples

                                                                                                                                                                                                                    Explanation 1

                                                                                                                                                                                                                    code 1

                                                                                                                                                                                                                    Explanation 2

                                                                                                                                                                                                                    code 2

                                                                                                                                                                                                                    Error Conditions

                                                                                                                                                                                                                    Advanced Notes

                                                                                                                                                                                                                    History

                                                                                                                                                                                                                    Calculator OS Version Description
                                                                                                                                                                                                                    TI-83 0.01013 Added
                                                                                                                                                                                                                    Property Value
                                                                                                                                                                                                                    Hex Value $5C09
                                                                                                                                                                                                                    Categories
                                                                                                                                                                                                                    Localizations
                                                                                                                                                                                                                    • FR: [J]

                                                                                                                                                                                                                    [J]

                                                                                                                                                                                                                    Overview

                                                                                                                                                                                                                    Syntax

                                                                                                                                                                                                                    [J]

                                                                                                                                                                                                                    Description

                                                                                                                                                                                                                    Examples

                                                                                                                                                                                                                    Explanation 1

                                                                                                                                                                                                                    code 1

                                                                                                                                                                                                                    Explanation 2

                                                                                                                                                                                                                    code 2

                                                                                                                                                                                                                    Error Conditions

                                                                                                                                                                                                                    Advanced Notes

                                                                                                                                                                                                                    History

                                                                                                                                                                                                                    Calculator OS Version Description
                                                                                                                                                                                                                    TI-83 0.01013 Added
                                                                                                                                                                                                                    Property Value
                                                                                                                                                                                                                    Hex Value $EF37
                                                                                                                                                                                                                    Categories
                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                      • FR: MATHPRINT

                                                                                                                                                                                                                      MATHPRINT

                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                      Displays most entries and answers the way they are displayed in textbooks, such as .

                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                      MATHPRINT

                                                                                                                                                                                                                      Location

                                                                                                                                                                                                                      mode

                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                      MATHPRINT will put the calculator into Mathprint mode as opposed to Classic mode. In MathPrint mode, enhanced homescreen input formatting is available. The Classic mode will make the calculator display everything as a calculator of lower OS would, including input. For instance, rather than superscripting exponents as Mathprint mode would, Classic mode uses the simple caret syntax (^).

                                                                                                                                                                                                                      Mathprint mode:
                                                                                                                                                                                                                      24
                                                                                                                                                                                                                           16

                                                                                                                                                                                                                      Classic mode:
                                                                                                                                                                                                                      2^4
                                                                                                                                                                                                                           16

                                                                                                                                                                                                                      When in Mathprint mode, text and numbers are displayed much slower than classic on the home screen and the function menus load slower. This can be inconvenient in games that use the home screen, but can also make solving equations that involve fractions and exponents easier as the numbers are in their correct positions and are the appropriate size.

                                                                                                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: burr, jonbush, Kydapoot.

                                                                                                                                                                                                                      History

                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                      TI-84+ 2.53 Added
                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                      Hex Value $6213
                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                      • FR: [Med]

                                                                                                                                                                                                                      [Med]

                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                      [Med]

                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                      History

                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                      Hex Value $6214
                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                      • FR: Q₁

                                                                                                                                                                                                                      Q₁

                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                      Q₁

                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                      History

                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                      Hex Value $6215
                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                      • FR: Q₃

                                                                                                                                                                                                                      Q₃

                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                      Q₃

                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                      History

                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                      Hex Value $6236
                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                      • FR: R²

                                                                                                                                                                                                                      R²

                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                      R²

                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                      History

                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                      Hex Value $6201
                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                      • FR: RegEQ

                                                                                                                                                                                                                      RegEQ

                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                      RegEQ

                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                      History

                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                      Hex Value $EF40
                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                        Localizations
                                                                                                                                                                                                                        • FR: STATWIZARD OFF

                                                                                                                                                                                                                        STATWIZARD OFF

                                                                                                                                                                                                                        Overview

                                                                                                                                                                                                                        Disables wizard syntax help for statistical commands, distributions, and seq(.

                                                                                                                                                                                                                        Availability: Token available everywhere.

                                                                                                                                                                                                                        Syntax

                                                                                                                                                                                                                        STATWIZARD OFF

                                                                                                                                                                                                                        Location

                                                                                                                                                                                                                        2nd, catalog, STATWIZARD OFF

                                                                                                                                                                                                                        Description

                                                                                                                                                                                                                        Examples

                                                                                                                                                                                                                        Explanation 1

                                                                                                                                                                                                                        code 1

                                                                                                                                                                                                                        Explanation 2

                                                                                                                                                                                                                        code 2

                                                                                                                                                                                                                        Error Conditions

                                                                                                                                                                                                                        Advanced Notes

                                                                                                                                                                                                                        History

                                                                                                                                                                                                                        Calculator OS Version Description
                                                                                                                                                                                                                        TI-84+ 2.55 Added
                                                                                                                                                                                                                        Property Value
                                                                                                                                                                                                                        Hex Value $EF3F
                                                                                                                                                                                                                        Categories
                                                                                                                                                                                                                          Localizations
                                                                                                                                                                                                                          • FR: STATWIZARD ON

                                                                                                                                                                                                                          STATWIZARD ON

                                                                                                                                                                                                                          Overview

                                                                                                                                                                                                                          Enables wizard syntax help for statistical commands, distributions, and seq(.

                                                                                                                                                                                                                          Availability: Token available everywhere.

                                                                                                                                                                                                                          Syntax

                                                                                                                                                                                                                          STATWIZARD ON

                                                                                                                                                                                                                          Location

                                                                                                                                                                                                                          2nd, catalog, STATWIZARD ON(

                                                                                                                                                                                                                          Description

                                                                                                                                                                                                                          Examples

                                                                                                                                                                                                                          Explanation 1

                                                                                                                                                                                                                          code 1

                                                                                                                                                                                                                          Explanation 2

                                                                                                                                                                                                                          code 2

                                                                                                                                                                                                                          Error Conditions

                                                                                                                                                                                                                          Advanced Notes

                                                                                                                                                                                                                          History

                                                                                                                                                                                                                          Calculator OS Version Description
                                                                                                                                                                                                                          TI-84+ 2.55 Added
                                                                                                                                                                                                                          Property Value
                                                                                                                                                                                                                          Hex Value $6204
                                                                                                                                                                                                                          Categories
                                                                                                                                                                                                                          Localizations
                                                                                                                                                                                                                          • FR: Σx

                                                                                                                                                                                                                          Σx

                                                                                                                                                                                                                          Overview

                                                                                                                                                                                                                          Syntax

                                                                                                                                                                                                                          Σx

                                                                                                                                                                                                                          Description

                                                                                                                                                                                                                          Examples

                                                                                                                                                                                                                          Explanation 1

                                                                                                                                                                                                                          code 1

                                                                                                                                                                                                                          Explanation 2

                                                                                                                                                                                                                          code 2

                                                                                                                                                                                                                          Error Conditions

                                                                                                                                                                                                                          Advanced Notes

                                                                                                                                                                                                                          History

                                                                                                                                                                                                                          Calculator OS Version Description
                                                                                                                                                                                                                          TI-82 1.0 Added
                                                                                                                                                                                                                          Property Value
                                                                                                                                                                                                                          Hex Value $6205
                                                                                                                                                                                                                          Categories
                                                                                                                                                                                                                          Localizations
                                                                                                                                                                                                                          • FR: Σx²

                                                                                                                                                                                                                          Σx²

                                                                                                                                                                                                                          Overview

                                                                                                                                                                                                                          Syntax

                                                                                                                                                                                                                          Σx²

                                                                                                                                                                                                                          Description

                                                                                                                                                                                                                          Examples

                                                                                                                                                                                                                          Explanation 1

                                                                                                                                                                                                                          code 1

                                                                                                                                                                                                                          Explanation 2

                                                                                                                                                                                                                          code 2

                                                                                                                                                                                                                          Error Conditions

                                                                                                                                                                                                                          Advanced Notes

                                                                                                                                                                                                                          History

                                                                                                                                                                                                                          Calculator OS Version Description
                                                                                                                                                                                                                          TI-82 1.0 Added
                                                                                                                                                                                                                          Property Value
                                                                                                                                                                                                                          Hex Value $6211
                                                                                                                                                                                                                          Categories
                                                                                                                                                                                                                          Localizations
                                                                                                                                                                                                                          • FR: Σxy

                                                                                                                                                                                                                          Σxy

                                                                                                                                                                                                                          Overview

                                                                                                                                                                                                                          Syntax

                                                                                                                                                                                                                          Σxy

                                                                                                                                                                                                                          Description

                                                                                                                                                                                                                          Examples

                                                                                                                                                                                                                          Explanation 1

                                                                                                                                                                                                                          code 1

                                                                                                                                                                                                                          Explanation 2

                                                                                                                                                                                                                          code 2

                                                                                                                                                                                                                          Error Conditions

                                                                                                                                                                                                                          Advanced Notes

                                                                                                                                                                                                                          History

                                                                                                                                                                                                                          Calculator OS Version Description
                                                                                                                                                                                                                          TI-82 1.0 Added
                                                                                                                                                                                                                          Property Value
                                                                                                                                                                                                                          Hex Value $620D
                                                                                                                                                                                                                          Categories
                                                                                                                                                                                                                          Localizations
                                                                                                                                                                                                                          • FR: Σy

                                                                                                                                                                                                                          Σy

                                                                                                                                                                                                                          Overview

                                                                                                                                                                                                                          Syntax

                                                                                                                                                                                                                          Σy

                                                                                                                                                                                                                          Description

                                                                                                                                                                                                                          Examples

                                                                                                                                                                                                                          Explanation 1

                                                                                                                                                                                                                          code 1

                                                                                                                                                                                                                          Explanation 2

                                                                                                                                                                                                                          code 2

                                                                                                                                                                                                                          Error Conditions

                                                                                                                                                                                                                          Advanced Notes

                                                                                                                                                                                                                          History

                                                                                                                                                                                                                          Calculator OS Version Description
                                                                                                                                                                                                                          TI-82 1.0 Added
                                                                                                                                                                                                                          Property Value
                                                                                                                                                                                                                          Hex Value $620E
                                                                                                                                                                                                                          Categories
                                                                                                                                                                                                                          Localizations
                                                                                                                                                                                                                          • FR: Σy²

                                                                                                                                                                                                                          Σy²

                                                                                                                                                                                                                          Overview

                                                                                                                                                                                                                          Syntax

                                                                                                                                                                                                                          Σy²

                                                                                                                                                                                                                          Description

                                                                                                                                                                                                                          Examples

                                                                                                                                                                                                                          Explanation 1

                                                                                                                                                                                                                          code 1

                                                                                                                                                                                                                          Explanation 2

                                                                                                                                                                                                                          code 2

                                                                                                                                                                                                                          Error Conditions

                                                                                                                                                                                                                          Advanced Notes

                                                                                                                                                                                                                          History

                                                                                                                                                                                                                          Calculator OS Version Description
                                                                                                                                                                                                                          TI-82 1.0 Added
                                                                                                                                                                                                                          Property Value
                                                                                                                                                                                                                          Hex Value $622C
                                                                                                                                                                                                                          Categories
                                                                                                                                                                                                                          Localizations
                                                                                                                                                                                                                          • FR: Éctypx₁

                                                                                                                                                                                                                          Sx₁

                                                                                                                                                                                                                          Overview

                                                                                                                                                                                                                          Syntax

                                                                                                                                                                                                                          Sx₁

                                                                                                                                                                                                                          Description

                                                                                                                                                                                                                          Examples

                                                                                                                                                                                                                          Explanation 1

                                                                                                                                                                                                                          code 1

                                                                                                                                                                                                                          Explanation 2

                                                                                                                                                                                                                          code 2

                                                                                                                                                                                                                          Error Conditions

                                                                                                                                                                                                                          Advanced Notes

                                                                                                                                                                                                                          History

                                                                                                                                                                                                                          Calculator OS Version Description
                                                                                                                                                                                                                          TI-82 1.0 Added
                                                                                                                                                                                                                          Property Value
                                                                                                                                                                                                                          Hex Value $622F
                                                                                                                                                                                                                          Categories
                                                                                                                                                                                                                          Localizations
                                                                                                                                                                                                                          • FR: Éctypx₂

                                                                                                                                                                                                                          Sx₂

                                                                                                                                                                                                                          Overview

                                                                                                                                                                                                                          Syntax

                                                                                                                                                                                                                          Sx₂

                                                                                                                                                                                                                          Description

                                                                                                                                                                                                                          Examples

                                                                                                                                                                                                                          Explanation 1

                                                                                                                                                                                                                          code 1

                                                                                                                                                                                                                          Explanation 2

                                                                                                                                                                                                                          code 2

                                                                                                                                                                                                                          Error Conditions

                                                                                                                                                                                                                          Advanced Notes

                                                                                                                                                                                                                          History

                                                                                                                                                                                                                          Calculator OS Version Description
                                                                                                                                                                                                                          TI-82 1.0 Added
                                                                                                                                                                                                                          Property Value
                                                                                                                                                                                                                          Hex Value $6206
                                                                                                                                                                                                                          Categories
                                                                                                                                                                                                                          Localizations
                                                                                                                                                                                                                          • FR: [Sx]

                                                                                                                                                                                                                          [Sx]

                                                                                                                                                                                                                          Overview

                                                                                                                                                                                                                          Syntax

                                                                                                                                                                                                                          [Sx]

                                                                                                                                                                                                                          Description

                                                                                                                                                                                                                          Examples

                                                                                                                                                                                                                          Explanation 1

                                                                                                                                                                                                                          code 1

                                                                                                                                                                                                                          Explanation 2

                                                                                                                                                                                                                          code 2

                                                                                                                                                                                                                          Error Conditions

                                                                                                                                                                                                                          Advanced Notes

                                                                                                                                                                                                                          History

                                                                                                                                                                                                                          Calculator OS Version Description
                                                                                                                                                                                                                          TI-82 1.0 Added
                                                                                                                                                                                                                          Property Value
                                                                                                                                                                                                                          Hex Value $6231
                                                                                                                                                                                                                          Categories
                                                                                                                                                                                                                          Localizations
                                                                                                                                                                                                                          • FR: Éctypxp

                                                                                                                                                                                                                          Sxp

                                                                                                                                                                                                                          Overview

                                                                                                                                                                                                                          Syntax

                                                                                                                                                                                                                          Sxp

                                                                                                                                                                                                                          Description

                                                                                                                                                                                                                          Examples

                                                                                                                                                                                                                          Explanation 1

                                                                                                                                                                                                                          code 1

                                                                                                                                                                                                                          Explanation 2

                                                                                                                                                                                                                          code 2

                                                                                                                                                                                                                          Error Conditions

                                                                                                                                                                                                                          Advanced Notes

                                                                                                                                                                                                                          History

                                                                                                                                                                                                                          Calculator OS Version Description
                                                                                                                                                                                                                          TI-82 1.0 Added
                                                                                                                                                                                                                          Property Value
                                                                                                                                                                                                                          Hex Value $620F
                                                                                                                                                                                                                          Categories
                                                                                                                                                                                                                          Localizations
                                                                                                                                                                                                                          • FR: [Sy]

                                                                                                                                                                                                                          [Sy]

                                                                                                                                                                                                                          Overview

                                                                                                                                                                                                                          Syntax

                                                                                                                                                                                                                          [Sy]

                                                                                                                                                                                                                          Description

                                                                                                                                                                                                                          Examples

                                                                                                                                                                                                                          Explanation 1

                                                                                                                                                                                                                          code 1

                                                                                                                                                                                                                          Explanation 2

                                                                                                                                                                                                                          code 2

                                                                                                                                                                                                                          Error Conditions

                                                                                                                                                                                                                          Advanced Notes

                                                                                                                                                                                                                          History

                                                                                                                                                                                                                          Calculator OS Version Description
                                                                                                                                                                                                                          TI-82 1.0 Added
                                                                                                                                                                                                                          Property Value
                                                                                                                                                                                                                          Hex Value $EF3A
                                                                                                                                                                                                                          Categories
                                                                                                                                                                                                                            Localizations
                                                                                                                                                                                                                            • FR: Un⁄d

                                                                                                                                                                                                                            Un⁄d

                                                                                                                                                                                                                            Overview

                                                                                                                                                                                                                            Displays results as a mixed number, if applicable.

                                                                                                                                                                                                                            Availability: Token available everywhere.

                                                                                                                                                                                                                            Syntax

                                                                                                                                                                                                                            Un/d

                                                                                                                                                                                                                            Location

                                                                                                                                                                                                                            math, NUMC: Un/d

                                                                                                                                                                                                                            Description

                                                                                                                                                                                                                            Un/d is a template that allows you to input a fraction with a whole number in front of it.
                                                                                                                                                                                                                            Un/d is accessible from most screens by pressing ALPHA and Y= then 2.
                                                                                                                                                                                                                            What this command does is that it adds the whole number to the fraction. It does not calculate a product but instead it calculates an addition.

                                                                                                                                                                                                                            Source: parts of this page were written by the following TI|BD contributors: burr, ccrh2009, DracoMhuuh.

                                                                                                                                                                                                                            History

                                                                                                                                                                                                                            Calculator OS Version Description
                                                                                                                                                                                                                            TI-84+ 2.53 Added
                                                                                                                                                                                                                            Property Value
                                                                                                                                                                                                                            Hex Value $6225
                                                                                                                                                                                                                            Categories
                                                                                                                                                                                                                            Localizations
                                                                                                                                                                                                                            • FR: χ²

                                                                                                                                                                                                                            χ²

                                                                                                                                                                                                                            Overview

                                                                                                                                                                                                                            Syntax

                                                                                                                                                                                                                            χ²

                                                                                                                                                                                                                            Description

                                                                                                                                                                                                                            Examples

                                                                                                                                                                                                                            Explanation 1

                                                                                                                                                                                                                            code 1

                                                                                                                                                                                                                            Explanation 2

                                                                                                                                                                                                                            code 2

                                                                                                                                                                                                                            Error Conditions

                                                                                                                                                                                                                            Advanced Notes

                                                                                                                                                                                                                            History

                                                                                                                                                                                                                            Calculator OS Version Description
                                                                                                                                                                                                                            TI-82 1.0 Added
                                                                                                                                                                                                                            Property Value
                                                                                                                                                                                                                            Hex Value $6227
                                                                                                                                                                                                                            Categories
                                                                                                                                                                                                                            Localizations
                                                                                                                                                                                                                            • FR: [df]

                                                                                                                                                                                                                            [df]

                                                                                                                                                                                                                            Overview

                                                                                                                                                                                                                            Syntax

                                                                                                                                                                                                                            [df]

                                                                                                                                                                                                                            Description

                                                                                                                                                                                                                            Examples

                                                                                                                                                                                                                            Explanation 1

                                                                                                                                                                                                                            code 1

                                                                                                                                                                                                                            Explanation 2

                                                                                                                                                                                                                            code 2

                                                                                                                                                                                                                            Error Conditions

                                                                                                                                                                                                                            Advanced Notes

                                                                                                                                                                                                                            History

                                                                                                                                                                                                                            Calculator OS Version Description
                                                                                                                                                                                                                            TI-82 1.0 Added
                                                                                                                                                                                                                            Property Value
                                                                                                                                                                                                                            Hex Value $623C
                                                                                                                                                                                                                            Categories
                                                                                                                                                                                                                            Localizations
                                                                                                                                                                                                                            • FR: [errorMS]

                                                                                                                                                                                                                            [errorMS]

                                                                                                                                                                                                                            Overview

                                                                                                                                                                                                                            Syntax

                                                                                                                                                                                                                            [errorMS]

                                                                                                                                                                                                                            Description

                                                                                                                                                                                                                            Examples

                                                                                                                                                                                                                            Explanation 1

                                                                                                                                                                                                                            code 1

                                                                                                                                                                                                                            Explanation 2

                                                                                                                                                                                                                            code 2

                                                                                                                                                                                                                            Error Conditions

                                                                                                                                                                                                                            Advanced Notes

                                                                                                                                                                                                                            History

                                                                                                                                                                                                                            Calculator OS Version Description
                                                                                                                                                                                                                            TI-82 1.0 Added
                                                                                                                                                                                                                            Property Value
                                                                                                                                                                                                                            Hex Value $623B
                                                                                                                                                                                                                            Categories
                                                                                                                                                                                                                            Localizations
                                                                                                                                                                                                                            • FR: [errorSS]

                                                                                                                                                                                                                            [errorSS]

                                                                                                                                                                                                                            Overview

                                                                                                                                                                                                                            Syntax

                                                                                                                                                                                                                            [errorSS]

                                                                                                                                                                                                                            Description

                                                                                                                                                                                                                            Examples

                                                                                                                                                                                                                            Explanation 1

                                                                                                                                                                                                                            code 1

                                                                                                                                                                                                                            Explanation 2

                                                                                                                                                                                                                            code 2

                                                                                                                                                                                                                            Error Conditions

                                                                                                                                                                                                                            Advanced Notes

                                                                                                                                                                                                                            History

                                                                                                                                                                                                                            Calculator OS Version Description
                                                                                                                                                                                                                            TI-82 1.0 Added
                                                                                                                                                                                                                            Property Value
                                                                                                                                                                                                                            Hex Value $623A
                                                                                                                                                                                                                            Categories
                                                                                                                                                                                                                            Localizations
                                                                                                                                                                                                                            • FR: [errordf]

                                                                                                                                                                                                                            [errordf]

                                                                                                                                                                                                                            Overview

                                                                                                                                                                                                                            Syntax

                                                                                                                                                                                                                            [errordf]

                                                                                                                                                                                                                            Description

                                                                                                                                                                                                                            Examples

                                                                                                                                                                                                                            Explanation 1

                                                                                                                                                                                                                            code 1

                                                                                                                                                                                                                            Explanation 2

                                                                                                                                                                                                                            code 2

                                                                                                                                                                                                                            Error Conditions

                                                                                                                                                                                                                            Advanced Notes

                                                                                                                                                                                                                            History

                                                                                                                                                                                                                            Calculator OS Version Description
                                                                                                                                                                                                                            TI-82 1.0 Added
                                                                                                                                                                                                                            Property Value
                                                                                                                                                                                                                            Hex Value $6239
                                                                                                                                                                                                                            Categories
                                                                                                                                                                                                                            Localizations
                                                                                                                                                                                                                            • FR: [factorMS]

                                                                                                                                                                                                                            [factorMS]

                                                                                                                                                                                                                            Overview

                                                                                                                                                                                                                            Syntax

                                                                                                                                                                                                                            [factorMS]

                                                                                                                                                                                                                            Description

                                                                                                                                                                                                                            Examples

                                                                                                                                                                                                                            Explanation 1

                                                                                                                                                                                                                            code 1

                                                                                                                                                                                                                            Explanation 2

                                                                                                                                                                                                                            code 2

                                                                                                                                                                                                                            Error Conditions

                                                                                                                                                                                                                            Advanced Notes

                                                                                                                                                                                                                            History

                                                                                                                                                                                                                            Calculator OS Version Description
                                                                                                                                                                                                                            TI-82 1.0 Added
                                                                                                                                                                                                                            Property Value
                                                                                                                                                                                                                            Hex Value $6238
                                                                                                                                                                                                                            Categories
                                                                                                                                                                                                                            Localizations
                                                                                                                                                                                                                            • FR: [factorSS]

                                                                                                                                                                                                                            [factorSS]

                                                                                                                                                                                                                            Overview

                                                                                                                                                                                                                            Syntax

                                                                                                                                                                                                                            [factorSS]

                                                                                                                                                                                                                            Description

                                                                                                                                                                                                                            Examples

                                                                                                                                                                                                                            Explanation 1

                                                                                                                                                                                                                            code 1

                                                                                                                                                                                                                            Explanation 2

                                                                                                                                                                                                                            code 2

                                                                                                                                                                                                                            Error Conditions

                                                                                                                                                                                                                            Advanced Notes

                                                                                                                                                                                                                            History

                                                                                                                                                                                                                            Calculator OS Version Description
                                                                                                                                                                                                                            TI-82 1.0 Added
                                                                                                                                                                                                                            Property Value
                                                                                                                                                                                                                            Hex Value $6237
                                                                                                                                                                                                                            Categories
                                                                                                                                                                                                                            Localizations
                                                                                                                                                                                                                            • FR: [factordf]

                                                                                                                                                                                                                            [factordf]

                                                                                                                                                                                                                            Overview

                                                                                                                                                                                                                            Syntax

                                                                                                                                                                                                                            [factordf]

                                                                                                                                                                                                                            Description

                                                                                                                                                                                                                            Examples

                                                                                                                                                                                                                            Explanation 1

                                                                                                                                                                                                                            code 1

                                                                                                                                                                                                                            Explanation 2

                                                                                                                                                                                                                            code 2

                                                                                                                                                                                                                            Error Conditions

                                                                                                                                                                                                                            Advanced Notes

                                                                                                                                                                                                                            History

                                                                                                                                                                                                                            Calculator OS Version Description
                                                                                                                                                                                                                            TI-82 1.0 Added
                                                                                                                                                                                                                            Property Value
                                                                                                                                                                                                                            Hex Value $6232
                                                                                                                                                                                                                            Categories
                                                                                                                                                                                                                            Localizations
                                                                                                                                                                                                                            • FR: borninf

                                                                                                                                                                                                                            lower

                                                                                                                                                                                                                            Overview

                                                                                                                                                                                                                            Availability: Token available everywhere.

                                                                                                                                                                                                                            Syntax

                                                                                                                                                                                                                            lower

                                                                                                                                                                                                                            Description

                                                                                                                                                                                                                            Examples

                                                                                                                                                                                                                            Explanation 1

                                                                                                                                                                                                                            code 1

                                                                                                                                                                                                                            Explanation 2

                                                                                                                                                                                                                            code 2

                                                                                                                                                                                                                            Error Conditions

                                                                                                                                                                                                                            Advanced Notes

                                                                                                                                                                                                                            History

                                                                                                                                                                                                                            Calculator OS Version Description
                                                                                                                                                                                                                            TI-82 1.0 Added
                                                                                                                                                                                                                            Property Value
                                                                                                                                                                                                                            Hex Value $6209
                                                                                                                                                                                                                            Categories
                                                                                                                                                                                                                            Localizations
                                                                                                                                                                                                                            • FR: [maxX]

                                                                                                                                                                                                                            [maxX]

                                                                                                                                                                                                                            Overview

                                                                                                                                                                                                                            Syntax

                                                                                                                                                                                                                            [maxX]

                                                                                                                                                                                                                            Description

                                                                                                                                                                                                                            Examples

                                                                                                                                                                                                                            Explanation 1

                                                                                                                                                                                                                            code 1

                                                                                                                                                                                                                            Explanation 2

                                                                                                                                                                                                                            code 2

                                                                                                                                                                                                                            Error Conditions

                                                                                                                                                                                                                            Advanced Notes

                                                                                                                                                                                                                            History

                                                                                                                                                                                                                            Calculator OS Version Description
                                                                                                                                                                                                                            TI-82 1.0 Added
                                                                                                                                                                                                                            Property Value
                                                                                                                                                                                                                            Hex Value $620B
                                                                                                                                                                                                                            Categories
                                                                                                                                                                                                                            Localizations
                                                                                                                                                                                                                            • FR: [maxY]

                                                                                                                                                                                                                            [maxY]

                                                                                                                                                                                                                            Overview

                                                                                                                                                                                                                            Syntax

                                                                                                                                                                                                                            [maxY]

                                                                                                                                                                                                                            Description

                                                                                                                                                                                                                            Examples

                                                                                                                                                                                                                            Explanation 1

                                                                                                                                                                                                                            code 1

                                                                                                                                                                                                                            Explanation 2

                                                                                                                                                                                                                            code 2

                                                                                                                                                                                                                            Error Conditions

                                                                                                                                                                                                                            Advanced Notes

                                                                                                                                                                                                                            History

                                                                                                                                                                                                                            Calculator OS Version Description
                                                                                                                                                                                                                            TI-82 1.0 Added
                                                                                                                                                                                                                            Property Value
                                                                                                                                                                                                                            Hex Value $6208
                                                                                                                                                                                                                            Categories
                                                                                                                                                                                                                            Localizations
                                                                                                                                                                                                                            • FR: [minX]

                                                                                                                                                                                                                            [minX]

                                                                                                                                                                                                                            Overview

                                                                                                                                                                                                                            Syntax

                                                                                                                                                                                                                            [minX]

                                                                                                                                                                                                                            Description

                                                                                                                                                                                                                            Examples

                                                                                                                                                                                                                            Explanation 1

                                                                                                                                                                                                                            code 1

                                                                                                                                                                                                                            Explanation 2

                                                                                                                                                                                                                            code 2

                                                                                                                                                                                                                            Error Conditions

                                                                                                                                                                                                                            Advanced Notes

                                                                                                                                                                                                                            History

                                                                                                                                                                                                                            Calculator OS Version Description
                                                                                                                                                                                                                            TI-82 1.0 Added
                                                                                                                                                                                                                            Property Value
                                                                                                                                                                                                                            Hex Value $620A
                                                                                                                                                                                                                            Categories
                                                                                                                                                                                                                            Localizations
                                                                                                                                                                                                                            • FR: [minY]

                                                                                                                                                                                                                            [minY]

                                                                                                                                                                                                                            Overview

                                                                                                                                                                                                                            Syntax

                                                                                                                                                                                                                            [minY]

                                                                                                                                                                                                                            Description

                                                                                                                                                                                                                            Examples

                                                                                                                                                                                                                            Explanation 1

                                                                                                                                                                                                                            code 1

                                                                                                                                                                                                                            Explanation 2

                                                                                                                                                                                                                            code 2

                                                                                                                                                                                                                            Error Conditions

                                                                                                                                                                                                                            Advanced Notes

                                                                                                                                                                                                                            History

                                                                                                                                                                                                                            Calculator OS Version Description
                                                                                                                                                                                                                            TI-82 1.0 Added
                                                                                                                                                                                                                            Property Value
                                                                                                                                                                                                                            Hex Value $622D
                                                                                                                                                                                                                            Categories
                                                                                                                                                                                                                            Localizations
                                                                                                                                                                                                                            • FR: n₁

                                                                                                                                                                                                                            n₁

                                                                                                                                                                                                                            Overview

                                                                                                                                                                                                                            Syntax

                                                                                                                                                                                                                            n₁

                                                                                                                                                                                                                            Description

                                                                                                                                                                                                                            Examples

                                                                                                                                                                                                                            Explanation 1

                                                                                                                                                                                                                            code 1

                                                                                                                                                                                                                            Explanation 2

                                                                                                                                                                                                                            code 2

                                                                                                                                                                                                                            Error Conditions

                                                                                                                                                                                                                            Advanced Notes

                                                                                                                                                                                                                            History

                                                                                                                                                                                                                            Calculator OS Version Description
                                                                                                                                                                                                                            TI-82 1.0 Added
                                                                                                                                                                                                                            Property Value
                                                                                                                                                                                                                            Hex Value $6230
                                                                                                                                                                                                                            Categories
                                                                                                                                                                                                                            Localizations
                                                                                                                                                                                                                            • FR: n₂

                                                                                                                                                                                                                            n₂

                                                                                                                                                                                                                            Overview

                                                                                                                                                                                                                            Syntax

                                                                                                                                                                                                                            n₂

                                                                                                                                                                                                                            Description

                                                                                                                                                                                                                            Examples

                                                                                                                                                                                                                            Explanation 1

                                                                                                                                                                                                                            code 1

                                                                                                                                                                                                                            Explanation 2

                                                                                                                                                                                                                            code 2

                                                                                                                                                                                                                            Error Conditions

                                                                                                                                                                                                                            Advanced Notes

                                                                                                                                                                                                                            History

                                                                                                                                                                                                                            Calculator OS Version Description
                                                                                                                                                                                                                            TI-82 1.0 Added
                                                                                                                                                                                                                            Property Value
                                                                                                                                                                                                                            Hex Value $6202
                                                                                                                                                                                                                            Categories
                                                                                                                                                                                                                            Localizations
                                                                                                                                                                                                                            • FR: n

                                                                                                                                                                                                                            n

                                                                                                                                                                                                                            Overview

                                                                                                                                                                                                                            Syntax

                                                                                                                                                                                                                            n

                                                                                                                                                                                                                            Description

                                                                                                                                                                                                                            Examples

                                                                                                                                                                                                                            Explanation 1

                                                                                                                                                                                                                            code 1

                                                                                                                                                                                                                            Explanation 2

                                                                                                                                                                                                                            code 2

                                                                                                                                                                                                                            Error Conditions

                                                                                                                                                                                                                            Advanced Notes

                                                                                                                                                                                                                            History

                                                                                                                                                                                                                            Calculator OS Version Description
                                                                                                                                                                                                                            TI-82 1.0 Added
                                                                                                                                                                                                                            Property Value
                                                                                                                                                                                                                            Hex Value $EF39
                                                                                                                                                                                                                            Categories
                                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                                              • FR: n⁄d

                                                                                                                                                                                                                              n⁄d

                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                              Displays results as a simple fraction.

                                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                              n/d

                                                                                                                                                                                                                              Location

                                                                                                                                                                                                                              alpha, F1, 1:n/d

                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                              n/d is the template for entering a simple fraction.
                                                                                                                                                                                                                              n/d is accessible by pressing ALPHA then Y= then enter.

                                                                                                                                                                                                                              Source: parts of this page were written by the following TI|BD contributors: ccrh2009.

                                                                                                                                                                                                                              History

                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                              TI-84+ 2.53 Added
                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                              Hex Value $6222
                                                                                                                                                                                                                              Categories
                                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                                              • FR: [p]

                                                                                                                                                                                                                              [p]

                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                              [p]

                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                                              code 1

                                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                                              code 2

                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                              History

                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                              TI-82 1.0 Added
                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                              Hex Value $6229
                                                                                                                                                                                                                              Categories
                                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                                              • FR: p̂₁

                                                                                                                                                                                                                              p̂₁

                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                              p̂₁

                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                                              code 1

                                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                                              code 2

                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                              History

                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                              TI-82 1.0 Added
                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                              Hex Value $622A
                                                                                                                                                                                                                              Categories
                                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                                              • FR: p̂₂

                                                                                                                                                                                                                              p̂₂

                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                              p̂₂

                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                                              code 1

                                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                                              code 2

                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                              History

                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                              TI-82 1.0 Added
                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                              Hex Value $6228
                                                                                                                                                                                                                              Categories
                                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                                              • FR: p̂

                                                                                                                                                                                                                              p̂

                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                              p̂

                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                                              code 1

                                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                                              code 2

                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                              History

                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                              TI-82 1.0 Added
                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                              Hex Value $6212
                                                                                                                                                                                                                              Categories
                                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                                              • FR: [r]

                                                                                                                                                                                                                              [r]

                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                              [r]

                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                                              code 1

                                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                                              code 2

                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                              History

                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                              TI-82 1.0 Added
                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                              Hex Value $6235
                                                                                                                                                                                                                              Categories
                                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                                              • FR: r²

                                                                                                                                                                                                                              r²

                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                              r²

                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                                              code 1

                                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                                              code 2

                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                              History

                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                              TI-82 1.0 Added
                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                              Hex Value $6221
                                                                                                                                                                                                                              Categories
                                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                                              • FR: 𝑛

                                                                                                                                                                                                                              𝑛

                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                              𝑛

                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                                              code 1

                                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                                              code 2

                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                              History

                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                              TI-82 1.0 Added
                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                              Hex Value $6234
                                                                                                                                                                                                                              Categories
                                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                                              • FR: [s]

                                                                                                                                                                                                                              [s]

                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                              [s]

                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                                              code 1

                                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                                              code 2

                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                              History

                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                              TI-82 1.0 Added
                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                              Hex Value $6207
                                                                                                                                                                                                                              Categories
                                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                                              • FR: σx

                                                                                                                                                                                                                              σx

                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                              σx

                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                                              code 1

                                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                                              code 2

                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                              History

                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                              TI-82 1.0 Added
                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                              Hex Value $6210
                                                                                                                                                                                                                              Categories
                                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                                              • FR: σy

                                                                                                                                                                                                                              σy

                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                              σy

                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                                              code 1

                                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                                              code 2

                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                              History

                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                              TI-82 1.0 Added
                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                              Hex Value $6224
                                                                                                                                                                                                                              Categories
                                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                                              • FR: [t]

                                                                                                                                                                                                                              [t]

                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                              [t]

                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                                              code 1

                                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                                              code 2

                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                              History

                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                              TI-82 1.0 Added
                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                              Hex Value $6233
                                                                                                                                                                                                                              Categories
                                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                                              • FR: bornsup

                                                                                                                                                                                                                              upper

                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                              upper

                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                                              code 1

                                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                                              code 2

                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                              History

                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                              TI-82 1.0 Added
                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                              Hex Value $621B
                                                                                                                                                                                                                              Categories
                                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                                              • FR: x₁

                                                                                                                                                                                                                              x₁

                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                              x₁

                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                                              code 1

                                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                                              code 2

                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                              History

                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                              TI-82 1.0 Added
                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                              Hex Value $621C
                                                                                                                                                                                                                              Categories
                                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                                              • FR: x₂

                                                                                                                                                                                                                              x₂

                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                              x₂

                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                                              code 1

                                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                                              code 2

                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                              History

                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                              TI-82 1.0 Added
                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                              Hex Value $621D
                                                                                                                                                                                                                              Categories
                                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                                              • FR: x₃

                                                                                                                                                                                                                              x₃

                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                              x₃

                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                                              code 1

                                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                                              code 2

                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                              History

                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                              TI-82 1.0 Added
                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                              Hex Value $622B
                                                                                                                                                                                                                              Categories
                                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                                              • FR: x̄₁

                                                                                                                                                                                                                              x̄₁

                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                              x̄₁

                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                                              code 1

                                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                                              code 2

                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                              History

                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                              TI-82 1.0 Added
                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                              Hex Value $622E
                                                                                                                                                                                                                              Categories
                                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                                              • FR: x̄₂

                                                                                                                                                                                                                              x̄₂

                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                              x̄₂

                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                                              code 1

                                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                                              code 2

                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                              History

                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                              TI-82 1.0 Added
                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                              Hex Value $6203
                                                                                                                                                                                                                              Categories
                                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                                              • FR: x̄

                                                                                                                                                                                                                              x̄

                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                              x̄

                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                                              code 1

                                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                                              code 2

                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                              History

                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                              TI-82 1.0 Added
                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                              Hex Value $621E
                                                                                                                                                                                                                              Categories
                                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                                              • FR: y₁

                                                                                                                                                                                                                              y₁

                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                              y₁

                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                                              code 1

                                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                                              code 2

                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                              History

                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                              TI-82 1.0 Added
                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                              Hex Value $621F
                                                                                                                                                                                                                              Categories
                                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                                              • FR: y₂

                                                                                                                                                                                                                              y₂

                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                              y₂

                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                                              code 1

                                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                                              code 2

                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                              History

                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                              TI-82 1.0 Added
                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                              Hex Value $6220
                                                                                                                                                                                                                              Categories
                                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                                              • FR: y₃

                                                                                                                                                                                                                              y₃

                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                              y₃

                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                                              code 1

                                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                                              code 2

                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                              History

                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                              TI-82 1.0 Added
                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                              Hex Value $620C
                                                                                                                                                                                                                              Categories
                                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                                              • FR: ȳ

                                                                                                                                                                                                                              ȳ

                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                              ȳ

                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                                              code 1

                                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                                              code 2

                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                              History

                                                                                                                                                                                                                              Calculator OS Version Description
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                                                                                                                                                                                                                              • FR: [z]

                                                                                                                                                                                                                              [z]

                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                              [z]

                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                                              code 1

                                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                                              code 2

                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                              History

                                                                                                                                                                                                                              Calculator OS Version Description
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                                                                                                                                                                                                                              • FR: ]

                                                                                                                                                                                                                              ]

                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                              ]

                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                                              code 1

                                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                                              code 2

                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                              History

                                                                                                                                                                                                                              Calculator OS Version Description
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                                                                                                                                                                                                                              • FR: ^

                                                                                                                                                                                                                              ^

                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                              ^

                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                                              code 1

                                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                                              code 2

                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                              History

                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                              TI-82 1.0 Added
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                                                                                                                                                                                                                              • FR: ⁻¹
                                                                                                                                                                                                                              ⁻¹

                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                              ⁻¹

                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                              The ֿ¹ command returns the reciprocal of a number, equivalent to dividing 1 by the number (although reciprocals are sometimes more convenient to type). It also works for lists, by calculating the reciprocal of each element.

                                                                                                                                                                                                                              The ֿ¹ command can also be used on matrices, but it is the matrix inverse that is computed, not the reciprocal of each element. If [A] is an N by N (square) matrix, then [A]ֿ¹ is the N by N matrix such that [A][A]ֿ¹=[A]ֿ¹[A] is the identity matrix. ֿ¹ does not work on non-square matrices.

                                                                                                                                                                                                                              4ֿ¹
        .25
{1,2,3}ֿ¹
        {1 .5 .3333333333}
[[3,2][4,3]]ֿ¹
        [[3  -2]
         [-4 3 ]]

                                                                                                                                                                                                                              Much like the number 0 does not have a reciprocal, some square matrices do not have inverses (they are called singular matrices) and you'll get an error when you try to invert them.

                                                                                                                                                                                                                              Optimization

                                                                                                                                                                                                                              Writing Aֿ¹B instead of B/A is sometimes beneficial when B is a complicated expression, because it allows you to take off closing parentheses of B. For example:

                                                                                                                                                                                                                              :(P+√(P²-4Q))/2
can be
:2ֿ¹(P+√(P²-4Q

                                                                                                                                                                                                                              This may be slower than dividing. There are also situations in which this optimization might lose precision, especially when the number being divided is large:

                                                                                                                                                                                                                              7fPart(4292/7
        1
7fPart(7ֿ¹4292
        .9999999999

                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                              Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, thornahawk, ztrumpet.

                                                                                                                                                                                                                              History

                                                                                                                                                                                                                              Calculator OS Version Description
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                                                                                                                                                                                                                              • FR: ²

                                                                                                                                                                                                                              ²

                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                              ²

                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                                              code 1

                                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                                              code 2

                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                              History

                                                                                                                                                                                                                              Calculator OS Version Description
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                                                                                                                                                                                                                              • FR: ³

                                                                                                                                                                                                                              ³

                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                              ³

                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                                              code 1

                                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                                              code 2

                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                              History

                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                              TI-82 1.0 Added
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                                                                                                                                                                                                                              • FR: ᵀ

                                                                                                                                                                                                                              ᵀ

                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                              ᵀ

                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                              T.GIF

                                                                                                                                                                                                                              Command Summary

                                                                                                                                                                                                                              This command calculates the transpose of a matrix.

                                                                                                                                                                                                                              Command Syntax

                                                                                                                                                                                                                              matrixT

                                                                                                                                                                                                                              Menu Location

                                                                                                                                                                                                                              Press:

                                                                                                                                                                                                                              1. MATRX (on the 83) or 2nd MATRX (83+ or higher) to access the Matrix menu.
                                                                                                                                                                                                                              2. LEFT to access the MATH submenu
                                                                                                                                                                                                                              3. 2 to select T, or use arrows

                                                                                                                                                                                                                              Calculator Compatibility

                                                                                                                                                                                                                              TI-83/84/+/SE

                                                                                                                                                                                                                              Token Size

                                                                                                                                                                                                                              1 byte

                                                                                                                                                                                                                              The T command is used to calculate the transpose of a matrix: it flips a matrix along its main diagonal. This means that the (i,j)th element becomes the (j,i)th element, and vice versa. As a result, the transpose of an M by N matrix is an N by M matrix.

                                                                                                                                                                                                                              [[1,2,3][4,5,6]]
                                                                                                                                                                                                                              ………… [[1 2 3]
                                                                                                                                                                                                                              …………. [4 5 6]]
                                                                                                                                                                                                                              AnsT
                                                                                                                                                                                                                              ………… [[1 4]
                                                                                                                                                                                                                              …………. [2 5]
                                                                                                                                                                                                                              …………. [3 6]]

                                                                                                                                                                                                                              Advanced Uses

                                                                                                                                                                                                                              In addition to its many uses in linear algebra, the T operation is useful to programmers: with operations such as Matr►list( and augment(, which normally deal with columns, T allows you to use rows instead. See the "Related Commands" section for the commands that this is useful for.

                                                                                                                                                                                                                              Source: parts of this page were written by the following TI|BD contributors: DarkerLine, Timothy Foster.

                                                                                                                                                                                                                              History

                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                              TI-82 1.0 Added
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                                                                                                                                                                                                                              • FR: °

                                                                                                                                                                                                                              °

                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                              °

                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                              Normally, when the calculator is in radian mode, the trigonometric functions only return values calculated in radians. With the ° symbol you can have the angle evaluated as if in degree mode because it converts the angle into radians.

                                                                                                                                                                                                                              You can insert the degree symbol by pressing [2ND] [ANGLE] [ENTER].

                                                                                                                                                                                                                              One full rotation around a circle is 2π radians, which is equal to 360°. To convert an angle in radians to degrees you multiply by 180/π, and to convert from degrees to radians multiply by π/180.

                                                                                                                                                                                                                              In radian mode:

                                                                                                                                                                                                                              sin(45)        \\ actually calculating sin(2578.31)
    .8509035245
sin(45°)
    .7071067812

                                                                                                                                                                                                                              In degree mode:

                                                                                                                                                                                                                              sin(45)
    .7071067812
sin(45°)
    .7071067812    \\ There's no difference when in degrees

                                                                                                                                                                                                                              Converting Degrees, Minutes & Seconds

                                                                                                                                                                                                                              The degree symbol also allows you to convert degrees, minutes and seconds into decimal degrees. For example:

                                                                                                                                                                                                                              90°30'
       90.5
90°30'09"
       90.5025

                                                                                                                                                                                                                              The minute symbol is inserted by pressing [2ND] [ANGLE] [2]. The seconds symbol is inserted via [ALPHA] [+].

                                                                                                                                                                                                                              To convert back the other way (decimal to degrees-minutes-seconds) use the ►DMS command, accessed via [2ND] [ANGLE] [4]:

                                                                                                                                                                                                                              90.5025►DMS
       90°30'09"

                                                                                                                                                                                                                              Optimization

                                                                                                                                                                                                                              When you only call the trig function once in a program and want it calculated in degrees, instead of changing the mode you can just use ° to save one-byte (the newline from using the command Degree)

                                                                                                                                                                                                                              :Degree
:sin(X)
can be
:sin(X°)

                                                                                                                                                                                                                              Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, simplethinker.

                                                                                                                                                                                                                              History

                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                              TI-82 1.0 Added
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                                                                                                                                                                                                                              Hex Value $0A
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                                                                                                                                                                                                                              • FR: ʳ

                                                                                                                                                                                                                              ʳ

                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                              ʳ

                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                              Normally, when the calculator is in degree mode, the trigonometric functions only return values calculated in degrees. With the r symbol you can have the angle evaluated as if in radian mode because it converts the angle into degrees.

                                                                                                                                                                                                                              One full rotation around a circle is 2π radians, which is equal to 360°. To convert an angle in radians to degrees you multiply by 180/π, and to convert from degrees to radians multiply by π/180.

                                                                                                                                                                                                                              In degree mode:

                                                                                                                                                                                                                              sin(π)        \\sine of Pi degrees
    .0548036651
sin(π^^r)
    0

                                                                                                                                                                                                                              In radian mode:

                                                                                                                                                                                                                              sin(π)
    0
sin(π^^r)
    0        \\There's no difference when in radians

                                                                                                                                                                                                                              Optimization

                                                                                                                                                                                                                              When you only call the trig function once in a program and want it calculated in radians, instead of changing the mode you can just use ° to save one-byte (the newline from using the command Radian)

                                                                                                                                                                                                                              :Radian
:sin(X)
can be
:sin(X^^r)
                                                                                                                                                                                                                              • ° (degree symbol)

                                                                                                                                                                                                                              Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Myles_Zadok.

                                                                                                                                                                                                                              History

                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                              TI-82 1.0 Added
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                                                                                                                                                                                                                              • FR: ˣ

                                                                                                                                                                                                                              ˣ

                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                              ˣ

                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                                              code 1

                                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                                              code 2

                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                              History

                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                              TI-83+ 1.16 Added
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                                                                                                                                                                                                                              • FR: ```

                                                                                                                                                                                                                              ```

                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                              ```

                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                                              code 1

                                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                                              code 2

                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                              History

                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                              TI-83+ 1.03 Added
                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                              Hex Value $BBD5
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                                                                                                                                                                                                                              • FR: ‛

                                                                                                                                                                                                                              ‛

                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                              ‛

                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                                              code 1

                                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                                              code 2

                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                              History

                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                              TI-83+ 1.15 Added
                                                                                                                                                                                                                              Property Value
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                                                                                                                                                                                                                              • FR: ```

                                                                                                                                                                                                                              ```

                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                              ```

                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                                              code 1

                                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                                              code 2

                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                              History

                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                              TI-83+ 1.03 Added
                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                              Hex Value $BB4F
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                                                                                                                                                                                                                              • FR: a+b𝑖

                                                                                                                                                                                                                              a+b𝑖

                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                              Sets the mode to rectangular complex number format (a+bi).

                                                                                                                                                                                                                              Availability: Token only available from within the Basic editor.

                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                              a+bi

                                                                                                                                                                                                                              Arguments

                                                                                                                                                                                                                              NameTypeOptional
                                                                                                                                                                                                                              i

                                                                                                                                                                                                                              Location

                                                                                                                                                                                                                              mode, a+b, 𝑖

                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                              The a+b𝑖 command puts the calculator into rectangular complex number mode. This means that:

                                                                                                                                                                                                                              • Taking square roots of negative numbers, and similar operations, no longer returns an error.
                                                                                                                                                                                                                              • Complex results are displayed in the form a+b𝑖 (hence the name of the command)

                                                                                                                                                                                                                              This is the standard way of displaying complex numbers, though they can also be displayed in polar form (see r𝑒^θ𝑖 for more details). To extract the coefficients a and b, use the real( and imag( commands.

                                                                                                                                                                                                                              Advanced Uses

                                                                                                                                                                                                                              Rather than switch to a+b𝑖 mode, you might want to force the calculations to use complex numbers by making the original argument complex. The general way to do this is by adding +0𝑖 to the number. However, there may be an optimization in any particular case. See the quadratic formula routine for a good example of this.

                                                                                                                                                                                                                              Real
        Done
√(-1)    
        (causes an error)
√(-1+0i)        
        i

                                                                                                                                                                                                                              See Also

                                                                                                                                                                                                                              Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Myles_Zadok, Trenly.

                                                                                                                                                                                                                              History

                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                              TI-83 0.01013 Added
                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                              Hex Value $BB4F
                                                                                                                                                                                                                              Categories
                                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                                              • FR: a+b𝑖

                                                                                                                                                                                                                              a+b𝑖

                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                              Sets the mode to rectangular complex number format (a+bi).

                                                                                                                                                                                                                              Availability: Token only available from within the Basic editor.

                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                              a+bi

                                                                                                                                                                                                                              Arguments

                                                                                                                                                                                                                              NameTypeOptional
                                                                                                                                                                                                                              i

                                                                                                                                                                                                                              Location

                                                                                                                                                                                                                              mode, a+b, 𝑖

                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                              The a+b𝑖 command puts the calculator into rectangular complex number mode. This means that:

                                                                                                                                                                                                                              • Taking square roots of negative numbers, and similar operations, no longer returns an error.
                                                                                                                                                                                                                              • Complex results are displayed in the form a+b𝑖 (hence the name of the command)

                                                                                                                                                                                                                              This is the standard way of displaying complex numbers, though they can also be displayed in polar form (see r𝑒^θ𝑖 for more details). To extract the coefficients a and b, use the real( and imag( commands.

                                                                                                                                                                                                                              Advanced Uses

                                                                                                                                                                                                                              Rather than switch to a+b𝑖 mode, you might want to force the calculations to use complex numbers by making the original argument complex. The general way to do this is by adding +0𝑖 to the number. However, there may be an optimization in any particular case. See the quadratic formula routine for a good example of this.

                                                                                                                                                                                                                              Real
        Done
√(-1)    
        (causes an error)
√(-1+0i)        
        i

                                                                                                                                                                                                                              See Also

                                                                                                                                                                                                                              Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Myles_Zadok, Trenly.

                                                                                                                                                                                                                              History

                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                              TI-83 0.01013 Added
                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                              Hex Value $BBB0
                                                                                                                                                                                                                              Categories
                                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                                              • FR: a

                                                                                                                                                                                                                              a

                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                              a

                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                                              code 1

                                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                                              code 2

                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                              History

                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                              TI-83+ 1.03 Added
                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                              Hex Value $6216
                                                                                                                                                                                                                              Categories
                                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                                              • FR: [|a]

                                                                                                                                                                                                                              [|a]

                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                              [|a]

                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                                              code 1

                                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                                              code 2

                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                              History

                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                              TI-82 1.0 Added
                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                              Hex Value $B2
                                                                                                                                                                                                                              Categories
                                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                                              • FR: abs(

                                                                                                                                                                                                                              abs(

                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                              Returns the absolute value of a real number, expression, list, or matrix.

                                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                              abs(value)

                                                                                                                                                                                                                              Arguments

                                                                                                                                                                                                                              NameTypeOptional
                                                                                                                                                                                                                              valuereal|expression|real[]|matrix

                                                                                                                                                                                                                              Location

                                                                                                                                                                                                                              math, NUM, 1:abs(

                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                              Returns the magnitude of a complex number or list.

                                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                              abs(complex value)

                                                                                                                                                                                                                              Arguments

                                                                                                                                                                                                                              NameTypeOptional
                                                                                                                                                                                                                              complex valuecomplex|complex[]

                                                                                                                                                                                                                              Location

                                                                                                                                                                                                                              math, CMPLX, 5:abs(

                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                              abs(x) returns the absolute value of the real number x. Also works on a list or matrix of real numbers.

                                                                                                                                                                                                                              abs(3)
     3

abs(‾3)
     3

                                                                                                                                                                                                                              For complex numbers, abs(z) returns the absolute value (also known as the complex modulus, norm, or a hundred other terms) of the complex number z. If z is represented as x+i_y_ where x and y are both real, abs(z) returns √(_x_²+_y_²). Also works on a list of complex numbers.

                                                                                                                                                                                                                              abs(3+4i)
     5

                                                                                                                                                                                                                              Optimization

                                                                                                                                                                                                                              The abs( command, used properly, may be a smaller method of testing if a variable is in some range. For example:

                                                                                                                                                                                                                              :If 10<X and X<20
can be
:If 5>abs(X-15

                                                                                                                                                                                                                              In general, the first number, A, in the expression A>abs(X-B) should be half the length of the range, half of 10 in this case, and the second number, B, should be the midpoint of the range (here, 15).

                                                                                                                                                                                                                              This can be taken to extreme degrees. For example, the following code uses abs( three times to test if X is the getKey keycode of one of the keys 1, 2, 3, 4, 5, 6, 7, 8, or 9:

                                                                                                                                                                                                                              :If 2>abs(5-abs(5-abs(X-83

                                                                                                                                                                                                                              For complex numbers given by a separate real and complex part, abs(X+iY) can be optimized to R►Pr(X,Y).

                                                                                                                                                                                                                              Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, kg583, Myles_Zadok, thornahawk, Trenly.

                                                                                                                                                                                                                              History

                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                              TI-82 1.0 abs added
                                                                                                                                                                                                                              TI-83 0.01013 Renamed abs to abs(
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                                                                                                                                                                                                                              • FR: α

                                                                                                                                                                                                                              α

                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                              α

                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                                              code 1

                                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                                              code 2

                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                              History

                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                              TI-83+ 1.03 Added
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                                                                                                                                                                                                                              Hex Value $BB28
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                                                                                                                                                                                                                              • FR: argument(

                                                                                                                                                                                                                              angle(

                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                              Returns the polar angle of a complex number or list of complex numbers.

                                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                              angle(value)

                                                                                                                                                                                                                              Arguments

                                                                                                                                                                                                                              NameTypeOptional
                                                                                                                                                                                                                              valuecomplex|complex[]

                                                                                                                                                                                                                              Location

                                                                                                                                                                                                                              math, CMPLX, 4:angle(

                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                              angle(z) returns the complex argument (also known as the polar angle) of the complex number z. If z is represented as x+i_y_ where x and y are both real, angle(z) returns R►Pθ(x,y) (which is equivalent to tanֿ¹(y__/x) if x is nonzero). Also works on a list of complex numbers.

                                                                                                                                                                                                                              angle(3+4i)
     .927295218
R►Pθ(3,4)
     .927295218

                                                                                                                                                                                                                              When writing a complex number z in the form \(re^{i\theta}\) (or, equivalently, \(r(\cos\theta+i\sin\theta)\)), then \(\theta\) is equal to the value of angle(z), suitably reduced so that the result returned is in the interval \(-\pi<\theta\leq\pi\).

                                                                                                                                                                                                                              The angle( command also works on matrices, though not in any useful way: angle([A] will return a matrix of the same size as [A], but with all elements 0. If you plan to use this, don't: 0[A] does the same thing, but is smaller and not as questionable (because this behavior is clearly unintentional on TI's part, and may be changed in an OS update).

                                                                                                                                                                                                                              Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583, Myles_Zadok, thornahawk, Trenly.

                                                                                                                                                                                                                              History

                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                              TI-83 0.01013 Added
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                                                                                                                                                                                                                              Hex Value $14
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                                                                                                                                                                                                                              • FR: chaîne(

                                                                                                                                                                                                                              augment(

                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                              Returns a matrix, which is matrixB appended to matrixA as new columns.

                                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                              augment( matrixA ,matrixB )

                                                                                                                                                                                                                              Arguments

                                                                                                                                                                                                                              NameTypeOptional
                                                                                                                                                                                                                              matrixAmatrix
                                                                                                                                                                                                                              matrixBmatrix

                                                                                                                                                                                                                              Location

                                                                                                                                                                                                                              2nd, matrix, MATH, 7:augment(

                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                              Returns a list, which is listB concatenated to the end of listA.

                                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                              augment(listA,listB)

                                                                                                                                                                                                                              Arguments

                                                                                                                                                                                                                              NameTypeOptional
                                                                                                                                                                                                                              listAlist
                                                                                                                                                                                                                              listBlist

                                                                                                                                                                                                                              Location

                                                                                                                                                                                                                              2nd, list, OPS, 9:augment(

                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                              The augment( command is used to combine two lists or two matrices into one. For lists, this is done the obvious way: adding the elements of the second on to the elements of the first. For example:

                                                                                                                                                                                                                              augment({1,2,3,4},{5,6,7
    {1 2 3 4 5 6 7}

                                                                                                                                                                                                                              For matrices, the columns of the second matrix are added after the columns of the first matrix: an R by C matrix augmented with an R by D matrix will result in an R by (C+D) matrix. For example:

                                                                                                                                                                                                                              augment([[1][2]],[[3][4]
    [[1 3]
     [2 4]]

                                                                                                                                                                                                                              Advanced Uses

                                                                                                                                                                                                                              Use the T (transpose) command if you want to combine two matrices vertically, rather than horizontally. For example:

                                                                                                                                                                                                                              augment([[1,2]]T,[[3,4]]T)T
    [[1 2]
     [3 4]]

                                                                                                                                                                                                                              Optimization

                                                                                                                                                                                                                              You may be tempted to use augment( to add one element to the end of a list:

                                                                                                                                                                                                                              :augment(L1,{X→L1

                                                                                                                                                                                                                              However, the following way is faster and more memory-efficient while the program is running (although it increases the program's size):

                                                                                                                                                                                                                              :X→L1(1+dim(L1

                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                              • ERR:DATA TYPE is thrown if you try to augment a single number to a list, a common error — use {X instead of X.
                                                                                                                                                                                                                              • ERR:DIM MISMATCH is thrown if you try to augment two matrices with a different number of rows.
                                                                                                                                                                                                                              • ERR:INVALID DIM is thrown if one of the arguments is a list with dimension 0, or if the result would have dimension over 999 (for lists) or 99x99 (for matrices).
                                                                                                                                                                                                                              • dim( – for retrieving the size of a list
                                                                                                                                                                                                                              • seq( – for creating a list based on a formula, or to create a subset of an existing list
                                                                                                                                                                                                                              • T – to transpose a 2D matrix

                                                                                                                                                                                                                              Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Myles_Zadok, Trenly.

                                                                                                                                                                                                                              History

                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                              TI-82 1.0 Added
                                                                                                                                                                                                                              Property Value
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                                                                                                                                                                                                                              • FR: b

                                                                                                                                                                                                                              b

                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                              b

                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                                              code 1

                                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                                              code 2

                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                              History

                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                              TI-83+ 1.03 Added
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                                                                                                                                                                                                                              • FR: [|b]

                                                                                                                                                                                                                              [|b]

                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                              [|b]

                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                                              code 1

                                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                                              code 2

                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                              History

                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                              TI-82 1.0 Added
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                                                                                                                                                                                                                              Hex Value $BB02
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                                                                                                                                                                                                                              • FR: paSolde(

                                                                                                                                                                                                                              bal(

                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                              Computes the balance at npmtfor an amortization schedule using stored values for PV, I%, and PMT and rounds the computation to roundvalue.

                                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                              bal(npmt[,roundvalue])

                                                                                                                                                                                                                              Arguments

                                                                                                                                                                                                                              NameTypeOptional
                                                                                                                                                                                                                              npmt
                                                                                                                                                                                                                              roundvalueYes

                                                                                                                                                                                                                              Location

                                                                                                                                                                                                                              apps, 1:Finance, CALC, 9:bal(

                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                              The bal( command calculates the remaining balance after n payments in an amortization schedule. It has only one required argument: n, the payment number. However, it also uses the values of the finance variables PV, PMT, and I% in its calculations.

                                                                                                                                                                                                                              The optional argument, roundvalue, is the number of digits to which the calculator will round all internal calculations. Since this rounding affects further steps, this isn't the same as using round( to round the result of bal( to the same number of digits.

                                                                                                                                                                                                                              Usually, you will know the values of N, PV, and I%, but not PMT. This means you'll have to use the finance solver to solve for PMT before calculating bal(); virtually always, FV will equal 0.

                                                                                                                                                                                                                              Sample Problem

                                                                                                                                                                                                                              Imagine that you have taken out a 30-year fixed-rate mortgage. The loan amount is $100000, and the annual interest rate (APR) is 8%. Payments will be made monthly. After 15 years, what amount is still left to pay?

                                                                                                                                                                                                                              We know the values of N, I%, and PV, though we still need to convert them to monthly values (since payments are made monthly). N is 30*12, and I% is 8/12. PV is just 100000.

                                                                                                                                                                                                                              Now, we use the finance solver to solve for PMT. Since you intend to pay out the entire loan, FV is 0. Using either the interactive TVM solver, or the tvm_Pmt command, we get a value of about -$733.76 for PMT.

                                                                                                                                                                                                                              We are ready to use bal(. We are interested in the payment made after 15 years; this is the 15*12=180th payment. bal(180) gives us the result $76781.55 — as you can see, most of the loan amount is still left to pay after 15 years.

                                                                                                                                                                                                                              Formulas

                                                                                                                                                                                                                              The calculator uses a recursive formula to calculate bal():

                                                                                                                                                                                                                              (1) \(\begin{align} \texttt{bal}(0)=\texttt{PV} \end{align}\) (2) \(\begin{align} \texttt{bal}(m)=\left(1-\frac{I\%}{100}\right)\texttt{bal}(m-1)+\texttt{PMT} \end{align}\)

                                                                                                                                                                                                                              In the case that roundvalue is given as an argument, the rounding is done at each step of the recurrence (which virtually forces us to use this formula). Otherwise, if no rounding is done (and assuming I% is not 0), we can solve the recurrence relation to get:

                                                                                                                                                                                                                              (3) \(\begin{align} \texttt{bal}(m)=\frac{1-\left(1-\frac{I\%}{100}\right)^m}{\frac{I\%}{100}}\texttt{PMT}+\left(1-\frac{I\%}{100}\right)^m\texttt{PV} \end{align}\)

                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                              • ERR:DOMAIN is thrown if the payment number is negative or a decimal.

                                                                                                                                                                                                                              Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Myles_Zadok, Timothy Foster, Trenly.

                                                                                                                                                                                                                              History

                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                              TI-83 0.01013 Added
                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                              Hex Value $BBA0
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                                                                                                                                                                                                                              • FR: β

                                                                                                                                                                                                                              β

                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                              β

                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                                              code 1

                                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                                              code 2

                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                              History

                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                              TI-83+ 1.03 Added
                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                              Hex Value $BB16
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                                                                                                                                                                                                                              • FR: binomFRép(

                                                                                                                                                                                                                              binomcdf(

                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                              Computes a cumulative probability at x for the discrete binomial distribution with the specified numtrials and probability p of success on each trial.

                                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                              binomcdf(numtrials,p[,x])

                                                                                                                                                                                                                              Arguments

                                                                                                                                                                                                                              NameTypeOptional
                                                                                                                                                                                                                              numtrials
                                                                                                                                                                                                                              p
                                                                                                                                                                                                                              xYes

                                                                                                                                                                                                                              Location

                                                                                                                                                                                                                              2nd, distr, DISTR, B:binomcdf(

                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                              This command is used to calculate the binomial cumulative probability function. In plainer language, it solves a specific type of often-encountered probability problem, that occurs under the following conditions:

                                                                                                                                                                                                                              1. A specific event has only two outcomes, which we will call "success" and "failure"
                                                                                                                                                                                                                              2. This event is going to repeat a specific number of times, or "trials"
                                                                                                                                                                                                                              3. Success or failure is determined randomly with the same probability of success each time the event occurs
                                                                                                                                                                                                                              4. We're interested in the probability that there are at most N successes

                                                                                                                                                                                                                              For example, consider a couple that intends to have 4 children. What is the probability that at most 2 are girls?

                                                                                                                                                                                                                              1. The event here is a child being born. It has two outcomes "boy" or "girl". In this case, since the question is about girls, it's easier to call "girl" a success.
                                                                                                                                                                                                                              2. The event is going to repeat 4 times, so we have 4 trials
                                                                                                                                                                                                                              3. The probability of a girl being born is 50% or 1/2 each time
                                                                                                                                                                                                                              4. We're interested in the probability that there are at most 2 successes (2 girls)

                                                                                                                                                                                                                              The syntax here is binomcdf(trials, probability, value). In this case:

                                                                                                                                                                                                                              :binomcdf(4,.5,2

                                                                                                                                                                                                                              This will give .6875 when you run it, so there's a .6875 probability out of 4 children, at most 2 will be girls.

                                                                                                                                                                                                                              An alternate syntax for binomcdf( leaves off the last argument, value. This tells the calculator to compute a list of the results for all values. For example:

                                                                                                                                                                                                                              :binomcdf(4,.5

                                                                                                                                                                                                                              This will come to {.0625 .3125 .6875 .9375 1} when you run it. These are all the probabilities we get when you replace "at most 2 girls" with "at most 0", "at most 1", etc. Here, .0625 is the probability of "at most 0" girls (or just 0 girls), .3125 is the probability of at most 1 girl (1 or 0 girls), etc.

                                                                                                                                                                                                                              Several other probability problems actually are the same as this one. For example, "less than N" girls, just means "at most N-1" girls. "At least N" girls means "at most (total-N)" boys (here we switch our definition of what a success is). "No more than", of course, means the same as "at most".

                                                                                                                                                                                                                              Advanced (for programmers)

                                                                                                                                                                                                                              The binompdf( and binomcdf( commands are the only ones apart from seq( that can return a list of a given length, and they do it much more quickly. It therefore makes sense, in some situations, to use these commands as substitutes for seq(.

                                                                                                                                                                                                                              Here's how to do it:

                                                                                                                                                                                                                              1. cumSum(binomcdf(N,0 gives the list {1 2 … N+1}, and cumSum(not(binompdf(N,0 gives the list {0 1 2 … N}.
                                                                                                                                                                                                                              2. With seq(, you normally do math inside the list: seq(3I2,I,0,5
                                                                                                                                                                                                                              3. With these commands, you do the same math outside the list: 3Ans2 where Ans is the list {0 1 … 5}.
                                                                                                                                                                                                                              :seq(2^I,I,1,5
can be
:cumSum(binomcdf(4,0
:2^Ans
which in turn can be
:2^cumSum(binomcdf(4,0

                                                                                                                                                                                                                              In general (where f() is some operation or even several operations):

                                                                                                                                                                                                                              :seq(f(I),I,1,N
can be
:cumSum(binomcdf(N-1,0
:f(Ans
which can sometimes be
:f(cumSum(binomcdf(N-1,0

                                                                                                                                                                                                                              If the lower bound on I in the seq( statement is 0 and not 1, you can use binompdf( instead:

                                                                                                                                                                                                                              :seq(f(I),I,0,N
can be
:cumSum(not(binompdf(N,0
:f(Ans
which can sometimes be
:f(cumSum(not(binompdf(N,0

                                                                                                                                                                                                                              This will not work if some command inside seq( can take only a number and not a list as an argument. For example, seq(L1(I),I,1,5 cannot be optimized this way.

                                                                                                                                                                                                                              Formulas

                                                                                                                                                                                                                              Since "at most N" is equivalent to "0 or 1 or 2 or 3 or … N", and since we can combine these probabilities by adding them, we can come up with an expression for binomcdf( by adding up values of binompdf(:

                                                                                                                                                                                                                              (1) \(\begin{align} \texttt{binomcdf}(n,p,k) = \sum_{i=0}^{k}\texttt{binompdf}(n,p,i) = \sum_{i=0}^{k}\binom{n}{i}\,p^i\,(1-p)^{n-i} \end{align}\)

                                                                                                                                                                                                                              (If you're not familiar with sigma notation, \(\sum_{i=0}^{k}\) just means "add the following up for each value of i 0 through k")

                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                              • ERR:DATATYPE is thrown if you try to generate a list of probabilities with p equal to 0 or 1, and at least 257 trials.
                                                                                                                                                                                                                              • ERR:DOMAIN is thrown if the number of trials is at least 1 000 000 (unless the other arguments make the problem trivial).
                                                                                                                                                                                                                              • ERR:INVALID DIM is thrown if you try to generate a list of probabilities with at least 999 trials.

                                                                                                                                                                                                                              Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583, Myles_Zadok, Timothy Foster, Trenly.

                                                                                                                                                                                                                              History

                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                              TI-83 0.01013 Added
                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                              Hex Value $BB15
                                                                                                                                                                                                                              Categories
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                                                                                                                                                                                                                              • FR: binomfdp(

                                                                                                                                                                                                                              binompdf(

                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                              Computes a probability at x for the discrete binomial distribution with the specified numtrials and probability p of success on each trial.

                                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                              binompdf(numtrials,p[,x])

                                                                                                                                                                                                                              Arguments

                                                                                                                                                                                                                              NameTypeOptional
                                                                                                                                                                                                                              numtrials
                                                                                                                                                                                                                              p
                                                                                                                                                                                                                              xYes

                                                                                                                                                                                                                              Location

                                                                                                                                                                                                                              2nd, distr, DISTR, A:binompdf(

                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                              This command is used to calculate the binomial probability. In plainer language, it solves a specific type of often-encountered probability problem, that occurs under the following conditions:

                                                                                                                                                                                                                              1. A specific event has only two outcomes, which we will call "success" and "failure"
                                                                                                                                                                                                                              2. This event is going to repeat a specific number of times, or "trials"
                                                                                                                                                                                                                              3. Success or failure is determined randomly with the same probability of success each time the event occurs
                                                                                                                                                                                                                              4. We're interested in the probability that there are exactly N successes

                                                                                                                                                                                                                              For example, consider a couple that intends to have 4 children. What is the probability that 3 of them are girls?

                                                                                                                                                                                                                              1. The event here is a child being born. It has two outcomes "boy" or "girl". We can call either one a success, but we'll choose to be sexist towards guys and call a girl a success in this problem
                                                                                                                                                                                                                              2. The event is going to repeat 4 times, so we have 4 trials
                                                                                                                                                                                                                              3. The probability of a girl being born is 50% or 1/2 each time
                                                                                                                                                                                                                              4. We're interested in the probability that there are exactly 3 successes (3 girls)

                                                                                                                                                                                                                              The syntax here is binompdf(trials, probability, value). In this case:

                                                                                                                                                                                                                              :binompdf(4,.5,3

                                                                                                                                                                                                                              This will give .25 when you run it, so there's a .25 (1/4) probability out of 4 children, 3 will be girls.

                                                                                                                                                                                                                              An alternate syntax for binompdf( leaves off the last argument, value. This tells the calculator to compute a list of the results for all values. For example:

                                                                                                                                                                                                                              :binompdf(4,.5

                                                                                                                                                                                                                              This will come to {.0625 .25 .375 .25 .0625} when you run it. These are the probabilities of all 5 outcomes (0 through 4 girls) for 4 children with an equal probability of being born. There's a .0625 probability of no girls, a .25 probability of 1 girl, etc.

                                                                                                                                                                                                                              Advanced (for programmers)

                                                                                                                                                                                                                              The binompdf( and binomcdf( commands are the only ones apart from seq( that can return a list of a given length, and they do it much more quickly. It therefore makes sense, in some situations, to use these commands as substitutes for seq(.

                                                                                                                                                                                                                              Here's how to do it:

                                                                                                                                                                                                                              1. cumSum(binomcdf(N,0 gives the list {1 2 … N+1}, and cumSum(not(binompdf(N,0 gives the list {0 1 2 … N}.
                                                                                                                                                                                                                              2. With seq(, you normally do math inside the list: for example, seq(3I2,I,0,5
                                                                                                                                                                                                                              3. With these commands, you do the same math outside the list: 3Ans2 where Ans is the list {0 1 … 5}.

                                                                                                                                                                                                                              An example:

                                                                                                                                                                                                                              :seq(2^I,I,1,5
can be
:cumSum(binomcdf(4,0
:2^Ans
which in turn can be
:2^cumSum(binomcdf(4,0

                                                                                                                                                                                                                              In general (where f() is some operation or even several operations):

                                                                                                                                                                                                                              :seq(f(I),I,1,N
can be
:cumSum(binomcdf(N-1,0
:f(Ans
which can sometimes be
:f(cumSum(binomcdf(N-1,0

                                                                                                                                                                                                                              If the lower bound on I in the seq( statement is 0 and not 1, you can use binompdf( instead:

                                                                                                                                                                                                                              :seq(f(I),I,0,N
can be
:cumSum(not(binompdf(N,0
:f(Ans
which can sometimes be
:f(cumSum(not(binompdf(N,0

                                                                                                                                                                                                                              This will not work if some command inside seq( can take only a number and not a list as an argument. For example, seq(L1(I),I,1,5 cannot be optimized this way.

                                                                                                                                                                                                                              Formulas

                                                                                                                                                                                                                              The value of binompdf( is given by the formula

                                                                                                                                                                                                                              (1) \(\begin{align} \texttt{binompdf}(n,p,k) = \binom{n}{k}\,p^k\,(1-p)^{n-k} = \frac{n!}{k!\,(n-k)!}\,p^k\,(1-p)^{n-k} \end{align}\)

                                                                                                                                                                                                                              This formula is fairly intuitive. We want to know the probability that out of n trials, exactly k will be successes, so we take the probability of k successes - \(p^k\) - multiplied by the probability of (n-k) failures - \((1-p)^{n-k}\) - multiplied by the number of ways to choose which k trials will be successes - \(\binom{n}{k}\).

                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                              • ERR:DOMAIN is thrown if the number of trials is at least 1 000 000 (unless the other arguments make the problem trivial).
                                                                                                                                                                                                                              • ERR:INVALID DIM is thrown if you try to generate a list of probabilities with at least 999 trials.

                                                                                                                                                                                                                              Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583, Myles_Zadok, Timothy Foster, Trenly.

                                                                                                                                                                                                                              History

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                                                                                                                                                                                                                              • FR: 🡇

                                                                                                                                                                                                                              🡇

                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                              🡇

                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                                              code 1

                                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                                              code 2

                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                              Advanced Notes

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                                                                                                                                                                                                                              • FR: 🡅

                                                                                                                                                                                                                              🡅

                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                              🡅

                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                                              code 1

                                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                                              code 2

                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                              Advanced Notes

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                                                                                                                                                                                                                              • FR: c

                                                                                                                                                                                                                              c

                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                              c

                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                                              code 1

                                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                                              code 2

                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                              Advanced Notes

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                                                                                                                                                                                                                              • FR: [|c]

                                                                                                                                                                                                                              [|c]

                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                              [|c]

                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                                              code 1

                                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                                              code 2

                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                              Advanced Notes

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                                                                                                                                                                                                                              checkTmr(

                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                              Returns the number of seconds since you used startTmr to start the timer. The starttime is the value displayed by startTmr.

                                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                              checkTmr(starttime)

                                                                                                                                                                                                                              Arguments

                                                                                                                                                                                                                              NameTypeOptional
                                                                                                                                                                                                                              starttime

                                                                                                                                                                                                                              Location

                                                                                                                                                                                                                              2nd, catalog, checkTmr(

                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                              The checkTmr( command is used together with the startTmr command to determine how much time has elapsed since the timer was started on the TI-84+/SE calculators. In particular, it returns the number of seconds since the built-in timer was started. An application of these commands is timing different commands or pieces of code, as well as countdowns in games, or a time-based score (such as in Minesweeper).

                                                                                                                                                                                                                              To use the timer, you first store startTmr to a variable (usually, a real variable) whenever you want the count to start. Now, whenever you want to check the elapsed time, you can use checkTmr( with the variable from above, giving you the number of seconds that have passed. Using checkTmr( doesn't stop the timer, you can do it as many times as you want to.

                                                                                                                                                                                                                              In the case of Minesweeper, for example, you would store startTmr to, for example, T, after setting up and displaying the board, display the result of checkTmr(T) in the game's key-reading loop, and store checkTmr(T) to the player's score if he wins.

                                                                                                                                                                                                                              Advanced Uses

                                                                                                                                                                                                                              To time a command or routine using startTmr and checkTmr(, use the following template:

                                                                                                                                                                                                                              :ClockOn
:startTmr→T
:Repeat checkTmr(Ans
:End
:For(n,1,(number)                    //sequence variable n
   (command(s) to be tested)
:End
:checkTmr(T+1)/(number)

                                                                                                                                                                                                                              Making (number) higher increases accuracy, but takes longer. Also, make sure not to modify the variables n or T inside the For( loop.

                                                                                                                                                                                                                              While this method eliminates human error from counting, it's prone to its own faults. For example, startTmr and checkTmr( always return the time rounded down to a whole second. To take this into account, replace the last line:

                                                                                                                                                                                                                              :(checkTmr(T+{1,0})/(number)

                                                                                                                                                                                                                              When testing code, be aware that many different things affect the time: the strength of the batteries, the amount of free RAM, and including the closing parenthesis on the For( loop. The last one, in particular, has an impact when using a single-line If statement or one of the IS>( and DS<( commands on the first line inside a For( loop.

                                                                                                                                                                                                                              Source: parts of this page were written by the following TI|BD contributors: Austin 332000, burr, DarkerLine, Electromagnet8, GoVegan, Kenta Lynn, kg583, lirtosiast, Xphoenix.

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                                                                                                                                                                                                                              • FR: χ

                                                                                                                                                                                                                              χ

                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                              χ

                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                                              code 1

                                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                                              code 2

                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                              History

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                                                                                                                                                                                                                              • FR: χ²-Test(

                                                                                                                                                                                                                              χ²-Test(

                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                              Performs a chi-square test. drawflag=1 draws results; drawflag=0 calculates results.
                                                                                                                                                                                                                              Color#: 10 - 24 or color name pasted from [vars] COLOR.

                                                                                                                                                                                                                              Availability: Token only available from within the Basic editor.

                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                              χ²-Test(observedmatrix,expectedmatrix[,drawflag,color#])

                                                                                                                                                                                                                              Arguments

                                                                                                                                                                                                                              NameTypeOptional
                                                                                                                                                                                                                              χ²-
                                                                                                                                                                                                                              observedmatrixmatrix
                                                                                                                                                                                                                              expectedmatrixmatrixYes
                                                                                                                                                                                                                              drawflagYes
                                                                                                                                                                                                                              color#colorNumYes

                                                                                                                                                                                                                              Location

                                                                                                                                                                                                                              stat, TESTS, C:Test(

                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                              This command performs a χ² test of independence. This test is used to assess the independence of two categorical variables with known frequencies. The test is only valid for a simple random sample from the population, and only if all the frequencies are sufficiently large (greater than 5).

                                                                                                                                                                                                                              Note: this test is different from the χ² goodness of fit test, which the TI-83 calculators don't have a command for. For a program that will perform the χ² goodness-of-fit test, see the goodness-of-fit test routine.

                                                                                                                                                                                                                              To use this test, you need a matrix containing a contingency table. This is a table in which every row corresponds to a value of the first variable, and every column to a value of the second. The number in each cell represents the frequency with which the corresponding values of the two variables occur together. For example: suppose that the two variables are sex (male and female) and eye color (blue, brown, and green). The contingency table would have two rows and three columns. The cell in the first row and column would be the number of blue-eyed men in the sample, the cell in the second row and first column would be the number of blue-eyed women, and so on.

                                                                                                                                                                                                                              The χ²-Test( command takes two arguments: the observed matrix and expected matrix. The first of these should be the contingency table you've already completed, presumably in the Matrix editor. The expected matrix does not need to already exist: the χ²-Test( command will calculate and store the expected frequencies (under the assumption that the variables are independent) to this matrix.

                                                                                                                                                                                                                              The command is primarily for use in a program. Although you can access the χ²-Test( command on the home screen, via the catalog, there's no need: you can use the χ²-Test… interactive solver found in the menu instead.

                                                                                                                                                                                                                              In either case, it's important to understand the output of χ²-Test(. Here are the meanings of each line:

                                                                                                                                                                                                                              • χ² is the test statistic, calculated from the differences between the observed and the expected matrices.
                                                                                                                                                                                                                              • p is the probability associated with the test statistic. We use p to test the null hypothesis that the two variables are independent. If p is low (usually, if it's <0.05) this means there's little chance that two independent variables would have a contingency table so different from the expected, and we reject the null hypothesis (so we'd conclude that the two variables are not independent).
                                                                                                                                                                                                                              • df is the degrees of freedom, defined as (# of rows - 1)*(# of columns - 1), important for calculating p.

                                                                                                                                                                                                                              Sample Problem

                                                                                                                                                                                                                              You want to compare the effectiveness of three treatments in curing a terminal disease. You have obtained data for 100 patients who had the disease, which contained information on the treatment used, and whether the patient lived or died. You put this information in a contingency table:

                                                                                                                                                                                                                              Lived

                                                                                                                                                                                                                              Died

                                                                                                                                                                                                                              Treatment A

                                                                                                                                                                                                                              40

                                                                                                                                                                                                                              10

                                                                                                                                                                                                                              Treatment B

                                                                                                                                                                                                                              27

                                                                                                                                                                                                                              6

                                                                                                                                                                                                                              Treatment C

                                                                                                                                                                                                                              11

                                                                                                                                                                                                                              6

                                                                                                                                                                                                                              To perform the test, you store this information to a matrix such as [A], either through the matrix editor or by hand:

                                                                                                                                                                                                                              :[[40,10],[27,6],[11,6→[A]

                                                                                                                                                                                                                              You submit this matrix as the first argument, and some other matrix (such as [B]) for the second:

                                                                                                                                                                                                                              :χ²-Test([A],[B]

                                                                                                                                                                                                                              The output looks something like this:

                                                                                                                                                                                                                              χ²-Test
 χ²=2.14776311
 p=.3416796916
 df=2

                                                                                                                                                                                                                              The most important part of this output is the line p=.3416796916 - the probability of getting such results under the hypothesis that the treatments and survival rate are independent. This value is greater than .05, so the data is not significant on a 5% level. There is not enough evidence to reject the null hypothesis, so treatment and survival rate may very well be independent. In non-mathematical language, this means that there's no reason to believe the treatments vary in effectiveness.

                                                                                                                                                                                                                              Advanced Uses

                                                                                                                                                                                                                              The final argument of χ²-Test(, draw?, will display the results in a graphical manner if you put in "1" for it. The calculator will draw the χ² distribution with the correct degrees of freedom, and shade the area of the graph beyond the χ² statistic. In addition, the same values as usually will be calculated and displayed. You would make your conclusions in the same way as for the regular output.

                                                                                                                                                                                                                              See Also

                                                                                                                                                                                                                              Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Myles_Zadok.

                                                                                                                                                                                                                              History

                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                              TI-83 0.01013 Added
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                                                                                                                                                                                                                                • FR: χ²GOF-Test(

                                                                                                                                                                                                                                χ²GOF-Test(

                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                Performs a test to confirm that sample data is from a population that conforms to a specified distribution.
                                                                                                                                                                                                                                Color#: 10 - 24 or color name pasted from [vars] COLOR.

                                                                                                                                                                                                                                Availability: Token only available from within the Basic editor.

                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                χ²GOF-Test(observedlist,expectedlist,df [,drawflag,color#])

                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                χ²
                                                                                                                                                                                                                                -
                                                                                                                                                                                                                                observedlistlist
                                                                                                                                                                                                                                expectedlistlist
                                                                                                                                                                                                                                df
                                                                                                                                                                                                                                drawflagYes
                                                                                                                                                                                                                                color#colorNumYes

                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                stat, TESTS, D:, GOF, Test(

                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                The χ²GOF-Test( command performs a χ² goodness-of-fit test. Given an expected ideal distribution of a variable across several categories, and a sample from this variable, it tests the hypothesis that the variable actually fits the ideal distribution. As a special case, you could take the ideal distribution to be evenly divided across all categories. Then, the goodness-of-fit test will test the hypothesis that the variable is independent of the category.

                                                                                                                                                                                                                                The command takes three arguments:

                                                                                                                                                                                                                                • An observed list with an element for each category: the element records the number of times this category appeared in the sample.
                                                                                                                                                                                                                                • An expected list with an element for each category: the element records the frequency with which the category was expected to appear.
                                                                                                                                                                                                                                • The degrees of freedom — usually taken to be one less than the number of categories.

                                                                                                                                                                                                                                The output is two-fold:

                                                                                                                                                                                                                                • The test statistic, χ². If the null hypothesis (that the variable fits the distribution) is true, this should be close to 1.
                                                                                                                                                                                                                                • The probability, p, of the observed distribution assuming the null hypothesis. If this value is low (usually, if it's lower than .05, or lower than .01) this is sufficient evidence to reject the null hypothesis, and conclude that the variable fits a different distribution.

                                                                                                                                                                                                                                Sample Problem

                                                                                                                                                                                                                                Working as a sales clerk, you're wondering if the number of customers depends on the day of week. You've taken a count of the number of customers every day for a week: 17 on Monday, 21 on Tuesday, 18 on Wednesday, 10 on Thursday, 24 on Friday, 28 on Saturday, and 24 on Sunday. Store this observed count: {17,21,18,10,24,28,24} to L1.

                                                                                                                                                                                                                                There were a total of sum(L1)=142 customers. So the expected number of customers on each day was 142/7. Store all the expected counts: {142/7,142/7,142/7,142/7,142/7,142/7,142/7} to L2 (as a shortcut, you can store 142/7{1,1,1,1,1,1,1}).

                                                                                                                                                                                                                                Since there are 7 days, there are 6 (one less) degrees of freedom. So the resulting command is χ²GOF-Test(L1,L2,6).

                                                                                                                                                                                                                                The output will give a χ² of 10.32394366, and a p value of 0.1116563376. This is higher than 5%, so the test is not significant on a 95 percent level. It's perfectly possible, in other words, that the number of customers is independent of the day of week.

                                                                                                                                                                                                                                (Note that in this case, if you suspected the number of customers to be higher on weekends, you could use a more sensitive test for only two categories: 2-SampTTest)

                                                                                                                                                                                                                                Advanced Uses

                                                                                                                                                                                                                                The χ²GOF-Test( command is only on TI-84 Plus and newer calculator models. However, it's possible to use the χ²cdf( command to simulate it on the other calculators: see the χ² Goodness-of-fit Test routine.

                                                                                                                                                                                                                                Formulas

                                                                                                                                                                                                                                The formula for calculating the test statistic is as follows (Oi is the observed count of the ith category, and Ei is the expected count):

                                                                                                                                                                                                                                (1) \(\begin{align} \chi_{n-1}^2 = \sum_{i=1}^n \frac{(O_i-E_i)^2}{E_i} \end{align}\)

                                                                                                                                                                                                                                The p-value, then, is the probability that the χ² statistic would be this high, using the χ²cdf( command with the appropriate value for degrees of freedom.

                                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                                • ERR:DIM MISMATCH is thrown if the two lists are of different length.
                                                                                                                                                                                                                                • ERR:DOMAIN is thrown if they only have one element, or if df is not a positive integer.

                                                                                                                                                                                                                                See Also

                                                                                                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Myles_Zadok.

                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                TI-84+ 2.30 Added
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                                                                                                                                                                                                                                • FR: X²FRép(

                                                                                                                                                                                                                                χ²cdf(

                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                Computes the χ²distribution probability between lowerbound andupperbound for the specified degrees of freedom df.

                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                χ²cdf(lowerbound,upperbound,df)

                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                χ²
                                                                                                                                                                                                                                lowerbound
                                                                                                                                                                                                                                upperbound
                                                                                                                                                                                                                                df

                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                2nd, distr, DISTR, 8:cdf(

                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                χ²cdf( is the χ² cumulative density function. If some random variable follows a χ² distribution, you can use this command to find the probability that this variable will fall in the interval you supply.

                                                                                                                                                                                                                                The command takes three arguments. lower and upper define the interval in which you're interested. df specifies the degrees of freedom (choosing one of a family of χ² distributions).

                                                                                                                                                                                                                                Advanced Uses

                                                                                                                                                                                                                                Often, you want to find a "tail probability" - a special case for which the interval has no lower or no upper bound. For example, "what is the probability x is greater than 2?". The TI-83+ has no special symbol for infinity, but you can use E99 to get a very large number that will work equally well in this case (E is the decimal exponent obtained by pressing [2nd] [EE]). Use E99 for positive infinity, and -E99 for negative infinity.

                                                                                                                                                                                                                                The χ²cdf( command is crucial to performing a χ² goodness of fit test, which the early TI-83 series calculators do not have a command for (the χ²-Test( command performs the χ² test of independence, which is not the same thing, although the manual always just refers to it as the "χ² Test"). This test is used to test if an observed frequency distribution differs from the expected, and can be used, for example, to tell if a coin or die is fair.

                                                                                                                                                                                                                                The Goodness-of-Fit Test routine on the routines page will perform a χ² goodness of fit test for you. Or, if you have a TI-84+/SE with OS version 2.30 or higher, you can use the χ²GOF-Test( command.

                                                                                                                                                                                                                                Formulas

                                                                                                                                                                                                                                As with other continuous distributions, we can define χ²cdf( in forms of the probability density function:

                                                                                                                                                                                                                                (1) \(\begin{align} \texttt{\chi^2cdf}(a,b,k) = \int_a^b \texttt{\chi^2pdf}(x,k)\,dx \end{align}\)

                                                                                                                                                                                                                                See Also

                                                                                                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583.

                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                Calculator OS Version Description
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                                                                                                                                                                                                                                • FR: Χ²Fdp(

                                                                                                                                                                                                                                χ²pdf(

                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                Computes the probability density function (pdf) for the χ² distribution at a specified x value for the specified degrees of freedom df.

                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                χ²pdf(x,df)

                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                χ²
                                                                                                                                                                                                                                x
                                                                                                                                                                                                                                df

                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                2nd, distr, DISTR, 7:pdf(

                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                χ²pdf( is the χ² probability density function.

                                                                                                                                                                                                                                Since the χ² distribution is continuous, the value of χ²pdf( doesn't represent an actual probability — in fact, one of the only uses for this command is to draw a graph of the χ² curve. You could also use it for various calculus purposes, such as finding inflection points.

                                                                                                                                                                                                                                The command takes two arguments: the value at which to evaluate the p.d.f., and df, the number of 'degrees of freedom'.

                                                                                                                                                                                                                                Formulas

                                                                                                                                                                                                                                The value of χ²pdf( is given by

                                                                                                                                                                                                                                (1) \(\begin{align} \texttt{\chi^2pdf}(x,k)=\frac{(1/2)^{k/2}}{(k/2-1)!}\,x^{k/2-1}e^{-x/2} \end{align}\)

                                                                                                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583.

                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                TI-83 0.01013 Added
                                                                                                                                                                                                                                Property Value
                                                                                                                                                                                                                                Hex Value $BB25
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                                                                                                                                                                                                                                • FR: conj(

                                                                                                                                                                                                                                conj(

                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                Returns the complex conjugate of a complex number or list of complex numbers.

                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                conj(value)

                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                valuecomplex|complex[]

                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                math, CMPLX, 1:conj(

                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                conj(z) returns the complex conjugate of the complex number z. If z is represented as x+i_y_ where x and y are both real, conj(z) returns x-i_y_. Also works on a list of complex numbers.

                                                                                                                                                                                                                                conj(3+4i)
     3-4i

                                                                                                                                                                                                                                The conjugate of a number \(z\) is often written \(\overline{z}\), and is useful because it has the property that \(z\overline{z}\) and \(z+\overline{z}\) are real numbers.

                                                                                                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583.

                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                TI-83 0.01013 Added
                                                                                                                                                                                                                                Property Value
                                                                                                                                                                                                                                Hex Value $C4
                                                                                                                                                                                                                                Categories
                                                                                                                                                                                                                                Localizations
                                                                                                                                                                                                                                • FR: cos(

                                                                                                                                                                                                                                cos(

                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                Returns cosine of a real number, expression, or list.

                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                cos(value)

                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                valuereal|expression|real[]

                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                cos

                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                cos(θ) returns the cosine of θ, which is defined as the x-value of the point of intersection of the unit circle and a line containing the origin that makes an angle θ with the positive x-axis

                                                                                                                                                                                                                                The value returned depends on whether the calculator is in Radian or Degree mode. A full rotation around a circle is 2π radians, which is equal to 360°. The conversion from radians to degrees is angle180/π and from degrees to radians is angleπ/180. The cos( command also works on a list of real numbers.

                                                                                                                                                                                                                                In radians:

                                                                                                                                                                                                                                cos(π/3)
    .5

                                                                                                                                                                                                                                In degrees:

                                                                                                                                                                                                                                cos(60)
    .5

                                                                                                                                                                                                                                Advanced Uses

                                                                                                                                                                                                                                You can bypass the mode setting by using the ° (degree) and ʳ (radian) symbols. These next two commands will return the same values no matter if your calculator is in degrees or radians:

                                                                                                                                                                                                                                cos(60°)
    .5

                                                                                                                                                                                                                                cos(π/3ֿ¹ )
    .5

                                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                                • ERR:DATA TYPE is thrown if you supply a matrix or a complex argument.
                                                                                                                                                                                                                                • ERR:ARGUMENT is thrown if you use more than one number.
                                                                                                                                                                                                                                • ERR:DOMAIN is thrown if you supply an input ≥1E12.

                                                                                                                                                                                                                                See Also

                                                                                                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Myles_Zadok, nap386, simplethinker, Xeda Elnara.

                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                TI-82 1.0 cos added
                                                                                                                                                                                                                                TI-83 0.01013 Renamed cos to cos(
                                                                                                                                                                                                                                Property Value
                                                                                                                                                                                                                                Hex Value $C5
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                                                                                                                                                                                                                                • FR: Arccos(

                                                                                                                                                                                                                                cos⁻¹(

                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                Returns arccosine of a real number, expression, or list.

                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                cos⁻¹(value)

                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                ⁻¹real|expression|real[]
                                                                                                                                                                                                                                valuereal|expression|real[]

                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                2nd, cos⁻¹

                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                cosֿ¹( returns the arccosine of its argument. It is the inverse of cos(, which means that cosֿ¹(n) produces an angle θ such that cos(θ)=n.

                                                                                                                                                                                                                                Like cos(, the result of cosֿ¹( depends on whether the calculator is in Radian or Degree mode. However, unlike cosine, the result is in degrees or radians, not the argument. A full rotation around a circle is 2π radians, which is equal to 360°. The conversion of θ=cosֿ¹(n) from radians to degrees is θ180/π and from degrees to radians is θπ/180. The cosֿ¹( command also works on a list.

                                                                                                                                                                                                                                The cosֿ¹( function can be defined for all real and complex numbers, but assumes real values only in the closed interval [-1,1]. Because Z80 calculators have their trigonometric functions and inverses restricted only to real values, the calculator will throw ERR:DOMAIN if the argument is outside of this interval, no matter what the mode setting may be.

                                                                                                                                                                                                                                In radians:

                                                                                                                                                                                                                                :cosֿ¹(-1)
    3.141592654

                                                                                                                                                                                                                                In degrees:

                                                                                                                                                                                                                                :cosֿ¹(-1)
    180

                                                                                                                                                                                                                                Advanced Uses

                                                                                                                                                                                                                                Since the function cosine itself doesn't have the restrictions that arccosine does, and since arccosine is the inverse of cosine, you can use cosֿ¹(cos( to keep a variable within a certain range (most useful for the home screen). Here is an example for a game like pong. The ball travels between 0 and 12.

                                                                                                                                                                                                                                You could use a flag like this:

                                                                                                                                                                                                                                :If X=12 or not(X     \\ X is the position
:-D→D        \\ D is the direction
:X+D→X        \\ new position
:Output(8,X,"=

                                                                                                                                                                                                                                An easier way to do this, without needing a flag or even an If statement, is using cosֿ¹(cos(

                                                                                                                                                                                                                                :X+1→X        \\ Note: the calculator is in Degree mode
:Output(8,cosֿ¹(cos(15X))/15,"=")    \\ I used 15 because cosֿ¹ ranges from [0,180]
                                        and X from [0,12],  so 180/12=15

                                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                                • ERR:DOMAIN is thrown if you supplied an argument outside the interval [-1,1]
                                                                                                                                                                                                                                • ERR:DATA TYPE is thrown if you input a complex value or a matrix.

                                                                                                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Myles_Zadok, simplethinker, thornahawk.

                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                TI-82 1.0 cos⁻¹ added
                                                                                                                                                                                                                                TI-83 0.01013 Renamed cos⁻¹ to cos⁻¹(
                                                                                                                                                                                                                                Property Value
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                                                                                                                                                                                                                                • FR: ch(

                                                                                                                                                                                                                                cosh(

                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                Returns hyperbolic cosine of a real number, expression, or list.

                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                cosh(value)

                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                valuereal|expression|real[]

                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                2nd, catalog, cosh(

                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                Calculates the hyperbolic cosine of a value. The hyperbolic trig functions sinh(, cosh(, and tanh( are an analog of normal trig functions, but for a hyperbola, rather than a circle. They can be expressed in terms of real powers of e, and don't depend on the Degree or Radian mode setting.

                                                                                                                                                                                                                                cosh(0)
    1
cosh(1)
    1.543080635

                                                                                                                                                                                                                                Like normal trig commands, cosh( works on lists as well, but not on complex numbers, even though the function is often extended to the complex numbers in mathematics.

                                                                                                                                                                                                                                Formulas

                                                                                                                                                                                                                                The definition of hyperbolic cosine is:

                                                                                                                                                                                                                                (1) \(\begin{align} \cosh{x}=\frac{e^x+e^{-x}}{2} \end{align}\)

                                                                                                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Myles_Zadok, thornahawk, Timothy Foster.

                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                TI-82 1.0 cosh added
                                                                                                                                                                                                                                TI-83 0.01013 Renamed cosh to cosh(
                                                                                                                                                                                                                                Property Value
                                                                                                                                                                                                                                Hex Value $CB
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                                                                                                                                                                                                                                • FR: Argch(

                                                                                                                                                                                                                                cosh⁻¹(

                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                Returns hyperbolic arccosine of a real number, expression, or list.

                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                cosh⁻¹ (value)

                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                ⁻¹real|expression|real[]
                                                                                                                                                                                                                                valuereal|expression|real[]

                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                2nd, catalog, cosh

                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                The coshֿ¹( function gives the inverse hyperbolic cosine of a value. coshֿ¹(x) is the number y such that x = cosh(y).

                                                                                                                                                                                                                                Although coshֿ¹(x) can be defined for all real and complex numbers, it assumes real values only for x≥1. Since hyperbolic functions in the Z80 calculators are restricted only to real values, ERR:DOMAIN is thrown when x<1.

                                                                                                                                                                                                                                The coshֿ¹( command also works for lists.

                                                                                                                                                                                                                                coshֿ¹(1)
    0
coshֿ¹({2,3})
    {1.316957897 1.762747174}

                                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                                • ERR:DOMAIN when taking the inverse cosh of a number less than 1.

                                                                                                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Myles_Zadok, thornahawk.

                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                TI-82 1.0 cosh⁻¹ added
                                                                                                                                                                                                                                TI-83 0.01013 Renamed cosh⁻¹ to cosh⁻¹(
                                                                                                                                                                                                                                Property Value
                                                                                                                                                                                                                                Hex Value $CB
                                                                                                                                                                                                                                Categories
                                                                                                                                                                                                                                Localizations
                                                                                                                                                                                                                                • FR: Argch(

                                                                                                                                                                                                                                cosh⁻¹(

                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                Returns hyperbolic arccosine of a real number, expression, or list.

                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                cosh⁻¹ (value)

                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                ⁻¹real|expression|real[]
                                                                                                                                                                                                                                valuereal|expression|real[]

                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                2nd, catalog, cosh

                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                The coshֿ¹( function gives the inverse hyperbolic cosine of a value. coshֿ¹(x) is the number y such that x = cosh(y).

                                                                                                                                                                                                                                Although coshֿ¹(x) can be defined for all real and complex numbers, it assumes real values only for x≥1. Since hyperbolic functions in the Z80 calculators are restricted only to real values, ERR:DOMAIN is thrown when x<1.

                                                                                                                                                                                                                                The coshֿ¹( command also works for lists.

                                                                                                                                                                                                                                coshֿ¹(1)
    0
coshֿ¹({2,3})
    {1.316957897 1.762747174}

                                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                                • ERR:DOMAIN when taking the inverse cosh of a number less than 1.

                                                                                                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Myles_Zadok, thornahawk.

                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                TI-82 1.0 cosh⁻¹ added
                                                                                                                                                                                                                                TI-83 0.01013 Renamed cosh⁻¹ to cosh⁻¹(
                                                                                                                                                                                                                                Property Value
                                                                                                                                                                                                                                Hex Value $C5
                                                                                                                                                                                                                                Categories
                                                                                                                                                                                                                                Localizations
                                                                                                                                                                                                                                • FR: Arccos(

                                                                                                                                                                                                                                cos⁻¹(

                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                Returns arccosine of a real number, expression, or list.

                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                cos⁻¹(value)

                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                ⁻¹real|expression|real[]
                                                                                                                                                                                                                                valuereal|expression|real[]

                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                2nd, cos⁻¹

                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                cosֿ¹( returns the arccosine of its argument. It is the inverse of cos(, which means that cosֿ¹(n) produces an angle θ such that cos(θ)=n.

                                                                                                                                                                                                                                Like cos(, the result of cosֿ¹( depends on whether the calculator is in Radian or Degree mode. However, unlike cosine, the result is in degrees or radians, not the argument. A full rotation around a circle is 2π radians, which is equal to 360°. The conversion of θ=cosֿ¹(n) from radians to degrees is θ180/π and from degrees to radians is θπ/180. The cosֿ¹( command also works on a list.

                                                                                                                                                                                                                                The cosֿ¹( function can be defined for all real and complex numbers, but assumes real values only in the closed interval [-1,1]. Because Z80 calculators have their trigonometric functions and inverses restricted only to real values, the calculator will throw ERR:DOMAIN if the argument is outside of this interval, no matter what the mode setting may be.

                                                                                                                                                                                                                                In radians:

                                                                                                                                                                                                                                :cosֿ¹(-1)
    3.141592654

                                                                                                                                                                                                                                In degrees:

                                                                                                                                                                                                                                :cosֿ¹(-1)
    180

                                                                                                                                                                                                                                Advanced Uses

                                                                                                                                                                                                                                Since the function cosine itself doesn't have the restrictions that arccosine does, and since arccosine is the inverse of cosine, you can use cosֿ¹(cos( to keep a variable within a certain range (most useful for the home screen). Here is an example for a game like pong. The ball travels between 0 and 12.

                                                                                                                                                                                                                                You could use a flag like this:

                                                                                                                                                                                                                                :If X=12 or not(X     \\ X is the position
:-D→D        \\ D is the direction
:X+D→X        \\ new position
:Output(8,X,"=

                                                                                                                                                                                                                                An easier way to do this, without needing a flag or even an If statement, is using cosֿ¹(cos(

                                                                                                                                                                                                                                :X+1→X        \\ Note: the calculator is in Degree mode
:Output(8,cosֿ¹(cos(15X))/15,"=")    \\ I used 15 because cosֿ¹ ranges from [0,180]
                                        and X from [0,12],  so 180/12=15

                                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                                • ERR:DOMAIN is thrown if you supplied an argument outside the interval [-1,1]
                                                                                                                                                                                                                                • ERR:DATA TYPE is thrown if you input a complex value or a matrix.

                                                                                                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Myles_Zadok, simplethinker, thornahawk.

                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                TI-82 1.0 cos⁻¹ added
                                                                                                                                                                                                                                TI-83 0.01013 Renamed cos⁻¹ to cos⁻¹(
                                                                                                                                                                                                                                Property Value
                                                                                                                                                                                                                                Hex Value $80
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                                                                                                                                                                                                                                • FR: ﹢

                                                                                                                                                                                                                                ﹢

                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                ﹢

                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                Examples

                                                                                                                                                                                                                                Explanation 1

                                                                                                                                                                                                                                code 1

                                                                                                                                                                                                                                Explanation 2

                                                                                                                                                                                                                                code 2

                                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                                Advanced Notes

                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                TI-82 1.0 Added
                                                                                                                                                                                                                                Property Value
                                                                                                                                                                                                                                Hex Value $BD
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                                                                                                                                                                                                                                • FR: ³√(

                                                                                                                                                                                                                                ³√(

                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                ³√(

                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                Examples

                                                                                                                                                                                                                                Explanation 1

                                                                                                                                                                                                                                code 1

                                                                                                                                                                                                                                Explanation 2

                                                                                                                                                                                                                                code 2

                                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                                Advanced Notes

                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                TI-82 1.0 ³√ added
                                                                                                                                                                                                                                TI-83 0.01013 Renamed ³√ to ³√(
                                                                                                                                                                                                                                Property Value
                                                                                                                                                                                                                                Hex Value $BB29
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                                                                                                                                                                                                                                • FR: somCum(

                                                                                                                                                                                                                                cumSum(

                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                Returns a list of the cumulative sums of the elements in list, starting with the first element.

                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                cumSum(list)

                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                listlist

                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                2nd, list, OPS, 6:cumSum(

                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                Returns a matrix of the cumulative sums of matrix elements. Each element in the returned matrix is a cumulative sum of a matrix column from top to bottom.

                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                cumSum(matrix)

                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                matrixmatrix

                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                2nd, matrix, MATH, 0:cumSum(

                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                cumSum( calculates the cumulative sums of a list, or of the columns of a matrix, and outputs them in a new list or matrix variable.

                                                                                                                                                                                                                                For a list, this means that the Nth element of the result is the sum of the first N elements of the list:

                                                                                                                                                                                                                                cumSum({1,3,5,7,9})
    {1 4 9 16 25}

                                                                                                                                                                                                                                For a matrix, cumSum( is applied to each column in the same way as it would be for a list (but numbers in different columns are never added):

                                                                                                                                                                                                                                [[0,1,1][0,1,3][0,1,5][0,1,7]]
    [[0 1 1]
     [0 1 3]
     [0 1 5]
     [0 1 7]]
cumSum(Ans)
    [[0 1 1]
     [0 2 4]
     [0 3 9]
     [0 4 16]]

                                                                                                                                                                                                                                Advanced Uses

                                                                                                                                                                                                                                The ΔList( command is very nearly the inverse of the cumSum( command - it calculates the differences between consecutive elements. For any list, ΔList(cumSum(list)) will return the same list, but without its first element:

                                                                                                                                                                                                                                ΔList(cumSum({1,2,3,4,5,6,7}))
    {2 3 4 5 6 7}

                                                                                                                                                                                                                                Removing the first element would otherwise be a difficult procedure involving the seq( command, so this is a useful trick to know.

                                                                                                                                                                                                                                For a matrix, if you want to sum up the rows instead of the columns, use the T (transpose) command.

                                                                                                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Myles_Zadok.

                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                TI-83 0.01013 Added
                                                                                                                                                                                                                                Property Value
                                                                                                                                                                                                                                Hex Value $BBB3
                                                                                                                                                                                                                                Categories
                                                                                                                                                                                                                                Localizations
                                                                                                                                                                                                                                • FR: d

                                                                                                                                                                                                                                d

                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                d

                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                Examples

                                                                                                                                                                                                                                Explanation 1

                                                                                                                                                                                                                                code 1

                                                                                                                                                                                                                                Explanation 2

                                                                                                                                                                                                                                code 2

                                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                                Advanced Notes

                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                TI-83+ 1.03 Added
                                                                                                                                                                                                                                Property Value
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                                                                                                                                                                                                                                • FR: [|d]

                                                                                                                                                                                                                                [|d]

                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                [|d]

                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                Examples

                                                                                                                                                                                                                                Explanation 1

                                                                                                                                                                                                                                code 1

                                                                                                                                                                                                                                Explanation 2

                                                                                                                                                                                                                                code 2

                                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                                Advanced Notes

                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                TI-82 1.0 Added
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                                                                                                                                                                                                                                Hex Value $EF06
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                                                                                                                                                                                                                                • FR: joursem(

                                                                                                                                                                                                                                dayOfWk(

                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                Returns an integer from 1 to 7, with each integer representing a day of the week. Use dayOfWk( to determine on which day of the week a particular date would occur. The year must be 4 digits; month and day can be 1 or 2 digits.

                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                dayOfWk(year,month,day)

                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                year
                                                                                                                                                                                                                                month
                                                                                                                                                                                                                                day

                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                2nd, catalog, dayOfWk(, 1:Sunday, 2:Monday, 3:Tuesday...

                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                dayOfWk(year,month,day) returns an integer from 1 to 7, each representing a separate day of the week. 1 represents Sunday, 2 represents Monday, and so on, with 7 representing Saturday. The date format is different than the normal American format (month/day/year), so be careful to put the arguments in the right order. You can remember this by thinking of the descending lengths of time in each of the arguments.

                                                                                                                                                                                                                                :dayOfWk(2007,12,30)

                                                                                                                                                                                                                                The above code returns 1, because the 30th of December, 2007, is a Sunday.

                                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                                • ERR:DOMAIN is thrown if any of the arguments are non-integers, or the date does not exist, such as the 42nd of February. However, the year does not matter (a date that takes place in the year 10000 is valid). However, there are exceptions, even if some dates do exist, this error may still occur. If you attempt to calculate the previous day of a week such as the previous day, the error may still occur.

                                                                                                                                                                                                                                See Also

                                                                                                                                                                                                                                • Day of Week — routine to calculate the day of the week

                                                                                                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, iPhoenixOnTIBD, Myles_Zadok, nap386, Weregoose, Xphoenix.

                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                TI-84+ 0.01 Added
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                                                                                                                                                                                                                                • FR: jed(

                                                                                                                                                                                                                                dbd(

                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                Calculates the number of days between date1 and date2 using the actual-day-count method.

                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                dbd(date1,date2)

                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                date1
                                                                                                                                                                                                                                date2

                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                apps, 1:Finance, CALC, D:dbd(

                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                The dbd( command calculates the number of days between two dates. Each date is encoded as a single number in one of two formats (two formats can be mixed in the same command):

                                                                                                                                                                                                                                • day, month, year — DDMM.YY (e.g. April 26, 1989 would be 2604.89)
                                                                                                                                                                                                                                • month, day, year — MM.DDYY (e.g. April 26, 1989 would be 04.2689 or just 4.2689)

                                                                                                                                                                                                                                Because this is just a number like any other, leading zeroes and trailing zeroes after the decimal can be dropped. For example, January 1, 2000 does not have to be formatted as 0101.00 but can be simply 101.

                                                                                                                                                                                                                                Since there are only two digits for the year, obviously only a century's worth of dates can be handled. The calculator assumes this range to be from January 1, 1950 to December 31, 2049.

                                                                                                                                                                                                                                If the second date comes before the first, dbd( will return a negative number of days, so the range of possible results is from -36524 to 36524.

                                                                                                                                                                                                                                Finally, dbd( will also work for list inputs in the usual manner: a single date will be compared against every date in a list, and two lists of dates will be paired up.

                                                                                                                                                                                                                                dbd(612.07,2512.07
    19
dbd(1.0207,1.0107
    -1
dbd(1.0107,{2.0107,3.0107,4.0107})
    {31 59 90}

                                                                                                                                                                                                                                Advanced Uses

                                                                                                                                                                                                                                The dbd( command can be used to calculate the day of week without using the dayOfWk( command, which is only available on the TI-84+ or higher.

                                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                                • ERR:DOMAIN is thrown if a date is improperly formatted.

                                                                                                                                                                                                                                See Also

                                                                                                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583, Weregoose.

                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                TI-83 0.01013 Added
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                                                                                                                                                                                                                                • FR: δ

                                                                                                                                                                                                                                δ

                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                δ

                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                Examples

                                                                                                                                                                                                                                Explanation 1

                                                                                                                                                                                                                                code 1

                                                                                                                                                                                                                                Explanation 2

                                                                                                                                                                                                                                code 2

                                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                                Advanced Notes

                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                TI-83+ 1.03 Added
                                                                                                                                                                                                                                Property Value
                                                                                                                                                                                                                                Hex Value $B3
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                                                                                                                                                                                                                                • FR: dét(

                                                                                                                                                                                                                                det(

                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                Returns determinant of matrix.

                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                det(matrix)

                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                matrixmatrix

                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                2nd, matrix, MATH, 1:det(

                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                The det( command calculates the determinant of a square matrix. If its argument is not a square matrix, ERR:INVALID DIM will be thrown.

                                                                                                                                                                                                                                Advanced Uses

                                                                                                                                                                                                                                If [A] is an N×N matrix, then the roots of det([A]-X identity(N)) are the eigenvalues of [A].

                                                                                                                                                                                                                                Formulas

                                                                                                                                                                                                                                For 2×2 matrices, the determinant is simply

                                                                                                                                                                                                                                (1) \(\begin{align} \det\left( \begin{bmatrix} a & b\\c & d \end{bmatrix} \right) = \begin{vmatrix} a & b\\c & d \end{vmatrix} = ad-bc \end{align}\)

                                                                                                                                                                                                                                For larger matrices, the determinant can be computed using the Laplace expansion, which allows you to express the determinant of an n×n matrix in terms of the determinants of (n-1)×(n-1) matrices. However, since the Laplace expansion takes \(O\left( n! \right)\) operations, the method usually used in calculators is Gaussian elimination, which only needs \(O\left( n^3 \right)\) operations.

                                                                                                                                                                                                                                The matrix is first decomposed into a unit lower-triangular matrix and an upper-triangular matrix using elementary row operations:

                                                                                                                                                                                                                                (2) \(\begin{pmatrix} {1}&{}&{}\\ {\vdots}&{\ddots}&{}\\ {\times}&{\cdots}&{1}\end{pmatrix} \begin{pmatrix}{\times}&{\cdots}&{\times}\\ {}&{\ddots}&{\vdots}\\ {}&{}&{\times} \end{pmatrix}\)

                                                                                                                                                                                                                                The determinant is then calculated as the product of the diagonal elements of the upper-triangular matrix.

                                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Myles_Zadok, thornahawk.

                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                TI-82 1.0 det added
                                                                                                                                                                                                                                TI-83 0.01013 Renamed det to det(
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                                                                                                                                                                                                                                Hex Value $B5
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                                                                                                                                                                                                                                • FR: dim(

                                                                                                                                                                                                                                dim(

                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                Returns the dimension of listname.

                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                dim(listname)

                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                listnamelist

                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                2nd, list, OPS, 3:dim(

                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                Returns the dimension of matrixname as a list.

                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                dim(matrixname)

                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                matrixnamematrix

                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                2nd, matrix, MATH, 3:dim(

                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                Assigns a new dimension (length) to a new or existing listname.

                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                length→dim(listname)

                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                lengthinteger
                                                                                                                                                                                                                                listnamelist

                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                2nd, list, OPS, 3:dim(

                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                Assigns new dimensions to a new or existing matrixname.

                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                {rows,columns}→dim(matrixname)

                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                rowsinteger
                                                                                                                                                                                                                                columnsinteger
                                                                                                                                                                                                                                matrixnamematrix

                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                2nd, matrix, MATH, 3:dim(

                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                The dim( command is used to find the size of an existing list or matrix. It takes only one argument - the list or matrix you want the size of. For a list, it returns the number of elements; for a matrix, it returns a two-element list of the number of rows and the number of columns.

                                                                                                                                                                                                                                :dim(L1
    5
:dim([A]
    {2,3}

                                                                                                                                                                                                                                The dim( command can also be used to change the size of a list or matrix; this is perhaps its most important use. To do this, just store the desired size to the list or matrix (the dim( command is the only one you can store in as though it were a variable).

                                                                                                                                                                                                                                :7→dim(L1
:{2,2→dim([A]

                                                                                                                                                                                                                                For a list, if this increases the size, zero elements will be added to the end of the list; if this decreases the size, elements will be removed starting from the end.

                                                                                                                                                                                                                                For a matrix, if this increases the number of rows or columns, new rows or columns filled with zeros will be added to the bottom and right respectively. If this decreases the number of rows and columns, those rows and columns will be removed starting from the bottom (for rows) and right (for columns).

                                                                                                                                                                                                                                If a list or matrix doesn't exist before its size is changed, the dim( command will actually create it with the correct size. All the elements, in this case, will be set to 0.

                                                                                                                                                                                                                                Advanced Uses

                                                                                                                                                                                                                                In the case of lists, the dim( command is used in adding an element to the end of a list. Although augment( can be used for the same task, dim( is faster - but takes more memory. For example, to add the element 5 to the end of L1:

                                                                                                                                                                                                                                :5→L1(1+dim(L1

                                                                                                                                                                                                                                It's also possible, using the dim( command, to set the size of a list to 0. In this case, the list exists, but doesn't take up any memory, and cannot be used in expressions (similar to the output of ClrList). This is not really useful.

                                                                                                                                                                                                                                Optimization

                                                                                                                                                                                                                                When creating a list or matrix using dim(, all the elements are preset to 0; this can be used in place of the Fill( command to set a list or matrix to a bunch of zeros in a program. Since we don't usually know for sure that the list or matrix doesn't exist, we must first delete it with DelVar.

                                                                                                                                                                                                                                :{5,5→dim([A]
:Fill(0,[A]
can be
:DelVar [A]{5,5→dim([A]

                                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                                • ERR:INVALID DIM is thrown if you try to make a list or matrix bigger than 999 or 99x99 elements respectively, or if you try to create a matrix that isn't 2-dimensional.

                                                                                                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Myles_Zadok.

                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                TI-82 1.0 dim added
                                                                                                                                                                                                                                TI-83 0.01013 Renamed dim to dim(
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                                                                                                                                                                                                                                • FR: ·

                                                                                                                                                                                                                                ·

                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                ·

                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                Examples

                                                                                                                                                                                                                                Explanation 1

                                                                                                                                                                                                                                code 1

                                                                                                                                                                                                                                Explanation 2

                                                                                                                                                                                                                                code 2

                                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                                Advanced Notes

                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                TI-82 1.0 Added
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                                                                                                                                                                                                                                Hex Value $BBEE
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                                                                                                                                                                                                                                • FR: ↓

                                                                                                                                                                                                                                ↓

                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                ↓

                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                Examples

                                                                                                                                                                                                                                Explanation 1

                                                                                                                                                                                                                                code 1

                                                                                                                                                                                                                                Explanation 2

                                                                                                                                                                                                                                code 2

                                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                                Advanced Notes

                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                TI-83+ 1.16 Added
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                                                                                                                                                                                                                                Hex Value $45
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                                                                                                                                                                                                                                • FR: E

                                                                                                                                                                                                                                E

                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                E

                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                The E symbol is used for entering numbers in scientific notation: it's short for *10^. This means that in many cases, its function is identical to that of the 10^( command (aside from the parenthesis). However, the exponent of E is limited to constant integer values ‾99 to 99.

                                                                                                                                                                                                                                The E symbol is used in display by the calculator for large numbers, or when in Sci (scientific) or Eng (engineering) mode.

                                                                                                                                                                                                                                Unlike the exponent of E, the mantissa (a special term for the A in A*10^B, in scientific notation) isn't limited in variable type: it can be a constant, a real or complex variable or expression, a list, a matrix, or even omitted entirely (and then it will be assumed to equal 1). The reason for this versatility is simple: internally, only the exponent is taken to be an actual argument for this command. The rest of the calculation is done through implied multiplication.

                                                                                                                                                                                                                                5E3
                                                                                                                                                                                                                                ………………5000
                                                                                                                                                                                                                                E‾5
                                                                                                                                                                                                                                ……………….00001

                                                                                                                                                                                                                                Advanced Uses

                                                                                                                                                                                                                                E99 and -E99 are often used for negative and positive infinity because the TI-83 series of calculators doesn't have an infinity symbol. Commands that often need to use infinity include solve(, fnInt(, normalcdf( (and the other distributions), and many others. The error introduced in this way is usually irrelevant, because it's less than the minimum calculator precision, anyway: E99 is mindbogglingly huge.

                                                                                                                                                                                                                                Optimization

                                                                                                                                                                                                                                Don't add the mantissa when it's 1:

                                                                                                                                                                                                                                1E5
                                                                                                                                                                                                                                should be
                                                                                                                                                                                                                                E5

                                                                                                                                                                                                                                In addition, E2 or E3 can be used as shorthand ways of writing 100 and 1000 respectively. This could be continued, in theory, for higher powers of 10, but those aren't necessary as often.

                                                                                                                                                                                                                                Command Timings

                                                                                                                                                                                                                                E is much faster than using the 10^( command or typing out 10^. The drawback, of course, is that it's limited to constant values.

                                                                                                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: alexrudd, burr, DarkerLine, GoVegan, Myles_Zadok, simplethinker, Timothy Foster.

                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                TI-82 1.0 Added
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                                                                                                                                                                                                                                • FR: 𝑒^(

                                                                                                                                                                                                                                𝑒^(

                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                Returns e raised to power.

                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                𝑒^(power)

                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                power

                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                2nd, eˣ

                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                Returns a list of e raised to a list of powers.

                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                𝑒^(list)

                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                listlist

                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                2nd, eˣ

                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                The e^( command raises the constant e to a power. Since it's possible to just type out e, ^, and (, the reason for having a separate function isn't immediately obvious but in fact most of the time you need to use e, it's to raise it to a power.

                                                                                                                                                                                                                                The trigonometric and hyperbolic functions can be expressed, and in fact are usually defined, in terms of e^(.

                                                                                                                                                                                                                                e^( accepts numbers and lists (but unfortunately not matrices) as arguments. It also works, and is often used for, complex numbers (in fact, one of the standard forms of complex numbers on TI-83 series calculators is r𝑒^θ𝑖, which uses the e^( function)

                                                                                                                                                                                                                                e^(2)
        7.389056099
𝑒^(πi)
        -1
𝑒^({-1,0,1})
        {.3678794412 1 2.718281828}

                                                                                                                                                                                                                                Formulas

                                                                                                                                                                                                                                The e^( is usually defined by an infinite series:

                                                                                                                                                                                                                                (1) \(\begin{align} e^x=\sum_{n=0}^\infty{\frac{x^n}{n!}} \end{align}\)

                                                                                                                                                                                                                                This is then used to define exponentiation in general (for all real and even complex numbers), rather than using some sort of definition of exponents that involves multiplying a number by itself many times (which only works for integers).

                                                                                                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Myles_Zadok, Timothy Foster.

                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                TI-82 1.0 𝑒^ added
                                                                                                                                                                                                                                TI-83 0.01013 Renamed 𝑒^ to 𝑒^(
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                                                                                                                                                                                                                                • FR: e

                                                                                                                                                                                                                                e

                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                e

                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                Examples

                                                                                                                                                                                                                                Explanation 1

                                                                                                                                                                                                                                code 1

                                                                                                                                                                                                                                Explanation 2

                                                                                                                                                                                                                                code 2

                                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                                Advanced Notes

                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                TI-83+ 1.03 Added
                                                                                                                                                                                                                                Property Value
                                                                                                                                                                                                                                Hex Value $621A
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                                                                                                                                                                                                                                • FR: [|e]

                                                                                                                                                                                                                                [|e]

                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                [|e]

                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                Examples

                                                                                                                                                                                                                                Explanation 1

                                                                                                                                                                                                                                code 1

                                                                                                                                                                                                                                Explanation 2

                                                                                                                                                                                                                                code 2

                                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                                Advanced Notes

                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                TI-82 1.0 Added
                                                                                                                                                                                                                                Property Value
                                                                                                                                                                                                                                Hex Value $BBA4
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                                                                                                                                                                                                                                • FR: ε

                                                                                                                                                                                                                                ε

                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                ε

                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                Examples

                                                                                                                                                                                                                                Explanation 1

                                                                                                                                                                                                                                code 1

                                                                                                                                                                                                                                Explanation 2

                                                                                                                                                                                                                                code 2

                                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                                Advanced Notes

                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                TI-83+ 1.03 Added
                                                                                                                                                                                                                                Property Value
                                                                                                                                                                                                                                Hex Value $EF98
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                                                                                                                                                                                                                                  • FR: eval(

                                                                                                                                                                                                                                  eval(

                                                                                                                                                                                                                                  Overview

                                                                                                                                                                                                                                  Returns an evaluated expression as a string with 8 significant digits. The expression must be real.

                                                                                                                                                                                                                                  Comment:CE OS 5.2+

                                                                                                                                                                                                                                  Availability: Token only available from within the Basic editor.

                                                                                                                                                                                                                                  Syntax

                                                                                                                                                                                                                                  eval(expression)

                                                                                                                                                                                                                                  Arguments

                                                                                                                                                                                                                                  NameTypeOptional
                                                                                                                                                                                                                                  expressionexpression

                                                                                                                                                                                                                                  Location

                                                                                                                                                                                                                                  prgm, I/O, C:eval(

                                                                                                                                                                                                                                  Overview

                                                                                                                                                                                                                                  Returns an evaluated expression as a string with 8 significant digits. The expression must simplify to a real expression.

                                                                                                                                                                                                                                  Comment:CE OS 5.2+

                                                                                                                                                                                                                                  Availability: Token only available from within the Basic editor.

                                                                                                                                                                                                                                  Syntax

                                                                                                                                                                                                                                  eval(expression)

                                                                                                                                                                                                                                  Arguments

                                                                                                                                                                                                                                  NameTypeOptional
                                                                                                                                                                                                                                  expressionexpression

                                                                                                                                                                                                                                  Location

                                                                                                                                                                                                                                  prgm, 6:eval(

                                                                                                                                                                                                                                  Special Category

                                                                                                                                                                                                                                  TI-Innovator™ Hub

                                                                                                                                                                                                                                  Description

                                                                                                                                                                                                                                  The eval( command, given an expression that evaluates to a real number, returns the string representation of that number.

                                                                                                                                                                                                                                  eval(1337       //returns "1337"

eval(2.0-3.0    //returns "‾1"

eval(.0001234   //returns "1.234ᴇ‾4"

                                                                                                                                                                                                                                  eval( has more limitations than the toString( command. It cannot handle lists, matrices, or complex numbers (even when the imaginary part of the complex number is zero). Another difference from toString( is that eval( is unaffected by display mode changes like Fix.

                                                                                                                                                                                                                                  Advanced Uses

                                                                                                                                                                                                                                  Use eval( in conjunction with expr( to evaluate a real expression in a string and return the answer in a string.

                                                                                                                                                                                                                                  3.14->X
eval(expr("2X+3
//returns "9.28"

                                                                                                                                                                                                                                  Error Conditions

                                                                                                                                                                                                                                  • ERR:DATA TYPE is thrown when the expression contains a list, matrix, imaginary number, or string.
                                                                                                                                                                                                                                  • ERR:SYNTAX is thrown when trying to evaluate a command that doesn't return a value.

                                                                                                                                                                                                                                  Source: parts of this page were written by the following TI|BD contributors: Battlesquid, jonbush, lirtosiast, Michael2_3B.

                                                                                                                                                                                                                                  History

                                                                                                                                                                                                                                  Calculator OS Version Description
                                                                                                                                                                                                                                  TI-84+CE 5.2.0 Added
                                                                                                                                                                                                                                  Property Value
                                                                                                                                                                                                                                  Hex Value $BB2A
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                                                                                                                                                                                                                                  • FR: expr(

                                                                                                                                                                                                                                  expr(

                                                                                                                                                                                                                                  Overview

                                                                                                                                                                                                                                  Converts the character string contained in string to an expression and executes the expression. string can be a string or a string variable.

                                                                                                                                                                                                                                  Availability: Token only available from within the Basic editor.

                                                                                                                                                                                                                                  Syntax

                                                                                                                                                                                                                                  expr(string)

                                                                                                                                                                                                                                  Arguments

                                                                                                                                                                                                                                  NameTypeOptional
                                                                                                                                                                                                                                  stringstring

                                                                                                                                                                                                                                  Location

                                                                                                                                                                                                                                  prgm

                                                                                                                                                                                                                                  Description

                                                                                                                                                                                                                                  The expr( command is used to evaluate an expression that's stored in a string (an expression is merely anything that returns a value - of any type). Expressions are occasionally stored to strings, rather than evaluated outright, so that their value has the capacity to change when the variables stored inside them change. The expr( command's result depends on the kind of expression that's in the string you pass it — it may return a number, a list, a matrix, or even another string.

                                                                                                                                                                                                                                  As a special case of an expression, the expr( command can also be used to convert a string like "123" to the number 123. Going in the reverse direction (123 to "123") is more complicated.

                                                                                                                                                                                                                                  The expr( command has limitations. Here are the situations in which expr( will not work:

                                                                                                                                                                                                                                  • When the code in the string does not return an answer, and thus is not an expression: e.g. expr("Line(0,0,1,1" or expr("prgmHELLO" is invalid

                                                                                                                                                                                                                                  • When the expression in the string contains an expr( command itself, e.g. expr("expr(Str1" — this will throw an ERR:ILLEGAL NEST error.

                                                                                                                                                                                                                                  • In place of a variable (rather than an expression), e.g. 5→expr("X" isn't a substitute for 5→X because expr("X" evaluates to the value of X and not to X itself.

                                                                                                                                                                                                                                  Advanced Usage with Lists

                                                                                                                                                                                                                                  expr( is often used in conjunction with the Input command to prompt the user to enter a list. Although the Input command can already handle lists, it requires the user to enter the opening bracket that signifies a list. With expr(, this can be avoided.

                                                                                                                                                                                                                                  If you want the user to enter a list separated by commas, instead of:

                                                                                                                                                                                                                                  Input L₁

                                                                                                                                                                                                                                  Use this:

                                                                                                                                                                                                                                  Input Str1
expr("{"+Str1→L₁

                                                                                                                                                                                                                                  This will automatically put the curly bracket in so the user does not have to.

                                                                                                                                                                                                                                  Just be aware that you cannot access individual list items directly after the expr() function, unlike how you can with Ans. The following code will multiply the entire list by 2 rather than return the second item:

                                                                                                                                                                                                                                  expr("{1,2}")(2)

                                                                                                                                                                                                                                  Instead, to access the second item in the list you could split this across two lines and use Ans:

                                                                                                                                                                                                                                  expr("{1,2}")
Ans(2)

                                                                                                                                                                                                                                  Optimization

                                                                                                                                                                                                                                  Evaluating an expression inside a string is more complicated than evaluating a normal expression; you should therefore try to take as much out of an expr( statement as possible to speed up your code. For example:

                                                                                                                                                                                                                                  expr("sum({"+Str1

                                                                                                                                                                                                                                  can be:

                                                                                                                                                                                                                                  sum(expr("{"+Str1

                                                                                                                                                                                                                                  Error Conditions

                                                                                                                                                                                                                                  • ERR:ILLEGAL NEST is thrown when the string to be evaluated contains an expr( itself.
                                                                                                                                                                                                                                  • ERR:INVALID is thrown when trying to evaluate the empty string.
                                                                                                                                                                                                                                  • ERR:SYNTAX is thrown when trying to evaluate a command that doesn't return a value.

                                                                                                                                                                                                                                  Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

                                                                                                                                                                                                                                  History

                                                                                                                                                                                                                                  Calculator OS Version Description
                                                                                                                                                                                                                                  TI-83 0.01013 Added
                                                                                                                                                                                                                                  Property Value
                                                                                                                                                                                                                                  Hex Value $28
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                                                                                                                                                                                                                                  • FR: fMax(

                                                                                                                                                                                                                                  fMax(

                                                                                                                                                                                                                                  Overview

                                                                                                                                                                                                                                  Returns the value of variable where the local maximum of expression occurs, between lower and upper,with specified tolerance.

                                                                                                                                                                                                                                  Availability: Token available everywhere.

                                                                                                                                                                                                                                  Syntax

                                                                                                                                                                                                                                  fMax(expression,variable,lower,upper[,tolerance])

                                                                                                                                                                                                                                  Arguments

                                                                                                                                                                                                                                  NameTypeOptional
                                                                                                                                                                                                                                  expressionexpression
                                                                                                                                                                                                                                  variable
                                                                                                                                                                                                                                  lower
                                                                                                                                                                                                                                  upper
                                                                                                                                                                                                                                  toleranceYes

                                                                                                                                                                                                                                  Location

                                                                                                                                                                                                                                  math, MATH, 7:fMax(

                                                                                                                                                                                                                                  Description

                                                                                                                                                                                                                                  fMax(f(var),var,lo,hi[,tol]) finds the value of var between lo and hi at which the maximum of f(var) occurs. tol controls the accuracy of the maximum value computed. The default value of tol is 10-5.

                                                                                                                                                                                                                                  fMax( only works for real numbers and expressions. Brent's method for optimization is used for approximating the maximum value.

                                                                                                                                                                                                                                  fMax(sin(X)cos(X),X,0,3)
        .7853995667

                                                                                                                                                                                                                                  Keep in mind that the result is the value of var, and not the value of f(var). In this example, .7853995667 is not the highest possible value of sin(X)cos(X), but rather the X-value at which sin(X)cos(X) is the highest.

                                                                                                                                                                                                                                  Error Conditions

                                                                                                                                                                                                                                  • ERR:BOUND is thrown if the lower bound is greater than the upper bound.
                                                                                                                                                                                                                                  • ERR:DOMAIN is thrown if tol is 0.
                                                                                                                                                                                                                                  • ERR:TOL NOT MET is thrown if the tolerance is too small for this specific function.

                                                                                                                                                                                                                                  Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583, thornahawk.

                                                                                                                                                                                                                                  History

                                                                                                                                                                                                                                  Calculator OS Version Description
                                                                                                                                                                                                                                  TI-82 1.0 Added
                                                                                                                                                                                                                                  Property Value
                                                                                                                                                                                                                                  Hex Value $27
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                                                                                                                                                                                                                                  • FR: fMin(

                                                                                                                                                                                                                                  fMin(

                                                                                                                                                                                                                                  Overview

                                                                                                                                                                                                                                  Returns the value of variable where the local minimum of expression occurs, between lower and upper, with specified tolerance.

                                                                                                                                                                                                                                  Availability: Token available everywhere.

                                                                                                                                                                                                                                  Syntax

                                                                                                                                                                                                                                  fMin(expression,variable,lower,upper[,tolerance])

                                                                                                                                                                                                                                  Arguments

                                                                                                                                                                                                                                  NameTypeOptional
                                                                                                                                                                                                                                  expressionexpression
                                                                                                                                                                                                                                  variable
                                                                                                                                                                                                                                  lower
                                                                                                                                                                                                                                  upper
                                                                                                                                                                                                                                  toleranceYes

                                                                                                                                                                                                                                  Location

                                                                                                                                                                                                                                  math, MATH, 6:fMin(

                                                                                                                                                                                                                                  Description

                                                                                                                                                                                                                                  fMin(f(var),var,lo,hi[,tol]) finds the value of var between lo and hi at which the minimum of f(var) occurs. tol controls the accuracy of the minimum value computed. The default value of tol is 10-5.

                                                                                                                                                                                                                                  fMin( only works for real numbers and expressions. Brent's method for optimization is used for approximating the minimum value.

                                                                                                                                                                                                                                  fMin(cos(sin(X)+Xcos(X)),X,0,2)
        1.076873875

                                                                                                                                                                                                                                  Keep in mind that the result is the value of var, and not the value of f(var). In this example, 1.076873875 is not the lowest possible value of cos(sin(X)+Xcos(X)), but rather the X-value at which cos(sin(X)+Xcos(X)) is the lowest.

                                                                                                                                                                                                                                  Advanced Uses

                                                                                                                                                                                                                                  fMin( is sometimes useful in finding so-called "multiple roots" of a function. If the graph of your function appears "flat" near the root, fMin( might be able to find the value of the root more accurately than solve(.

                                                                                                                                                                                                                                  Error Conditions

                                                                                                                                                                                                                                  • ERR:BOUND is thrown if the lower bound is greater than the upper bound.
                                                                                                                                                                                                                                  • ERR:DOMAIN is thrown if tol is 0.
                                                                                                                                                                                                                                  • ERR:TOL NOT MET is thrown if the tolerance is too small for this specific function.

                                                                                                                                                                                                                                  Source: parts of this page were written by the following TI|BD contributors: alexrudd, burr, DarkerLine, GoVegan, kg583, thornahawk.

                                                                                                                                                                                                                                  History

                                                                                                                                                                                                                                  Calculator OS Version Description
                                                                                                                                                                                                                                  TI-82 1.0 Added
                                                                                                                                                                                                                                  Property Value
                                                                                                                                                                                                                                  Hex Value $BA
                                                                                                                                                                                                                                  Categories
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                                                                                                                                                                                                                                  • FR: partDéc(

                                                                                                                                                                                                                                  fPart(

                                                                                                                                                                                                                                  Overview

                                                                                                                                                                                                                                  Returns the fractional part or parts of a real or complex number, expression, list, or matrix.

                                                                                                                                                                                                                                  Availability: Token available everywhere.

                                                                                                                                                                                                                                  Syntax

                                                                                                                                                                                                                                  fPart(value)

                                                                                                                                                                                                                                  Arguments

                                                                                                                                                                                                                                  NameTypeOptional
                                                                                                                                                                                                                                  value

                                                                                                                                                                                                                                  Location

                                                                                                                                                                                                                                  math, NUM, 4:fPart(

                                                                                                                                                                                                                                  Description

                                                                                                                                                                                                                                  fPart(value) returns the fractional part of value, be it a variable, list, or matrix.

                                                                                                                                                                                                                                  fPart(5.32)
             .32
fPart(4/5)
              .8
fPart(‾5.32)
             ‾.32
fPart(‾4/5)
              ‾.8

                                                                                                                                                                                                                                  fPart is sometimes used with it's corresponding partner iPart. While iPart trims off the part before the decimal point, fPart trims off the part after it.

                                                                                                                                                                                                                                  Watch Out For Precision Issues

                                                                                                                                                                                                                                  1/3*3→X   // X is expected to be 1
X         // Displays 1, but is actually 0.99999999999999 in memory
iPart(X)  // Displays 0
fPart(X)  // Displays 1, but is actually 0.99999999999999 in memory

                                                                                                                                                                                                                                  Somewhat unintuitively, the code above displays the results 1, 0 and 1. This is due to the calculator storing values to 14 digits of precision, but rounding the value to 10 digits to fit on the home screen. Because of this, fPart() can appear to return values of 1 or -1.

                                                                                                                                                                                                                                  Tip: If you enter a value in the list editor screen, you will be able to see all 14 digits of precision. This can help you troubleshoot issues like these.

                                                                                                                                                                                                                                  One workaround is to round the numbers prior to calling iPart() or fPart(), if you don't mind the slight loss in precision from 14 significant digits to 9 decimal places:

                                                                                                                                                                                                                                  1/3*3→X
iPart(round(X,9))   // Displays the expected result 1
fPart(round(X,9))   // Displays the expected result 0

                                                                                                                                                                                                                                  (The parameter 9 is not technically required here since 9 is the default, but is shown for clarity and in case you want to customize the level of precision.)

                                                                                                                                                                                                                                  Advanced Uses

                                                                                                                                                                                                                                  Modulus

                                                                                                                                                                                                                                  fPart( is an easy way to find A mod B (the positive remainder when A is divided by B).

                                                                                                                                                                                                                                  B(A<0)+iPart(BfPart(A/B))

                                                                                                                                                                                                                                  If A is guaranteed to be positive, the following shorter code can be used, omitting B(A<0):

                                                                                                                                                                                                                                  iPart(BfPart(A/B))

                                                                                                                                                                                                                                  Detect Whole Numbers

                                                                                                                                                                                                                                  The easiest way to check if a number is a whole number is not(fPart(X:

                                                                                                                                                                                                                                  If not(fPart(X:Then
  // X is an integer
Else
  // X is not an integer
End

                                                                                                                                                                                                                                  This can be used, for example, to check if a number is divisible by another: if X is divisible by N, then X/N is a whole number. This is useful for finding the factors of a number.

                                                                                                                                                                                                                                  Compression

                                                                                                                                                                                                                                  fPart(, along with int( or iPart(, can be used for integer compression.

                                                                                                                                                                                                                                  See Also

                                                                                                                                                                                                                                  Source: parts of this page were written by the following TI|BD contributors: burr, CloudVariable, DarkerLine, ePIi, GoVegan, kg583.

                                                                                                                                                                                                                                  History

                                                                                                                                                                                                                                  Calculator OS Version Description
                                                                                                                                                                                                                                  TI-82 1.0 fPart added
                                                                                                                                                                                                                                  TI-83 0.01013 Renamed fPart to fPart(
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                                                                                                                                                                                                                                  Hex Value $BBB5
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                                                                                                                                                                                                                                  • FR: f

                                                                                                                                                                                                                                  f

                                                                                                                                                                                                                                  Overview

                                                                                                                                                                                                                                  Availability: Token available everywhere.

                                                                                                                                                                                                                                  Syntax

                                                                                                                                                                                                                                  f

                                                                                                                                                                                                                                  Description

                                                                                                                                                                                                                                  Examples

                                                                                                                                                                                                                                  Explanation 1

                                                                                                                                                                                                                                  code 1

                                                                                                                                                                                                                                  Explanation 2

                                                                                                                                                                                                                                  code 2

                                                                                                                                                                                                                                  Error Conditions

                                                                                                                                                                                                                                  Advanced Notes

                                                                                                                                                                                                                                  History

                                                                                                                                                                                                                                  Calculator OS Version Description
                                                                                                                                                                                                                                  TI-83+ 1.03 Added
                                                                                                                                                                                                                                  Property Value
                                                                                                                                                                                                                                  Hex Value $24
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                                                                                                                                                                                                                                  • FR: fnInt(

                                                                                                                                                                                                                                  fnInt(

                                                                                                                                                                                                                                  Overview

                                                                                                                                                                                                                                  Returns the function integral of expression with respect to variable, between lower and upper, with specified tolerance.

                                                                                                                                                                                                                                  Availability: Token available everywhere.

                                                                                                                                                                                                                                  Syntax

                                                                                                                                                                                                                                  fnInt(expression,variable,lower,upper[,tolerance])

                                                                                                                                                                                                                                  Arguments

                                                                                                                                                                                                                                  NameTypeOptional
                                                                                                                                                                                                                                  expressionexpression
                                                                                                                                                                                                                                  variable
                                                                                                                                                                                                                                  lower
                                                                                                                                                                                                                                  upper
                                                                                                                                                                                                                                  toleranceYes

                                                                                                                                                                                                                                  Location

                                                                                                                                                                                                                                  math, MATH, 9:fnInt(

                                                                                                                                                                                                                                  Description

                                                                                                                                                                                                                                  fnInt(f(var),var,a,b[,tol]) computes an approximation to the definite integral of f with respect to var from a to b. tol controls the accuracy of the integral computed. The default value of tol is 10-5. fnInt( returns exact results for functions that are polynomials of small degree.

                                                                                                                                                                                                                                  fnInt( only works for real numbers and expressions. The Gauss-Kronrod method is used for approximating the integral.

                                                                                                                                                                                                                                  Tip: Sometimes, to get an answer of acceptable accuracy out of fnInt(, substitution of variables and analytic manipulation may be needed.

                                                                                                                                                                                                                                  fnInt(1/X,X,1,2)
        .6931471806
fnInt(ln(X),X,0,1) <a difficult example>
        -.999998347
fnInt(ln(X),X,0,1,e-11)
        -1

                                                                                                                                                                                                                                  Error Conditions

                                                                                                                                                                                                                                  Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Myles_Zadok.

                                                                                                                                                                                                                                  History

                                                                                                                                                                                                                                  Calculator OS Version Description
                                                                                                                                                                                                                                  TI-82 1.0 Added
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                                                                                                                                                                                                                                  Hex Value $BBB6
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                                                                                                                                                                                                                                  • FR: g

                                                                                                                                                                                                                                  g

                                                                                                                                                                                                                                  Overview

                                                                                                                                                                                                                                  Availability: Token available everywhere.

                                                                                                                                                                                                                                  Syntax

                                                                                                                                                                                                                                  g

                                                                                                                                                                                                                                  Description

                                                                                                                                                                                                                                  Examples

                                                                                                                                                                                                                                  Explanation 1

                                                                                                                                                                                                                                  code 1

                                                                                                                                                                                                                                  Explanation 2

                                                                                                                                                                                                                                  code 2

                                                                                                                                                                                                                                  Error Conditions

                                                                                                                                                                                                                                  Advanced Notes

                                                                                                                                                                                                                                  History

                                                                                                                                                                                                                                  Calculator OS Version Description
                                                                                                                                                                                                                                  TI-83+ 1.03 Added
                                                                                                                                                                                                                                  Property Value
                                                                                                                                                                                                                                  Hex Value $BBA1
                                                                                                                                                                                                                                  Categories
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                                                                                                                                                                                                                                  • FR: γ

                                                                                                                                                                                                                                  γ

                                                                                                                                                                                                                                  Overview

                                                                                                                                                                                                                                  Availability: Token available everywhere.

                                                                                                                                                                                                                                  Syntax

                                                                                                                                                                                                                                  γ

                                                                                                                                                                                                                                  Description

                                                                                                                                                                                                                                  Examples

                                                                                                                                                                                                                                  Explanation 1

                                                                                                                                                                                                                                  code 1

                                                                                                                                                                                                                                  Explanation 2

                                                                                                                                                                                                                                  code 2

                                                                                                                                                                                                                                  Error Conditions

                                                                                                                                                                                                                                  Advanced Notes

                                                                                                                                                                                                                                  History

                                                                                                                                                                                                                                  Calculator OS Version Description
                                                                                                                                                                                                                                  TI-83+ 1.03 Added
                                                                                                                                                                                                                                  Property Value
                                                                                                                                                                                                                                  Hex Value $BB09
                                                                                                                                                                                                                                  Categories
                                                                                                                                                                                                                                  Localizations
                                                                                                                                                                                                                                  • FR: pgcd(

                                                                                                                                                                                                                                  gcd(

                                                                                                                                                                                                                                  Overview

                                                                                                                                                                                                                                  Returns the greatest common divisor of valueA and valueB, which can be real numbers or lists.

                                                                                                                                                                                                                                  Availability: Token available everywhere.

                                                                                                                                                                                                                                  Syntax

                                                                                                                                                                                                                                  gcd(valueA,valueB)

                                                                                                                                                                                                                                  Arguments

                                                                                                                                                                                                                                  NameTypeOptional
                                                                                                                                                                                                                                  valueAreal|expression|real[]
                                                                                                                                                                                                                                  valueBreal|expression|real[]

                                                                                                                                                                                                                                  Location

                                                                                                                                                                                                                                  math, NUM, 9:gcd(

                                                                                                                                                                                                                                  Description

                                                                                                                                                                                                                                  The gcd( command returns the greatest common divisor (GCD) of two nonnegative integers. It also works on lists.

                                                                                                                                                                                                                                  gcd(8,6)
     2
gcd({9,12},6)
     {3 6}
gcd({14,12},{6,8})
     {2 4}

                                                                                                                                                                                                                                  Advanced Uses

                                                                                                                                                                                                                                  A gcd( command can be nested inside another gcd( command to compare up to four numbers.

                                                                                                                                                                                                                                  Error Conditions

                                                                                                                                                                                                                                  • ERR:DIM MISMATCH is thrown if the arguments are two lists that don't have the same number of elements.
                                                                                                                                                                                                                                  • ERR:DOMAIN is thrown if the arguments aren't positive integers (or lists of positive integers) less than 1E12.

                                                                                                                                                                                                                                  See Also

                                                                                                                                                                                                                                  Source: parts of this page were written by the following TI|BD contributors: burr, CloudVariable, DarkerLine, GoVegan, kg583, Myles_Zadok, thornahawk, Trenly.

                                                                                                                                                                                                                                  History

                                                                                                                                                                                                                                  Calculator OS Version Description
                                                                                                                                                                                                                                  TI-83 0.01013 Added
                                                                                                                                                                                                                                  Property Value
                                                                                                                                                                                                                                  Hex Value $BB1A
                                                                                                                                                                                                                                  Categories
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                                                                                                                                                                                                                                  • FR: géomtFRép(

                                                                                                                                                                                                                                  geometcdf(

                                                                                                                                                                                                                                  Overview

                                                                                                                                                                                                                                  Computes a cumulative probability at x, the number of the trial on which the first success occurs, for the discrete geometric distribution with the specified probability of success p.

                                                                                                                                                                                                                                  Availability: Token available everywhere.

                                                                                                                                                                                                                                  Syntax

                                                                                                                                                                                                                                  geometcdf(p,x)

                                                                                                                                                                                                                                  Arguments

                                                                                                                                                                                                                                  NameTypeOptional
                                                                                                                                                                                                                                  p
                                                                                                                                                                                                                                  x

                                                                                                                                                                                                                                  Location

                                                                                                                                                                                                                                  2nd, distr, DISTR, F:geometcdf(

                                                                                                                                                                                                                                  Description

                                                                                                                                                                                                                                  This command is used to calculate cumulative geometric probability. In plainer language, it solves a specific type of often-encountered probability problem, that occurs under the following conditions:

                                                                                                                                                                                                                                  1. A specific event has only two outcomes, which we will call "success" and "failure"
                                                                                                                                                                                                                                  2. The event is going to keep happening until a success occurs
                                                                                                                                                                                                                                  3. Success or failure is determined randomly with the same probability of success each time the event occurs
                                                                                                                                                                                                                                  4. We're interested in the probability that it takes at most a specific amount of trials to get a success.

                                                                                                                                                                                                                                  For example, consider a basketball player that always makes a shot with 1/4 probability. He will keep throwing the ball until he makes a shot. What is the probability that it takes him no more than 4 shots?

                                                                                                                                                                                                                                  1. The event here is throwing the ball. A "success", obviously, is making the shot, and a "failure" is missing.
                                                                                                                                                                                                                                  2. The event is going to happen until he makes the shot: a success.
                                                                                                                                                                                                                                  3. The probability of a success - making a shot - is 1/4
                                                                                                                                                                                                                                  4. We're interested in the probability that it takes at most 4 trials to get a success

                                                                                                                                                                                                                                  The syntax here is geometcdf(probability, trials). In this case:

                                                                                                                                                                                                                                  :geometcdf(1/4,4

                                                                                                                                                                                                                                  This will give about .684 when you run it, so there's a .684 probability that he'll make a shot within 4 throws.

                                                                                                                                                                                                                                  Note the relationship between geometpdf( and geometcdf(. Since geometpdf( is the probability it will take exactly N trials, we can write that geometcdf(1/4,4) = geometpdf(1/4,1) + geometpdf(1/4,2) + geometpdf(1/4,3) + geometpdf(1/4,4).

                                                                                                                                                                                                                                  Formulas

                                                                                                                                                                                                                                  Going off of the relationship between geometpdf( and geometcdf(, we can write a formula for geometcdf( in terms of geometpdf(:

                                                                                                                                                                                                                                  (1) \(\begin{align} \texttt{geometcdf}(p,n) = \sum_{i=1}^{n} \texttt{geometpdf}(p,i) = \sum_{i=1}^{n} p\,(1-p)^{i-1} \end{align}\)

                                                                                                                                                                                                                                  (If you're unfamiliar with sigma notation, \(\sum_{i=1}^{n}\) just means "add up the following for all values of i from 1 to n")

                                                                                                                                                                                                                                  However, we can take a shortcut to arrive at a much simpler expression for geometcdf(. Consider the opposite probability to the one we're interested in, the probability that it will not take "at most N trials", that is, the probability that it will take more than N trials. This means that the first N trials are failures. So geometcdf(p,N) = (1 - "probability that the first N trials are failures"), or:

                                                                                                                                                                                                                                  (2) \(\begin{align} \texttt{geometcdf}(p,n) = 1-(1-p)^n \end{align}\)

                                                                                                                                                                                                                                  Source: parts of this page were written by the following TI|BD contributors: burr, CloudVariable, DarkerLine, GoVegan, Joe_Young, kg583, Timothy Foster, Weregoose.

                                                                                                                                                                                                                                  History

                                                                                                                                                                                                                                  Calculator OS Version Description
                                                                                                                                                                                                                                  TI-83 0.01013 Added
                                                                                                                                                                                                                                  Property Value
                                                                                                                                                                                                                                  Hex Value $BB19
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                                                                                                                                                                                                                                  • FR: géomtFdp(

                                                                                                                                                                                                                                  geometpdf(

                                                                                                                                                                                                                                  Overview

                                                                                                                                                                                                                                  Computes a probability at x, the number of the trial on which the first success occurs, for the discrete geometric distribution with the specified probability of success p.

                                                                                                                                                                                                                                  Availability: Token available everywhere.

                                                                                                                                                                                                                                  Syntax

                                                                                                                                                                                                                                  geometpdf(p,x)

                                                                                                                                                                                                                                  Arguments

                                                                                                                                                                                                                                  NameTypeOptional
                                                                                                                                                                                                                                  p
                                                                                                                                                                                                                                  x

                                                                                                                                                                                                                                  Location

                                                                                                                                                                                                                                  2nd, distr, DISTR, E:geometpdf(

                                                                                                                                                                                                                                  Description

                                                                                                                                                                                                                                  This command is used to calculate geometric probability. In plainer language, it solves a specific type of often-encountered probability problem, that occurs under the following conditions:

                                                                                                                                                                                                                                  1. A specific event has only two outcomes, which we will call "success" and "failure"
                                                                                                                                                                                                                                  2. The event is going to keep happening until a success occurs
                                                                                                                                                                                                                                  3. Success or failure is determined randomly with the same probability of success each time the event occurs
                                                                                                                                                                                                                                  4. We're interested in the probability that it takes a specific amount of trials to get a success.

                                                                                                                                                                                                                                  For example, consider a basketball player that always makes a shot with 1/3 probability. He will keep throwing the ball until he makes a shot. What is the probability that it takes him 3 shots?

                                                                                                                                                                                                                                  1. The event here is throwing the ball. A "success", obviously, is making the shot, and a "failure" is missing.
                                                                                                                                                                                                                                  2. The event is going to happen until he makes the shot: a success.
                                                                                                                                                                                                                                  3. The probability of a success - making a shot - is 1/3
                                                                                                                                                                                                                                  4. We're interested in the probability that it takes 3 trials to get a success

                                                                                                                                                                                                                                  The syntax here is geometpdf(probability, trials). In this case:

                                                                                                                                                                                                                                  :geometpdf(1/3,3

                                                                                                                                                                                                                                  This will give about .148 when you run it, so there's a .148 probability that it will take him 3 shots until he makes one (he'll make it on the 3rd try).

                                                                                                                                                                                                                                  Formulas

                                                                                                                                                                                                                                  The value of geometpdf( is given by the formula

                                                                                                                                                                                                                                  (1) \(\begin{align} \texttt{geometpdf}(p,n) = p(1-p)^{n-1} \end{align}\)

                                                                                                                                                                                                                                  This formula can be intuitively understood: the probability that the first success is the nth trial is the probability of getting a success - \(p\) - times the probability of missing it the first n-1 times - \((1-p)^{n-1}\).

                                                                                                                                                                                                                                  For the trivial value of n=0, however, the above formula gives the incorrect value of 1. It should actually be 0, since the first success can never be the 0th trial. However, since you're not likely to ever be interested in this probability, this drawback doesn't really matter.

                                                                                                                                                                                                                                  Source: parts of this page were written by the following TI|BD contributors: burr, CloudVariable, DarkerLine, GoVegan, kg583, Timothy Foster, Trenly.

                                                                                                                                                                                                                                  History

                                                                                                                                                                                                                                  Calculator OS Version Description
                                                                                                                                                                                                                                  TI-83 0.01013 Added
                                                                                                                                                                                                                                  Property Value
                                                                                                                                                                                                                                  Hex Value $EF09
                                                                                                                                                                                                                                  Categories
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                                                                                                                                                                                                                                  • FR: affDate

                                                                                                                                                                                                                                  getDate

                                                                                                                                                                                                                                  Overview

                                                                                                                                                                                                                                  Returns a list giving the date according to the current value of the clock. The list is in {year,month,day} format.

                                                                                                                                                                                                                                  Availability: Token available everywhere.

                                                                                                                                                                                                                                  Syntax

                                                                                                                                                                                                                                  getDate

                                                                                                                                                                                                                                  Location

                                                                                                                                                                                                                                  2nd, catalog, getDate

                                                                                                                                                                                                                                  Description

                                                                                                                                                                                                                                  The getDate command returns the current date that the clock has on the TI-84+/SE/CE calculators in list format — {year, month, day}. You can store this list to a variable for later use, or manipulate it the same way you do with other lists. Of course, this command only works if the date has actually been set, so you should use the setDate( command before using it.

                                                                                                                                                                                                                                  An interesting note about this command is that you cannot index getDate directly to get individual elements; if you try, each element of the clock is instead multiplied by the number. You may, however, call the command and thus store it in Ans, then retrieve individual elements.

                                                                                                                                                                                                                                  SCREEN02.BMP

                                                                                                                                                                                                                                  Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Jonathan King, kg583, RandomProductions.

                                                                                                                                                                                                                                  History

                                                                                                                                                                                                                                  Calculator OS Version Description
                                                                                                                                                                                                                                  TI-84+ 0.01 Added
                                                                                                                                                                                                                                  Property Value
                                                                                                                                                                                                                                  Hex Value $EF0C
                                                                                                                                                                                                                                  Categories
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                                                                                                                                                                                                                                  • FR: affFmtDt

                                                                                                                                                                                                                                  getDtFmt

                                                                                                                                                                                                                                  Overview

                                                                                                                                                                                                                                  Returns an integer representing the date format that is currently set on the device.
                                                                                                                                                                                                                                  1 = M/D/Y2 = D/M/Y3 = Y/M/D

                                                                                                                                                                                                                                  Availability: Token available everywhere.

                                                                                                                                                                                                                                  Syntax

                                                                                                                                                                                                                                  getDtFmt

                                                                                                                                                                                                                                  Location

                                                                                                                                                                                                                                  2nd, catalog, getDtFmt

                                                                                                                                                                                                                                  Description

                                                                                                                                                                                                                                  The getDtFmt( command returns the current date format of the clock on the TI-84+/SE/CE calculators as an integer. There are three different date formats available: 1 (M/D/Y), 2 (D/M/Y), and 3 (Y/M/D). You can store this value to a variable for later use. Of course, this command only works if the date format has actually been set, so you should use the setDtFmt( command before using it.

                                                                                                                                                                                                                                  Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Jonathan King, kg583, RandomProductions.

                                                                                                                                                                                                                                  History

                                                                                                                                                                                                                                  Calculator OS Version Description
                                                                                                                                                                                                                                  TI-84+ 0.01 Added
                                                                                                                                                                                                                                  Property Value
                                                                                                                                                                                                                                  Hex Value $EF07
                                                                                                                                                                                                                                  Categories
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                                                                                                                                                                                                                                  • FR: AffChDt(

                                                                                                                                                                                                                                  getDtStr(

                                                                                                                                                                                                                                  Overview

                                                                                                                                                                                                                                  Returns a string of the current date in the format specified by integer, where:
                                                                                                                                                                                                                                  1 = M/D/Y2 = D/M/Y3 = Y/M/D

                                                                                                                                                                                                                                  Availability: Token available everywhere.

                                                                                                                                                                                                                                  Syntax

                                                                                                                                                                                                                                  getDtStr(integer)

                                                                                                                                                                                                                                  Arguments

                                                                                                                                                                                                                                  NameTypeOptional
                                                                                                                                                                                                                                  integer

                                                                                                                                                                                                                                  Location

                                                                                                                                                                                                                                  2nd, catalog, getDtStr(

                                                                                                                                                                                                                                  Description

                                                                                                                                                                                                                                  The getDtStr( command returns the current date of the clock on the TI-84+/SE/CE calculators as a string based on the date format that is specified. There are three different date formats available: 1 (M/D/Y), 2 (D/M/Y), or 3 (Y/M/D). You can store this value to a string variable for later use, or manipulate it the same way you do with other strings. Of course, this command only works if the date format has actually been set, so you should use the setDtFmt( command before using it.

                                                                                                                                                                                                                                  Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583, RandomProductions.

                                                                                                                                                                                                                                  History

                                                                                                                                                                                                                                  Calculator OS Version Description
                                                                                                                                                                                                                                  TI-84+ 0.01 Added
                                                                                                                                                                                                                                  Property Value
                                                                                                                                                                                                                                  Hex Value $AD
                                                                                                                                                                                                                                  Categories
                                                                                                                                                                                                                                  Localizations
                                                                                                                                                                                                                                  • FR: codetouch(

                                                                                                                                                                                                                                  getKey

                                                                                                                                                                                                                                  Overview

                                                                                                                                                                                                                                  Returns the key code for the current keystroke, or 0, if no key is pressed.

                                                                                                                                                                                                                                  Availability: Token only available from within the Basic editor.

                                                                                                                                                                                                                                  Syntax

                                                                                                                                                                                                                                  getKey

                                                                                                                                                                                                                                  Location

                                                                                                                                                                                                                                  prgm, I/O, 7:getKey

                                                                                                                                                                                                                                  Description

                                                                                                                                                                                                                                  The getKey command returns the value of the last key pressed since the last time getKey was executed. Reading key presses with getKey allows a program to transfer control to the user, and you can combine getKey with other commands to create menus, movement, or whatever else you want.

                                                                                                                                                                                                                                  Every key has a number assigned to it, except for ON (which is used for breaking out of programs). The numbering system consists of a row and column: the rows go from one to ten, starting at the top; and the columns go from one to six, starting from the left. You just put the row and column together to get the key's number — for example, the ENTER key is located in row 10, column 5, making its value 105. The arrow keys look like they would be numbered separately from the other keys, but they actually follow this pattern as well. See the key codes page for a picture of the key codes on the calculator.

                                                                                                                                                                                                                                  The value of getKey is cleared every time you read from it, until a new key is pressed. For this reason, except in very rare cases, you do not want to use the value of getKey in an expression directly, but store it to a variable first. It is also common to use getKey inside of a Repeat loop, so that the program can wait for the user to press a key.

                                                                                                                                                                                                                                  :Repeat Ans
:getKey
:End
:Ans→K

                                                                                                                                                                                                                                  Advanced Uses

                                                                                                                                                                                                                                  You can put getKey in the condition of a loop, to make the loop repeat until any key or a particular key is pressed by the user. The same thing can be done with conditionals as well. This is useful if you don't want to store getKey to a variable, but you still want to have the user press a key. This works because of the way 'true' and 'false' get interpreted in TI-Basic.

                                                                                                                                                                                                                                  :Repeat max(getKey={24,25,26,34
:End

                                                                                                                                                                                                                                  Unlike the other keys, the arrow and DEL keys can actually be held down, which will cause the key to keep being repeated until it is unpressed. This functionality is very useful in games where the user needs to repeatedly press a key to move or shoot, although it does completely disable the other keys from being able to be pressed (which is important in multiplayer games, where everybody must share the keys).

                                                                                                                                                                                                                                  Sometimes your program may do something for several seconds without user input (say, playing an animation), then pause and wait for a key to be pressed. The problem is that if a key is pressed during the animation, the next getKey will return the value of that key, and any loop set up to wait for a key press will exit immediately. The solution is to run a "dummy" getKey just before the loop begins — its value won't be used for anything, and it will reset the value of getKey to 0. This can also be used to clear keypresses meant for loading programs from inside a shell.

                                                                                                                                                                                                                                  Error Conditions

                                                                                                                                                                                                                                  • ERR:INVALID occurs if this statement is used outside a program.

                                                                                                                                                                                                                                  See Also

                                                                                                                                                                                                                                  Source: parts of this page were written by the following TI|BD contributors: basickevin, burr, DarkerLine, Edward H, GoVegan, iPhoenixOnTIBD, Myles_Zadok, Weregoose.

                                                                                                                                                                                                                                  History

                                                                                                                                                                                                                                  Calculator OS Version Description
                                                                                                                                                                                                                                  TI-82 1.0 Added
                                                                                                                                                                                                                                  Property Value
                                                                                                                                                                                                                                  Hex Value $EF0A
                                                                                                                                                                                                                                  Categories
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                                                                                                                                                                                                                                  • FR: affHeure

                                                                                                                                                                                                                                  getTime

                                                                                                                                                                                                                                  Overview

                                                                                                                                                                                                                                  Returns a list giving the time according to the current value of the clock. The list is in {hour,minute,second} format. The time is returned in the 24 hour format.

                                                                                                                                                                                                                                  Availability: Token available everywhere.

                                                                                                                                                                                                                                  Syntax

                                                                                                                                                                                                                                  getTime

                                                                                                                                                                                                                                  Location

                                                                                                                                                                                                                                  2nd, catalog, getTime

                                                                                                                                                                                                                                  Description

                                                                                                                                                                                                                                  The getTime command returns the current time that the clock has on the TI-84+/SE/CE calculators in list format — {hour, minute, second}. You can store this list to a variable for later use, or manipulate it the same way you do with other lists. Of course, this command only works if the time has actually been set, so you should use the setTime( command before using it.

                                                                                                                                                                                                                                  An interesting note about this command is that you cannot index individual elements directly; if you try, each element of the clock is multiplied by the index. You can, however, call the demand and thus store the result in Ans, and then retrieve the individual elements.

                                                                                                                                                                                                                                  SCREEN01.JPG

                                                                                                                                                                                                                                  Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Jonathan King, kg583, RandomProductions, Socks.

                                                                                                                                                                                                                                  History

                                                                                                                                                                                                                                  Calculator OS Version Description
                                                                                                                                                                                                                                  TI-84+ 0.01 Added
                                                                                                                                                                                                                                  Property Value
                                                                                                                                                                                                                                  Hex Value $EF0D
                                                                                                                                                                                                                                  Categories
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                                                                                                                                                                                                                                  • FR: affFmtHr

                                                                                                                                                                                                                                  getTmFmt

                                                                                                                                                                                                                                  Overview

                                                                                                                                                                                                                                  Returns an integer representing the clock time format that is currently set on the device.
                                                                                                                                                                                                                                  12 = 12 hour format24 = 24 hour format

                                                                                                                                                                                                                                  Availability: Token available everywhere.

                                                                                                                                                                                                                                  Syntax

                                                                                                                                                                                                                                  getTmFmt

                                                                                                                                                                                                                                  Location

                                                                                                                                                                                                                                  2nd, catalog, getTmFmt

                                                                                                                                                                                                                                  Description

                                                                                                                                                                                                                                  The getTmFmt( command returns the current time format of the clock on the TI-84+/SE/CE calculators as an integer. There are two different time formats available: 12 (12 hour) and 24 (24 hours). You can store this value to a variable for later use. Of course, this command only works if the time format has actually been set, so you should use the setTmFmt( command before using it.

                                                                                                                                                                                                                                  Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583, RandomProductions.

                                                                                                                                                                                                                                  History

                                                                                                                                                                                                                                  Calculator OS Version Description
                                                                                                                                                                                                                                  TI-84+ 0.01 Added
                                                                                                                                                                                                                                  Property Value
                                                                                                                                                                                                                                  Hex Value $EF08
                                                                                                                                                                                                                                  Categories
                                                                                                                                                                                                                                  Localizations
                                                                                                                                                                                                                                  • FR: affChHr(

                                                                                                                                                                                                                                  getTmStr(

                                                                                                                                                                                                                                  Overview

                                                                                                                                                                                                                                  Returns a string of the current clock time in the format specified by integer, where:
                                                                                                                                                                                                                                  12 = 12 hour format24 = 24 hour format

                                                                                                                                                                                                                                  Availability: Token available everywhere.

                                                                                                                                                                                                                                  Syntax

                                                                                                                                                                                                                                  getTmStr(integer)

                                                                                                                                                                                                                                  Arguments

                                                                                                                                                                                                                                  NameTypeOptional
                                                                                                                                                                                                                                  integer

                                                                                                                                                                                                                                  Location

                                                                                                                                                                                                                                  2nd, catalog, getTmStr(

                                                                                                                                                                                                                                  Description

                                                                                                                                                                                                                                  The getTmStr( command returns the current time of the clock on the TI-84+/SE calculators as a string based on the time format that is specified. There are two different time formats available: 12 (12 hour) or 24 (24 hour). You can store this value to a string variable for later use, or manipulate it the same way you do with other strings. Of course, this command only works if the time format has actually been set, so you should use the setTmFmt( command before using it.

                                                                                                                                                                                                                                  Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, RandomProductions.

                                                                                                                                                                                                                                  History

                                                                                                                                                                                                                                  Calculator OS Version Description
                                                                                                                                                                                                                                  TI-84+ 0.01 Added
                                                                                                                                                                                                                                  Property Value
                                                                                                                                                                                                                                  Hex Value $BBA7
                                                                                                                                                                                                                                  Categories
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                                                                                                                                                                                                                                  • FR: |π

                                                                                                                                                                                                                                  |π

                                                                                                                                                                                                                                  Overview

                                                                                                                                                                                                                                  Syntax

                                                                                                                                                                                                                                  |π

                                                                                                                                                                                                                                  Description

                                                                                                                                                                                                                                  Examples

                                                                                                                                                                                                                                  Explanation 1

                                                                                                                                                                                                                                  code 1

                                                                                                                                                                                                                                  Explanation 2

                                                                                                                                                                                                                                  code 2

                                                                                                                                                                                                                                  Error Conditions

                                                                                                                                                                                                                                  Advanced Notes

                                                                                                                                                                                                                                  History

                                                                                                                                                                                                                                  Calculator OS Version Description
                                                                                                                                                                                                                                  TI-83+ 1.03 Added
                                                                                                                                                                                                                                  Property Value
                                                                                                                                                                                                                                  Hex Value $BBB7
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                                                                                                                                                                                                                                  • FR: h
                                                                                                                                                                                                                                  h

                                                                                                                                                                                                                                  Overview

                                                                                                                                                                                                                                  Availability: Token available everywhere.

                                                                                                                                                                                                                                  Syntax

                                                                                                                                                                                                                                  h

                                                                                                                                                                                                                                  Description

                                                                                                                                                                                                                                  Examples

                                                                                                                                                                                                                                  Explanation 1

                                                                                                                                                                                                                                  code 1

                                                                                                                                                                                                                                  Explanation 2

                                                                                                                                                                                                                                  code 2

                                                                                                                                                                                                                                  Error Conditions

                                                                                                                                                                                                                                  Advanced Notes

                                                                                                                                                                                                                                  History

                                                                                                                                                                                                                                  Calculator OS Version Description
                                                                                                                                                                                                                                  TI-83+ 1.03 Added
                                                                                                                                                                                                                                  Property Value
                                                                                                                                                                                                                                  Hex Value $B9
                                                                                                                                                                                                                                  Categories
                                                                                                                                                                                                                                  Localizations
                                                                                                                                                                                                                                  • FR: ent(

                                                                                                                                                                                                                                  iPart(

                                                                                                                                                                                                                                  Overview

                                                                                                                                                                                                                                  Returns the integer part of a real or complex number, expression, list, or matrix.

                                                                                                                                                                                                                                  Availability: Token available everywhere.

                                                                                                                                                                                                                                  Syntax

                                                                                                                                                                                                                                  iPart(value)

                                                                                                                                                                                                                                  Arguments

                                                                                                                                                                                                                                  NameTypeOptional
                                                                                                                                                                                                                                  value

                                                                                                                                                                                                                                  Location

                                                                                                                                                                                                                                  math, NUM, 3:iPart(

                                                                                                                                                                                                                                  Description

                                                                                                                                                                                                                                  iPart(value) returns the integer part of value, and extends to complex numbers, lists, and matrices.

                                                                                                                                                                                                                                  iPart(5.32)
               5
iPart(4/5)
               0
iPart(‾5.32)
               ‾5
iPart(‾4/5)
               0

                                                                                                                                                                                                                                  iPart is sometimes used with it's corresponding partner fPart. While iPart trims off the part before the decimal point, fPart trims off the part after it.

                                                                                                                                                                                                                                  The difference between iPart( and int( is subtle; while iPart( always truncates its parameters, simply removing the integer part, int( always rounds down. This means that they return the same answers for positive numbers, but int( will return an answer 1 less than iPart( for (non-integer) negative numbers. For example, iPart(-5.32) is -5, while int(-5.32) is -6.

                                                                                                                                                                                                                                  In this case of positive values, though, the decision to use iPart( or int( is mostly a matter of preference - some people only use int( because it is shorter, some people use iPart( when there is a corresponding fPart( taken. However, see the Command Timings section.

                                                                                                                                                                                                                                  Watch Out For Precision Issues

                                                                                                                                                                                                                                  1/3*3→X   // X is expected to be 1
X         // Displays 1, but is actually 0.99999999999999 in memory
iPart(X)  // Displays 0
fPart(X)  // Displays 1, but is actually 0.99999999999999 in memory

                                                                                                                                                                                                                                  Somewhat unintuitively, the code above displays the results 1, 0 and 1. This is due to the calculator storing values to 14 digits of precision, but rounding the value to 10 digits to fit on the home screen.

                                                                                                                                                                                                                                  Tip: If you enter a value in the list editor screen, you will be able to see all 14 digits of precision. This can help you troubleshoot issues like these.

                                                                                                                                                                                                                                  One workaround is to round the numbers prior to calling iPart() or fPart(), if you don't mind the slight loss in precision from 14 significant digits to 9 decimal places:

                                                                                                                                                                                                                                  1/3*3→X
iPart(round(X,9))   // Displays the expected result 1
fPart(round(X,9))   // Displays the expected result 0

                                                                                                                                                                                                                                  (The parameter 9 is not technically required here since 9 is the default, but is shown for clarity and in case you want to customize the level of precision.)

                                                                                                                                                                                                                                  Advanced Uses

                                                                                                                                                                                                                                  iPart(, along with fPart( and int(, can be used for integer compression.

                                                                                                                                                                                                                                  Command Timings

                                                                                                                                                                                                                                  The following table compares the speeds of int( and iPart(. Each command was timed over 2000 iterations to find a noticeable difference.

                                                                                                                                                                                                                                  Format

                                                                                                                                                                                                                                  Bars

                                                                                                                                                                                                                                  Pixels

                                                                                                                                                                                                                                  Total

                                                                                                                                                                                                                                  iPart(1

                                                                                                                                                                                                                                  10

                                                                                                                                                                                                                                  1

                                                                                                                                                                                                                                  81

                                                                                                                                                                                                                                  iPart(1.643759

                                                                                                                                                                                                                                  10

                                                                                                                                                                                                                                  1

                                                                                                                                                                                                                                  81

                                                                                                                                                                                                                                  int(1

                                                                                                                                                                                                                                  8

                                                                                                                                                                                                                                  7

                                                                                                                                                                                                                                  71

                                                                                                                                                                                                                                  int(1.643759

                                                                                                                                                                                                                                  10

                                                                                                                                                                                                                                  2

                                                                                                                                                                                                                                  82

                                                                                                                                                                                                                                  Conclusion: With 5 or fewer decimal places, you should consider using int( because of its speed, but with more decimals, iPart( remains constant to eventually beat out its counterpart.

                                                                                                                                                                                                                                  See Also

                                                                                                                                                                                                                                  Source: parts of this page were written by the following TI|BD contributors: burr, CloudVariable, DarkerLine, GoVegan, kg583, Timtech.

                                                                                                                                                                                                                                  History

                                                                                                                                                                                                                                  Calculator OS Version Description
                                                                                                                                                                                                                                  TI-82 1.0 iPart added
                                                                                                                                                                                                                                  TI-83 0.01013 Renamed iPart to iPart(
                                                                                                                                                                                                                                  Property Value
                                                                                                                                                                                                                                  Hex Value $BBB8
                                                                                                                                                                                                                                  Categories
                                                                                                                                                                                                                                  Localizations
                                                                                                                                                                                                                                  • FR: i

                                                                                                                                                                                                                                  i

                                                                                                                                                                                                                                  Overview

                                                                                                                                                                                                                                  Availability: Token available everywhere.

                                                                                                                                                                                                                                  Syntax

                                                                                                                                                                                                                                  i

                                                                                                                                                                                                                                  Description

                                                                                                                                                                                                                                  Examples

                                                                                                                                                                                                                                  Explanation 1

                                                                                                                                                                                                                                  code 1

                                                                                                                                                                                                                                  Explanation 2

                                                                                                                                                                                                                                  code 2

                                                                                                                                                                                                                                  Error Conditions

                                                                                                                                                                                                                                  Advanced Notes

                                                                                                                                                                                                                                  History

                                                                                                                                                                                                                                  Calculator OS Version Description
                                                                                                                                                                                                                                  TI-83+ 1.03 Added
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                                                                                                                                                                                                                                  • FR: identité(

                                                                                                                                                                                                                                  identity(

                                                                                                                                                                                                                                  Overview

                                                                                                                                                                                                                                  Returns the identity matrix of dimension rows x dimension columns.

                                                                                                                                                                                                                                  Availability: Token available everywhere.

                                                                                                                                                                                                                                  Syntax

                                                                                                                                                                                                                                  identity(dimension)

                                                                                                                                                                                                                                  Arguments

                                                                                                                                                                                                                                  NameTypeOptional
                                                                                                                                                                                                                                  dimension

                                                                                                                                                                                                                                  Location

                                                                                                                                                                                                                                  2nd, matrix, MATH, 5:identity(

                                                                                                                                                                                                                                  Description

                                                                                                                                                                                                                                  The identity( command generates an identity matrix: that is, a matrix [B] such that for any other matrix [A], [A]*[B]=[A] (if [A] is the right size to make the multiplication valid).

                                                                                                                                                                                                                                  The identity matrix is square (that is, the row dimension equals the column dimension); all of its elements are 0 except for the elements along the main diagonal (the diagonal going from top left to bottom right).

                                                                                                                                                                                                                                  The command itself takes one argument: the size of the matrix, used for both row and column size, that is, identity(n) creates an n by n matrix.

                                                                                                                                                                                                                                  :dim([A]
:identity(Ans(2→[B]
:[A][B]=[A]  // should always return 1, meaning 'true'

                                                                                                                                                                                                                                  Optimization

                                                                                                                                                                                                                                  The identity( command can be used as a quick way to create an empty square matrix: 0identity(n) will create an n by n matrix containing only 0 as an element. This is faster and smaller than the dim( and Fill( commands used for the same purpose:

                                                                                                                                                                                                                                  :{5,5→dim([A]
:Fill(0,[A]
can be
:0identity(5→[A]

                                                                                                                                                                                                                                  Error Conditions

                                                                                                                                                                                                                                  • ERR:INVALID DIM occurs if the size is not an integer 1-99. In practice, however, identity(21) is already too large for the calculator to generate.
                                                                                                                                                                                                                                  • ERR:MEMORY occurs if the size of the created matrix exceeds memory limits. This limit is hard-fixed to 3611 bytes (the size of a 20x20 matrix), regardless of having sufficient RAM to hold a larger matrix.

                                                                                                                                                                                                                                  Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583.

                                                                                                                                                                                                                                  History

                                                                                                                                                                                                                                  Calculator OS Version Description
                                                                                                                                                                                                                                  TI-82 1.0 identity added
                                                                                                                                                                                                                                  TI-83 0.01013 Renamed identity to identity(
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                                                                                                                                                                                                                                  Hex Value $BB27
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                                                                                                                                                                                                                                  • FR: imag(

                                                                                                                                                                                                                                  imag(

                                                                                                                                                                                                                                  Overview

                                                                                                                                                                                                                                  Returns the imaginary (non-real) part of a complex number or list of complex numbers.

                                                                                                                                                                                                                                  Availability: Token available everywhere.

                                                                                                                                                                                                                                  Syntax

                                                                                                                                                                                                                                  imag(value)

                                                                                                                                                                                                                                  Arguments

                                                                                                                                                                                                                                  NameTypeOptional
                                                                                                                                                                                                                                  valuecomplex|complex[]

                                                                                                                                                                                                                                  Location

                                                                                                                                                                                                                                  math, CMPLX, 3:imag(

                                                                                                                                                                                                                                  Description

                                                                                                                                                                                                                                  imag(z) returns the imaginary part of the complex number z. If z is represented as x+i_y_ where x and y are both real, imag(z) returns y. Also works on a list of complex numbers.

                                                                                                                                                                                                                                  imag(3+4i)
     4

imag({3+4i,-2i,17})
     {4,-2,0}

                                                                                                                                                                                                                                  Source: parts of this page were written by the following TI|BD contributors: alexrudd, DarkerLine, GoVegan, kg583, Weregoose.

                                                                                                                                                                                                                                  History

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                                                                                                                                                                                                                                  TI-83 0.01013 Added
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                                                                                                                                                                                                                                  • FR: carChaine(

                                                                                                                                                                                                                                  inString(

                                                                                                                                                                                                                                  Overview

                                                                                                                                                                                                                                  Returns the character position in string of the first character of substringbeginning at start.

                                                                                                                                                                                                                                  Availability: Token available everywhere.

                                                                                                                                                                                                                                  Syntax

                                                                                                                                                                                                                                  inString(string,substring[,start])

                                                                                                                                                                                                                                  Arguments

                                                                                                                                                                                                                                  NameTypeOptional
                                                                                                                                                                                                                                  stringstring
                                                                                                                                                                                                                                  substringstring
                                                                                                                                                                                                                                  startYes

                                                                                                                                                                                                                                  Location

                                                                                                                                                                                                                                  2nd, catalog, inString(

                                                                                                                                                                                                                                  Description

                                                                                                                                                                                                                                  The inString( command searches a string for occurrences of a smaller string (similar to the Find feature on a computer), and returns the first such occurrence.

                                                                                                                                                                                                                                  The source string is the string you want to search through; the search string is the substring you want to find. inString( will return the index of the first letter of the first occurrence of the search string found, or 0 if the search string is not present. For example:

                                                                                                                                                                                                                                  :inString("TI-BASIC","BASIC
    4
:inString("TI-BASIC","TI
    1
:inString("TI-BASIC","I
    2
:inString("TI-BASIC","ELEPHANT
    0

                                                                                                                                                                                                                                  You can also provide the optional starting point argument, 1 by default, that will tell the command where it should start looking. If you provide a value higher than 1 here, the command will skip the beginning of the string. This can be used to find where the search string occurs past the first occurrence. For example:

                                                                                                                                                                                                                                  :inString("TI-BASIC","I
    2
:inString("TI-BASIC","I",2
    2
:inString("TI-BASIC","I",3
    7

                                                                                                                                                                                                                                  Advanced Uses

                                                                                                                                                                                                                                  You can use inString( to convert a character to a number. For example:

                                                                                                                                                                                                                                  :inString("ABCDEFGHIJKLMNOPQRSTUVWXYZ",Str1→N

                                                                                                                                                                                                                                  Assuming Str1 is one character long and contains a capital letter, N will hold a value of 1-26 that corresponds to that letter. This value can then be stored in a real number, list, or matrix, where a character of a string couldn't be stored. To get the character value of the number, you can use the sub( command:

                                                                                                                                                                                                                                  :sub("ABCDEFGHIJKLMNOPQRSTUVWXYZ",N,1→Str1

                                                                                                                                                                                                                                  Using the starting point argument of inString(, you can write a routine to return all occurrences of the search string in the source string:

                                                                                                                                                                                                                                  :0→dim(L1
:inString(Str0,Str1
:Repeat not(Ans
:Ans→L1(1+dim(L1
:inString(Str0,Str1,Ans+1
:End

                                                                                                                                                                                                                                  If the search string is not found, this routine will return {0} in L₁. If it is found, the result will be a list of all the places the string was found.

                                                                                                                                                                                                                                  Optimization

                                                                                                                                                                                                                                  The inString( command can replace checking if a string is one of a number of values. Just put all the values in a string, one after the other, and try to find the string to be checked in the string of those values:

                                                                                                                                                                                                                                  :If Str1="." or Str1=",
can be
:If inString(".,",Str1

                                                                                                                                                                                                                                  Be careful, because if Str1 were ".," in the above example, this would also be treated like "." or ",". If this is a problem, you can separate the values you want to check for by a character you know can't be in the string:

                                                                                                                                                                                                                                  :If Str1="HELLO" or Str1="HI
can be
:If inString("HELLO,HI",Str1

                                                                                                                                                                                                                                  This approach assumes that a comma would never be in Str1, and words like "HELL" or "I" are also impossible. If words like these can appear in the input, the following works:

                                                                                                                                                                                                                                  :If inString("HELLO,HI,",Str+",

                                                                                                                                                                                                                                  (still assumes commas aren't in Str1)

                                                                                                                                                                                                                                  Error Conditions

                                                                                                                                                                                                                                  • ERR:DOMAIN is thrown if starting point is not a positive integer (starting point may be longer than the length of the source string, though).

                                                                                                                                                                                                                                  Source: parts of this page were written by the following TI|BD contributors: brt93yoda, burr, CloudVariable, ConorOBrien, DarkerLine, GoVegan, kg583, Lionel Foxcroft, Mr Dino, Trenly.

                                                                                                                                                                                                                                  History

                                                                                                                                                                                                                                  Calculator OS Version Description
                                                                                                                                                                                                                                  TI-83 0.01013 Added
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                                                                                                                                                                                                                                  • FR: partEnt(

                                                                                                                                                                                                                                  int(

                                                                                                                                                                                                                                  Overview

                                                                                                                                                                                                                                  Returns the largest integer ≤ a real or complex number, expression, list, or matrix.

                                                                                                                                                                                                                                  Availability: Token available everywhere.

                                                                                                                                                                                                                                  Syntax

                                                                                                                                                                                                                                  int(value)

                                                                                                                                                                                                                                  Arguments

                                                                                                                                                                                                                                  NameTypeOptional
                                                                                                                                                                                                                                  value

                                                                                                                                                                                                                                  Location

                                                                                                                                                                                                                                  math, NUM, 5:int(

                                                                                                                                                                                                                                  Description

                                                                                                                                                                                                                                  int(X) is the floor function. It returns the greatest integer less than or equal to X, and also works on complex numbers, lists and matrices.

                                                                                                                                                                                                                                  int(5.32)
               5
int(4/5)
               0
int(‾5.32)
               ‾6
int(‾4/5)
               ‾1

                                                                                                                                                                                                                                  The difference between iPart( and int( is subtle, and many people aren't even aware of it, but it exists. Whereas iPart( always truncates its parameters, simply removing the fractional part, int( always rounds down. This means that they return the same answers for positive numbers, but int( will return an answer 1 less than iPart( for (non-integer) negative numbers. For example, iPart(-5.32) is -5, while int(-5.32) is -6.

                                                                                                                                                                                                                                  Most of the time, however, you're dealing with only positive numbers anyway. In this case, the decision to use iPart( or int( is mostly a matter of preference - some people use int( because it is shorter; some use iPart( when there is a corresponding fPart( taken. However, if speed is a consideration, one should check the Command Timings section.

                                                                                                                                                                                                                                  Advanced Uses

                                                                                                                                                                                                                                  int(, along with iPart( and fPart(, can be used for integer compression.

                                                                                                                                                                                                                                  Command Timings

                                                                                                                                                                                                                                  The following table compares the speeds of int( and iPart(. Each command was timed over 2000 iterations to find a noticeable difference.

                                                                                                                                                                                                                                  Format

                                                                                                                                                                                                                                  Bars

                                                                                                                                                                                                                                  Pixels

                                                                                                                                                                                                                                  Total

                                                                                                                                                                                                                                  iPart(1

                                                                                                                                                                                                                                  10

                                                                                                                                                                                                                                  1

                                                                                                                                                                                                                                  81

                                                                                                                                                                                                                                  iPart(1.643759

                                                                                                                                                                                                                                  10

                                                                                                                                                                                                                                  1

                                                                                                                                                                                                                                  81

                                                                                                                                                                                                                                  int(1

                                                                                                                                                                                                                                  8

                                                                                                                                                                                                                                  7

                                                                                                                                                                                                                                  71

                                                                                                                                                                                                                                  int(1.643759

                                                                                                                                                                                                                                  10

                                                                                                                                                                                                                                  2

                                                                                                                                                                                                                                  82

                                                                                                                                                                                                                                  Conclusion: int( scales with the length of its input while iPart( does not. For fewer than 6 decimals, int( will most often be faster; for 6 or more decimals, consider using iPart(.

                                                                                                                                                                                                                                  See Also

                                                                                                                                                                                                                                  Source: parts of this page were written by the following TI|BD contributors: burr, CloudVariable, DarkerLine, GoVegan, kg583, Timtech.

                                                                                                                                                                                                                                  History

                                                                                                                                                                                                                                  Calculator OS Version Description
                                                                                                                                                                                                                                  TI-82 1.0 int added
                                                                                                                                                                                                                                  TI-83 0.01013 Renamed int to int(
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                                                                                                                                                                                                                                  • FR: ∫

                                                                                                                                                                                                                                  ∫

                                                                                                                                                                                                                                  Overview

                                                                                                                                                                                                                                  Syntax

                                                                                                                                                                                                                                  ∫

                                                                                                                                                                                                                                  Description

                                                                                                                                                                                                                                  Examples

                                                                                                                                                                                                                                  Explanation 1

                                                                                                                                                                                                                                  code 1

                                                                                                                                                                                                                                  Explanation 2

                                                                                                                                                                                                                                  code 2

                                                                                                                                                                                                                                  Error Conditions

                                                                                                                                                                                                                                  Advanced Notes

                                                                                                                                                                                                                                  History

                                                                                                                                                                                                                                  Calculator OS Version Description
                                                                                                                                                                                                                                  TI-83+ 1.16 Added
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                                                                                                                                                                                                                                    • FR: invBinom(

                                                                                                                                                                                                                                    invBinom(

                                                                                                                                                                                                                                    Overview

                                                                                                                                                                                                                                    The inverse binomial cumulative distribution function results in the minimum number of successes, such that the cumulative probability for that minimum number of successes ≥ the given cumulative probability (area). If more information is needed, also find the binomcdf for the result from invBinom( as shown below for a full analysis.
                                                                                                                                                                                                                                    Details:
                                                                                                                                                                                                                                    Assume the toss of a fair coin 30 times. What is the minimum number of heads you must observe such that the cumulative probability for that number of observed heads is at least 0.95?
                                                                                                                                                                                                                                    The results on the screen first show that the minimum number of successes to obtain at least the given cumulative probability of 0.95 is 19. Next, the cumulative probability for up to 19 is computed using binomcdf( and is approximately 0.9506314271 which meets the criteria of 0.9506314271≥0.95

                                                                                                                                                                                                                                    Alternate Method:
                                                                                                                                                                                                                                    Set Y1=binomcdf(30,0.5,X) and use the table of values (starting at 0 and increment by 1) to find when the cumulative probability is at or just above the given cumulative probability. This gives you a view of all values to make decisions. For this example, search in the table to find the cumulative probability just larger than 0.95. Again, the number of successes is 19.

                                                                                                                                                                                                                                    Comment:CE OS 5.2+

                                                                                                                                                                                                                                    Availability: Token available everywhere.

                                                                                                                                                                                                                                    Syntax

                                                                                                                                                                                                                                    invBinom(area,trial,p)

                                                                                                                                                                                                                                    Arguments

                                                                                                                                                                                                                                    NameTypeOptional
                                                                                                                                                                                                                                    area
                                                                                                                                                                                                                                    trial
                                                                                                                                                                                                                                    p

                                                                                                                                                                                                                                    Location

                                                                                                                                                                                                                                    2nd, distr, DISTR, C:invBinom(

                                                                                                                                                                                                                                    Description

                                                                                                                                                                                                                                    Examples

                                                                                                                                                                                                                                    Explanation 1

                                                                                                                                                                                                                                    code 1

                                                                                                                                                                                                                                    Explanation 2

                                                                                                                                                                                                                                    code 2

                                                                                                                                                                                                                                    Error Conditions

                                                                                                                                                                                                                                    Advanced Notes

                                                                                                                                                                                                                                    History

                                                                                                                                                                                                                                    Calculator OS Version Description
                                                                                                                                                                                                                                    TI-84+CE 5.2.0 Added
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                                                                                                                                                                                                                                    • FR: FracNormale(

                                                                                                                                                                                                                                    invNorm(

                                                                                                                                                                                                                                    Overview

                                                                                                                                                                                                                                    Computes the inverse cumulative normal distribution function for a given area under the normal distribution curve specified by μ and s.. The optional argument tail can be LEFT (-∞,-a), CENTER [-a,a] or RIGHT (a, ∞) for Real a.
                                                                                                                                                                                                                                    The tokens LEFT, CENTER and RIGHT can be found in [catalog].

                                                                                                                                                                                                                                    Availability: Token available everywhere.

                                                                                                                                                                                                                                    Syntax

                                                                                                                                                                                                                                    invNorm(area[,µ,σ,tail])

                                                                                                                                                                                                                                    Arguments

                                                                                                                                                                                                                                    NameTypeOptional
                                                                                                                                                                                                                                    area
                                                                                                                                                                                                                                    µ
                                                                                                                                                                                                                                    σ
                                                                                                                                                                                                                                    tail

                                                                                                                                                                                                                                    Location

                                                                                                                                                                                                                                    2nd, distr, DISTR, 3:invNorm(

                                                                                                                                                                                                                                    Overview

                                                                                                                                                                                                                                    Computes the inverse cumulative normal distribution function for a given area under the normal distribution curve specified by μ and s.. The optional argument tail can be LEFT (-∞,-a), CENTER [-a,a] or RIGHT (a, ∞) for Real a.
                                                                                                                                                                                                                                    The tokens LEFT, CENTER and RIGHT can be found in [catalog].

                                                                                                                                                                                                                                    Availability: Token available everywhere.

                                                                                                                                                                                                                                    Syntax

                                                                                                                                                                                                                                    tail [catalog]: LEFT, CENTER, RIGHT

                                                                                                                                                                                                                                    Arguments

                                                                                                                                                                                                                                    NameTypeOptional
                                                                                                                                                                                                                                    tail catalog: LEFT
                                                                                                                                                                                                                                    CENTER
                                                                                                                                                                                                                                    RIGHT

                                                                                                                                                                                                                                    Location

                                                                                                                                                                                                                                    2nd, distr, DISTR, 3:invNorm(

                                                                                                                                                                                                                                    Description

                                                                                                                                                                                                                                    invNorm( is the inverse of the cumulative normal distribution function: given a probability, it will give you a z-score with that tail probability. The probability argument of invNorm( is between 0 and 1; 0 will give -1E99 instead of negative infinity, and 1 will give 1E99 instead of positive infinity

                                                                                                                                                                                                                                    There are two ways to use invNorm(. With three arguments, the inverse of the cumulative normal distribution for a probability with specified mean and standard deviation is calculated. With one argument, the standard normal distribution is assumed (zero mean and unit standard deviation). For example:

                                                                                                                                                                                                                                    for the standard normal distribution
:invNorm(.975

for the normal distribution with mean 10 and std. dev. 2.5
:invNorm(.975,10,2.5

                                                                                                                                                                                                                                    Advanced

                                                                                                                                                                                                                                    This is the only inverse of a probability distribution function available (at least on the TI-83/84/+/SE calculators), so it makes sense to use it as an approximation for other distributions. Since the normal distribution is a good approximation for a binomial distribution with many trials, we can use invNorm( as an approximation for the nonexistent "invBinom(". The following code gives the number of trials out of N that will succeed with probability X if the probability of any trial succeeding is P (rounded to the nearest whole number):

                                                                                                                                                                                                                                    :int(.5+invNorm(X,NP,√(NP(1-P

                                                                                                                                                                                                                                    You can also use invNorm() to approximate the inverse of a t-distribution. Since a normal distribution is a t-distribution with infinite degrees of freedom, this will be an overestimate for probabilities below 1/2, and an underestimate for probabilities above 1/2.

                                                                                                                                                                                                                                    Formulas

                                                                                                                                                                                                                                    Unlike the normalpdf( and normalcdf( commands, the invNorm( command does not have a closed-form formula. It can however be expressed in terms of the inverse error function:

                                                                                                                                                                                                                                    (1) \(\begin{align} \texttt{invNorm}(p) = \sqrt{2}\,\texttt{erf}^{-1}(2p-1) \end{align}\)

                                                                                                                                                                                                                                    For the arbitrary normal distribution with mean μ and standard deviation σ:

                                                                                                                                                                                                                                    (2) \(\begin{align} \texttt{invNorm}(p,\mu,\sigma)=\mu+\sigma\texttt{invNorm}(p) \end{align}\)

                                                                                                                                                                                                                                    Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, kg583, thornahawk.

                                                                                                                                                                                                                                    History

                                                                                                                                                                                                                                    Calculator OS Version Description
                                                                                                                                                                                                                                    TI-83 0.01013 Added
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                                                                                                                                                                                                                                      • FR: invT(

                                                                                                                                                                                                                                      invT(

                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                      Computes the inverse cumulative student-t probability function specified by degree of freedom, df for a given area under the curve.

                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                      invT(area,df)

                                                                                                                                                                                                                                      Arguments

                                                                                                                                                                                                                                      NameTypeOptional
                                                                                                                                                                                                                                      area
                                                                                                                                                                                                                                      df

                                                                                                                                                                                                                                      Location

                                                                                                                                                                                                                                      2nd, distr, DISTR, 4:invT(

                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                      invT( is the inverse of the cumulative Student t distribution function: given a probability p and a specified degrees of freedom v, it will return the number x such that tcdf(E-99,x,v) is equal to p

                                                                                                                                                                                                                                      :invT(.95,24
    1.710882023

                                                                                                                                                                                                                                      Advanced

                                                                                                                                                                                                                                      invT( is meant for use with so-called "one-tailed' tests; for two-tailed tests, the proper expression to use (corresponding to the inverse of tcdf(-x,x,v)) is invT(.5(1+p),v)

                                                                                                                                                                                                                                      Formulas

                                                                                                                                                                                                                                      Unlike the tpdf( and tcdf( commands, the invT( command does not have a closed-form formula. However, it can be expressed in terms of the inverse incomplete beta function.

                                                                                                                                                                                                                                      For one degree of freedom, invT( is expressible in terms of simpler functions:

                                                                                                                                                                                                                                      (1) \(\begin{align} \texttt{invT}(p,1)=\tan\left(\pi\left(p-\frac1{2}\right)\right) \end{align}\)

                                                                                                                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, jonbush, kg583, Thom M, thornahawk.

                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                      TI-84+ 2.30 Added
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                                                                                                                                                                                                                                      • FR: ⌸

                                                                                                                                                                                                                                      ⌸

                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                      Comment:inverted equal

                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                      ⌸

                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                      TI-83+ 1.16 Added
                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                      Hex Value $BB01
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                                                                                                                                                                                                                                      • FR: tauxRi(

                                                                                                                                                                                                                                      irr(

                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                      Returns the interest rate at which the net present value of the cash flow is equal to zero.

                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                      irr(CF0,CFList[,CFFreq])

                                                                                                                                                                                                                                      Arguments

                                                                                                                                                                                                                                      NameTypeOptional
                                                                                                                                                                                                                                      CF0
                                                                                                                                                                                                                                      CFList
                                                                                                                                                                                                                                      CFFreqYes

                                                                                                                                                                                                                                      Location

                                                                                                                                                                                                                                      apps, 1:Finance, CALC, 8:irr(

                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                      The irr( command finds the Internal Rate of Return of an investment, which is a measure of its efficiency. Its mathematical interpretation is the interest rate for which npv( will return 0 for the same cash flows.

                                                                                                                                                                                                                                      irr( takes three arguments: an initial cash flow (CF0), a list of further cash flows (CFList), and an optional frequency list.

                                                                                                                                                                                                                                      Advanced Uses

                                                                                                                                                                                                                                      irr( can be used to find a root of a polynomial of any degree, give by a list of its coefficients:

                                                                                                                                                                                                                                      1+.01irr(0,{list of coefficients})

                                                                                                                                                                                                                                      However, this method is limited to finding roots greater than 0, and will throw an error (ERR:NO SIGN CHG or ERR:DIVIDE BY 0) if it can't find such roots. By reversing the list of coefficients and taking the reciprocal of the roots found, you could find roots less than 0, but this would still result in errors if such roots don't exist either.

                                                                                                                                                                                                                                      Using solve( to find roots of polynomials is less efficient, but more reliable, since it doesn't throw an error unless there are no roots at all to be found.

                                                                                                                                                                                                                                      Formulas

                                                                                                                                                                                                                                      Solving for irr( requires solving a polynomial with degree equal to the total number of cash flows. As such, there is no general formula for calculating irr(, though numerical methods are possible for finding an approximate solution.

                                                                                                                                                                                                                                      The polynomial associated with the calculation is:

                                                                                                                                                                                                                                      (1) \(\begin{align} \sum_{i=0}^{N}{C_i\left(1+\frac{\mathrm{Irr}}{100}\right)^{N-i}}=0 \end{align}\)

                                                                                                                                                                                                                                      Here, Irr is the internal rate of return, N is the number of cash flows, and Ct is the t th cash flow.

                                                                                                                                                                                                                                      To the calculator, only roots for which Irr>0 are considered to be viable.

                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, kg583.

                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                      TI-83 0.01013 Added
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                                                                                                                                                                                                                                      Hex Value $EF0E
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                                                                                                                                                                                                                                      • FR: actHorl

                                                                                                                                                                                                                                      isClockOn

                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                      Identifies if clock is ON or OFF. Returns 1 if the clock is ON. Returns 0 if the clock is OFF.

                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                      isClockOn

                                                                                                                                                                                                                                      Location

                                                                                                                                                                                                                                      2nd, catalog, isClockOn

                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                      The isClockOn command returns whether the clock on the TI-84+/SE calculators is on or off. The command will return 1 if the clock is enabled and 0 if it is not. You can store it to a variable for later use, or use it in conditionals and loops as part of the condition. For example, here is how you would check to see if the clock is on:

                                                                                                                                                                                                                                      :If isClockOn
:Then
  (code if clock is on)
:Else
  (code if clock is off)
:End

                                                                                                                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Jonathan King, kg583, Xphoenix.

                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                      TI-84+ 0.01 Added
                                                                                                                                                                                                                                      Property Value
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                                                                                                                                                                                                                                      • FR: j

                                                                                                                                                                                                                                      j

                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                      j

                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                      TI-83+ 1.03 Added
                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                      Hex Value $BBBA
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                                                                                                                                                                                                                                      • FR: k

                                                                                                                                                                                                                                      k

                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                      k

                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                      TI-83+ 1.03 Added
                                                                                                                                                                                                                                      Property Value
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                                                                                                                                                                                                                                      • FR: l

                                                                                                                                                                                                                                      l

                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                      l

                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                      TI-83+ 1.03 Added
                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                      Hex Value $BBA5
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                                                                                                                                                                                                                                      • FR: λ

                                                                                                                                                                                                                                      λ

                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                      λ

                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                      TI-83+ 1.03 Added
                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                      Hex Value $BB08
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                                                                                                                                                                                                                                      • FR: ppcm(

                                                                                                                                                                                                                                      lcm(

                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                      Returns the least common multiple of valueA and valueB, which can be real numbers or lists.

                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                      lcm(valueA,valueB)

                                                                                                                                                                                                                                      Arguments

                                                                                                                                                                                                                                      NameTypeOptional
                                                                                                                                                                                                                                      valueAreal|expression|real[]
                                                                                                                                                                                                                                      valueBreal|expression|real[]

                                                                                                                                                                                                                                      Location

                                                                                                                                                                                                                                      math, NUM, 8:lcm(

                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                      Returns the least common multiple (LCM) of two nonnegative integers; lcm(a,b) is equivalent to a__b/gcd(a,b). Also works on lists.

                                                                                                                                                                                                                                      lcm(8,6)
     24
lcm({9,12},6)
     {18 12}
lcm({14,12},{6,8})
     {42 24}

                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                      • ERR:DIM MISMATCH is thrown if the arguments are two lists that don't have the same number of elements.
                                                                                                                                                                                                                                      • ERR:DOMAIN is thrown if the arguments aren't positive integers (or lists of positive integers) less than 1e12.

                                                                                                                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, thornahawk.

                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                      TI-83 0.01013 Added
                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                      Hex Value $BB2B
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                                                                                                                                                                                                                                      • FR: longueur(

                                                                                                                                                                                                                                      length(

                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                      Returns the number of characters in string.

                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                      length(string)

                                                                                                                                                                                                                                      Arguments

                                                                                                                                                                                                                                      NameTypeOptional
                                                                                                                                                                                                                                      stringstring

                                                                                                                                                                                                                                      Location

                                                                                                                                                                                                                                      2nd, catalog, length(

                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                      This command is used to determine the length of a string. Unlike the dim( command for lists and matrices, it cannot be used to change this length, as there is no null character for strings (the null value is 0 for lists and matrices).

                                                                                                                                                                                                                                      :length("HELLO
    5

                                                                                                                                                                                                                                      Keep in mind that the length is measured in the number of tokens, and not the number of letters in the string. For example, although the sin( command contains 4 characters ("s", "i", "n", and "("), it will only add 1 to the total length of a string it's in. The execution time for length( is directly proportional to the length of the string.

                                                                                                                                                                                                                                      Advanced Uses

                                                                                                                                                                                                                                      The code for looping over each character (technically, each token) of a string involves length(:

                                                                                                                                                                                                                                      :For(N,1,length(Str1
...
use sub(Str1,N,1 for the Nth character
...
:End

                                                                                                                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, jonbush, kg583, Michael2_3B.

                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                      TI-83 0.01013 Added
                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                      Hex Value $BE
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                                                                                                                                                                                                                                      • FR: ln(

                                                                                                                                                                                                                                      ln(

                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                      Returns the natural logarithm of a real or complex number, expression, or list.

                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                      ln(value)

                                                                                                                                                                                                                                      Arguments

                                                                                                                                                                                                                                      NameTypeOptional
                                                                                                                                                                                                                                      value

                                                                                                                                                                                                                                      Location

                                                                                                                                                                                                                                      ln

                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                      The ln( command computes the natural logarithm of a value — the exponent to which the constant e must be raised, to get that value. This makes it the inverse of the e^( command.

                                                                                                                                                                                                                                      ln( is a real number for all positive real values. For negative numbers, ln( is an imaginary number (so taking ln( of a negative number will cause ERR:NONREAL ANS to be thrown in Real mode), and of course it's a complex number for complex values. ln( is not defined at 0, even if you're in a complex mode.

                                                                                                                                                                                                                                      Advanced Uses

                                                                                                                                                                                                                                      Using either the ln( or the log( command, logarithms of any base can be calculated, using the identity:

                                                                                                                                                                                                                                      (1) \(\begin{align} \log_b{x} = \frac{\ln{x}}{\ln{b}} = \frac{\log{x}}{\log{b}} \end{align}\)

                                                                                                                                                                                                                                      So, to take the base B log of a number X, you could use either of the following equivalent ways:

                                                                                                                                                                                                                                      :log(X)/log(B)

                                                                                                                                                                                                                                      :ln(X)/ln(B)

                                                                                                                                                                                                                                      This is the exponent to which B must be raised, to get X.

                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Timothy Foster.

                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                      TI-82 1.0 ln added
                                                                                                                                                                                                                                      TI-83 0.01013 Renamed ln to ln(
                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                      Hex Value $C0
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                                                                                                                                                                                                                                      • FR: log(

                                                                                                                                                                                                                                      log(

                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                      Returns logarithm of a real or complex number, expression, or list.

                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                      log(value)

                                                                                                                                                                                                                                      Arguments

                                                                                                                                                                                                                                      NameTypeOptional
                                                                                                                                                                                                                                      value

                                                                                                                                                                                                                                      Location

                                                                                                                                                                                                                                      log

                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                      The log( command computes the base 10 logarithm of a value — the exponent to which 10 must be raised, to get that value. This makes it the inverse of the 10^( command.

                                                                                                                                                                                                                                      log( is a real number for all positive real values. For negative numbers, log( is an imaginary number (so taking log( of a negative number will cause ERR:NONREAL ANS to be thrown in Real mode), and of course it's a complex number for complex values. log( is not defined at 0, even if you're in a complex mode.

                                                                                                                                                                                                                                      Advanced Uses

                                                                                                                                                                                                                                      Using either the ln( or the log( command, logarithms of any base can be calculated, using the identity:

                                                                                                                                                                                                                                      (1) \(\begin{align} \log_b{x} = \frac{\ln{x}}{\ln{b}} = \frac{\log{x}}{\log{b}} \end{align}\)

                                                                                                                                                                                                                                      So, to take the base B log of a number X, you could use either of the following equivalent ways:

                                                                                                                                                                                                                                      :log(X)/log(B)

                                                                                                                                                                                                                                      :ln(X)/ln(B)

                                                                                                                                                                                                                                      This is the exponent to which B must be raised, to get X. If using OS 2.53 MP or higher, this formula can be circumvented entirely with an optional second argument:

                                                                                                                                                                                                                                      :log(X,B)

                                                                                                                                                                                                                                      This form is functionally identical to the logBASE command with the same arguments available with the same OS, but unlike its counterpart does not have any special visual rendering when in MATHPRINT mode. Both logBASE and the second argument of log( are disabled in exam mode.

                                                                                                                                                                                                                                      The base 10 logarithm specifically can also be used to calculate the number of digits a whole number has:

                                                                                                                                                                                                                                      :1+int(log(N))

                                                                                                                                                                                                                                      This will return the number of digits N has, if N is a whole number. If N is a decimal, it will ignore the decimal digits of N.

                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: DarkerLine, Deflect, GoVegan, kg583, Timothy Foster.

                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                      TI-82 1.0 log added
                                                                                                                                                                                                                                      TI-83 0.01013 Renamed log to log(
                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                      Hex Value $EF34
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                                                                                                                                                                                                                                        • FR: logBASE(

                                                                                                                                                                                                                                        logBASE(

                                                                                                                                                                                                                                        Overview

                                                                                                                                                                                                                                        Returns the logarithm of a specifed value determined from a specified base: logBASE(value, base).

                                                                                                                                                                                                                                        Availability: Token available everywhere.

                                                                                                                                                                                                                                        Syntax

                                                                                                                                                                                                                                        logBASE(value, base)

                                                                                                                                                                                                                                        Arguments

                                                                                                                                                                                                                                        NameTypeOptional
                                                                                                                                                                                                                                        value
                                                                                                                                                                                                                                        base

                                                                                                                                                                                                                                        Location

                                                                                                                                                                                                                                        math

                                                                                                                                                                                                                                        Description

                                                                                                                                                                                                                                        The logBASE( command is a visual upgrade to the log( command to compute logarithms in any base b. That is, the command finds the exponent that base b must be raised to obtain the given value.

                                                                                                                                                                                                                                        This command can be used on both the home screen and while programming. If you are using CLASSIC mode, the command appears as:

                                                                                                                                                                                                                                        logBASE(8,2)
            3

                                                                                                                                                                                                                                        But in MATHPRINT mode, this is improved to:

                                                                                                                                                                                                                                        log2(8)
                                                                                                                                                                                                                                                    3

                                                                                                                                                                                                                                        Formulas

                                                                                                                                                                                                                                        The log in base b can also be found using the ln( or log( commands. This can be done indirectly using the change-of-base formula:

                                                                                                                                                                                                                                        (1) \(\begin{align} \log_bx = {\ln x \over \ln b} = {\log x \over \log b} \end{align}\)

                                                                                                                                                                                                                                        Or directly, using the optional second argument of log(:

                                                                                                                                                                                                                                        logBASE(X,B

can be

log(X,B

                                                                                                                                                                                                                                        The logBASE( command costs one extra byte compared to log(, providing only a visual improvement over its counterpart in MATHPRINT mode. The log( command is also compatible with older OS's, although its second argument is not. Both logBASE( and the second argument of log( are disabled in exam mode.

                                                                                                                                                                                                                                        Error Conditions

                                                                                                                                                                                                                                        Source: parts of this page were written by the following TI|BD contributors: Deflect, kg583, Myles_Zadok, Timothy Foster.

                                                                                                                                                                                                                                        History

                                                                                                                                                                                                                                        Calculator OS Version Description
                                                                                                                                                                                                                                        TI-84+ 2.53 Added
                                                                                                                                                                                                                                        Property Value
                                                                                                                                                                                                                                        Hex Value $6232
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                                                                                                                                                                                                                                        • FR: borninf

                                                                                                                                                                                                                                        lower

                                                                                                                                                                                                                                        Overview

                                                                                                                                                                                                                                        Availability: Token available everywhere.

                                                                                                                                                                                                                                        Syntax

                                                                                                                                                                                                                                        lower

                                                                                                                                                                                                                                        Description

                                                                                                                                                                                                                                        Examples

                                                                                                                                                                                                                                        Explanation 1

                                                                                                                                                                                                                                        code 1

                                                                                                                                                                                                                                        Explanation 2

                                                                                                                                                                                                                                        code 2

                                                                                                                                                                                                                                        Error Conditions

                                                                                                                                                                                                                                        Advanced Notes

                                                                                                                                                                                                                                        History

                                                                                                                                                                                                                                        Calculator OS Version Description
                                                                                                                                                                                                                                        TI-82 1.0 Added
                                                                                                                                                                                                                                        Property Value
                                                                                                                                                                                                                                        Hex Value $BBBD
                                                                                                                                                                                                                                        Categories
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                                                                                                                                                                                                                                        • FR: m

                                                                                                                                                                                                                                        m

                                                                                                                                                                                                                                        Overview

                                                                                                                                                                                                                                        Availability: Token available everywhere.

                                                                                                                                                                                                                                        Syntax

                                                                                                                                                                                                                                        m

                                                                                                                                                                                                                                        Description

                                                                                                                                                                                                                                        Examples

                                                                                                                                                                                                                                        Explanation 1

                                                                                                                                                                                                                                        code 1

                                                                                                                                                                                                                                        Explanation 2

                                                                                                                                                                                                                                        code 2

                                                                                                                                                                                                                                        Error Conditions

                                                                                                                                                                                                                                        Advanced Notes

                                                                                                                                                                                                                                        History

                                                                                                                                                                                                                                        Calculator OS Version Description
                                                                                                                                                                                                                                        TI-83+ 1.03 Added
                                                                                                                                                                                                                                        Property Value
                                                                                                                                                                                                                                        Hex Value $EF1E
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                                                                                                                                                                                                                                        • FR: ⬚

                                                                                                                                                                                                                                        ⬚

                                                                                                                                                                                                                                        Overview

                                                                                                                                                                                                                                        Syntax

                                                                                                                                                                                                                                        ⬚

                                                                                                                                                                                                                                        Description

                                                                                                                                                                                                                                        Examples

                                                                                                                                                                                                                                        Explanation 1

                                                                                                                                                                                                                                        code 1

                                                                                                                                                                                                                                        Explanation 2

                                                                                                                                                                                                                                        code 2

                                                                                                                                                                                                                                        Error Conditions

                                                                                                                                                                                                                                        Advanced Notes

                                                                                                                                                                                                                                        History

                                                                                                                                                                                                                                        Calculator OS Version Description
                                                                                                                                                                                                                                        TI-84+ 2.53 Added
                                                                                                                                                                                                                                        Property Value
                                                                                                                                                                                                                                        Hex Value $19
                                                                                                                                                                                                                                        Categories
                                                                                                                                                                                                                                        Localizations
                                                                                                                                                                                                                                        • FR: max(

                                                                                                                                                                                                                                        max(

                                                                                                                                                                                                                                        Overview

                                                                                                                                                                                                                                        Returns the larger of valueA and valueB.

                                                                                                                                                                                                                                        Availability: Token available everywhere.

                                                                                                                                                                                                                                        Syntax

                                                                                                                                                                                                                                        max(valueA,valueB)

                                                                                                                                                                                                                                        Arguments

                                                                                                                                                                                                                                        NameTypeOptional
                                                                                                                                                                                                                                        valueA
                                                                                                                                                                                                                                        valueB

                                                                                                                                                                                                                                        Location

                                                                                                                                                                                                                                        math, NUM, 7:max(

                                                                                                                                                                                                                                        Overview

                                                                                                                                                                                                                                        Returns the larger of valueA and valueB.

                                                                                                                                                                                                                                        Availability: Token available everywhere.

                                                                                                                                                                                                                                        Syntax

                                                                                                                                                                                                                                        max(list)

                                                                                                                                                                                                                                        Arguments

                                                                                                                                                                                                                                        NameTypeOptional
                                                                                                                                                                                                                                        listlist

                                                                                                                                                                                                                                        Location

                                                                                                                                                                                                                                        math, NUM, 7:max(

                                                                                                                                                                                                                                        Overview

                                                                                                                                                                                                                                        Returns largest real or complex element in list.

                                                                                                                                                                                                                                        Availability: Token available everywhere.

                                                                                                                                                                                                                                        Syntax

                                                                                                                                                                                                                                        max(list)

                                                                                                                                                                                                                                        Arguments

                                                                                                                                                                                                                                        NameTypeOptional
                                                                                                                                                                                                                                        listlist

                                                                                                                                                                                                                                        Location

                                                                                                                                                                                                                                        2nd, list, MATH, 2:max(

                                                                                                                                                                                                                                        Overview

                                                                                                                                                                                                                                        Returns a real or complex list of the larger of each pair of elements in listA and listB.

                                                                                                                                                                                                                                        Availability: Token available everywhere.

                                                                                                                                                                                                                                        Syntax

                                                                                                                                                                                                                                        max(listA,listB)

                                                                                                                                                                                                                                        Arguments

                                                                                                                                                                                                                                        NameTypeOptional
                                                                                                                                                                                                                                        listAlist
                                                                                                                                                                                                                                        listBlist

                                                                                                                                                                                                                                        Location

                                                                                                                                                                                                                                        2nd, list, MATH, 2:max(

                                                                                                                                                                                                                                        Overview

                                                                                                                                                                                                                                        Returns a real or complex list of the larger of value or each list element.

                                                                                                                                                                                                                                        Availability: Token available everywhere.

                                                                                                                                                                                                                                        Syntax

                                                                                                                                                                                                                                        max(value,list)

                                                                                                                                                                                                                                        Arguments

                                                                                                                                                                                                                                        NameTypeOptional
                                                                                                                                                                                                                                        value
                                                                                                                                                                                                                                        listlist

                                                                                                                                                                                                                                        Location

                                                                                                                                                                                                                                        2nd, list, MATH, 2:max(

                                                                                                                                                                                                                                        Description

                                                                                                                                                                                                                                        max(X,Y) returns the largest of the two numbers X and Y. max(list) returns the largest element of list. max(list1,list2) returns the pairwise maxima of the two lists. max(list1,X) (equivalently, max(X,list1)) returns a list whose elements are the larger of X or the corresponding element of the original list.

                                                                                                                                                                                                                                        max(2,3)
     3
max({2,3,4})
     4
max({1,3},{4,2})
     {4 3}
max({1,3},2)
     {2 3}

                                                                                                                                                                                                                                        Unlike comparison operators such as < and >, max( can also compare complex numbers. To do this, both arguments must be complex — either complex numbers or complex lists: max(2,𝑖) will throw an error even though max(2+0𝑖,𝑖) won't. In the case of complex numbers, the number with the largest absolute value will be returned. When the two numbers have the same absolute value, the first one will be returned: max(𝑖,-𝑖) returns 𝑖 and max(-𝑖,𝑖) returns -𝑖.

                                                                                                                                                                                                                                        Advanced Uses

                                                                                                                                                                                                                                        max( can be used in Boolean comparisons to see if at least one of a list is 1 (true) — useful because commands like If or While only deal with numbers, and not lists, but comparisons like L₁=L₂ return a list of values. In general, the behavior you want varies, and you will use the min( function or the max( function accordingly.

                                                                                                                                                                                                                                        Using max( will give you a lenient test — if any one element of the list is 1 (true), then the max( of the list is true — this is equivalent to putting an or in between every element. For example, this tests if K is equal to any of 24, 25, 26, or 34 (the getKey arrow key values):

                                                                                                                                                                                                                                        :If max(K={24,25,26,34
:Disp "ARROW KEY

                                                                                                                                                                                                                                        To get the element of a real list in Ans with the greatest absolute value, use imag(max(𝑖Ans)) or max(abs(Ans)).

                                                                                                                                                                                                                                        max( can be also used along with min( to constrain a value between a lower and upper number:

                                                                                                                                                                                                                                        :max(-1,min(1,100)) // returns 1 because 1 is between -1 & 100
:max(-1,min(1,0)) // returns 0 because 1 is not between -1 & 0

                                                                                                                                                                                                                                        where the bounds for which the number 1 must fall between are first argument of max( and the second argument of min( in the above code.

                                                                                                                                                                                                                                        Error Conditions

                                                                                                                                                                                                                                        • ERR:DATA TYPE is thrown when comparing a real and a complex number. This can be avoided by adding +0𝑖 to the real number (or i^4 right after it, for those who are familiar with complex numbers)
                                                                                                                                                                                                                                        • ERR:DIM MISMATCH is thrown, when using max( with two lists, if they have different dimensions.

                                                                                                                                                                                                                                        Source: parts of this page were written by the following TI|BD contributors: burr, coltonj96, DarkerLine, GoVegan, kg583, lirtosiast, Mapar007, simplethinker.

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                                                                                                                                                                                                                                        • FR: moyenne(

                                                                                                                                                                                                                                        mean(

                                                                                                                                                                                                                                        Overview

                                                                                                                                                                                                                                        Returns the mean of list with frequency freqlist.

                                                                                                                                                                                                                                        Availability: Token available everywhere.

                                                                                                                                                                                                                                        Syntax

                                                                                                                                                                                                                                        mean(list[,freqlist])

                                                                                                                                                                                                                                        Arguments

                                                                                                                                                                                                                                        NameTypeOptional
                                                                                                                                                                                                                                        listlist
                                                                                                                                                                                                                                        freqlistlistYes

                                                                                                                                                                                                                                        Location

                                                                                                                                                                                                                                        2nd, list, MATH, 3:mean(

                                                                                                                                                                                                                                        Description

                                                                                                                                                                                                                                        The mean( command finds the mean, or the average, of a list. It's pretty elementary. It takes a list of real numbers as a parameter. For example:

                                                                                                                                                                                                                                        :Prompt L1
:Disp "MEAN OF L1",mean(L1

                                                                                                                                                                                                                                        That's not all, however. Awesome as the mean( command is, it can also take a frequency list argument, for situations when your elements occur more than once. For example:

                                                                                                                                                                                                                                        :Disp mean({1,2,3},{5,4,4})

                                                                                                                                                                                                                                        is short for

                                                                                                                                                                                                                                        :mean({1,1,1,1,1,2,2,2,2,3,3,3,3})

                                                                                                                                                                                                                                        The frequency list {5,4,4} means that the first element, 1, occurs 5 times, the second element, 2, occurs 4 times, and the third element, 3, occurs 4 times.

                                                                                                                                                                                                                                        Advanced Uses

                                                                                                                                                                                                                                        You can also use the frequency list version of mean( to calculate weighted averages. For example, suppose you're trying to average grades in a class where homework is worth 50%, quizzes 20%, and tests 30%. You have a 90% average on homework, 75% on quizzes (didn't study too well), but 95% average on tests. You can now calculate your grade with the mean( command:

                                                                                                                                                                                                                                        :mean({90,75,95},{50,20,30

                                                                                                                                                                                                                                        You should get a 88.5 if you did everything right.

                                                                                                                                                                                                                                        Frequency lists don't need to be whole numbers. Amazing as that may sound, your calculator can handle being told that one element of the list occurs 1/3 of a time, and another occurs 22.7 times. It can even handle a frequency of 0 - it will just ignore that element, as though it weren't there. In particular, mean(L1,L2) is effectively equivalent to sum (L1*L2)/sum(L2).

                                                                                                                                                                                                                                        One caveat, though - if all of the elements occur 0 times, there's nothing to take an average of and your calculator will throw an error.

                                                                                                                                                                                                                                        Error Conditions

                                                                                                                                                                                                                                        • ERR:DATA TYPE is thrown, among other cases, if the data list is complex, or if the frequencies are not all positive and real.
                                                                                                                                                                                                                                        • ERR:DIM MISMATCH is thrown if the frequency list and the data list have a different number of elements.
                                                                                                                                                                                                                                        • ERR:DIVIDE BY 0 is thrown if the frequency list's elements are all 0.

                                                                                                                                                                                                                                        Source: parts of this page were written by the following TI|BD contributors: alexrudd, burr, DarkerLine, GoVegan, Mr Dino, thornahawk.

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                                                                                                                                                                                                                                        • FR: médianne

                                                                                                                                                                                                                                        median(

                                                                                                                                                                                                                                        Overview

                                                                                                                                                                                                                                        Returns the median of list with frequency freqlist.

                                                                                                                                                                                                                                        Availability: Token available everywhere.

                                                                                                                                                                                                                                        Syntax

                                                                                                                                                                                                                                        median(list[,freqlist])

                                                                                                                                                                                                                                        Arguments

                                                                                                                                                                                                                                        NameTypeOptional
                                                                                                                                                                                                                                        listlist
                                                                                                                                                                                                                                        freqlistlistYes

                                                                                                                                                                                                                                        Location

                                                                                                                                                                                                                                        2nd, list, MATH, 4:median(

                                                                                                                                                                                                                                        Description

                                                                                                                                                                                                                                        The median( command finds the median of a list. It takes a list of real numbers as a parameter. For example:

                                                                                                                                                                                                                                        :Prompt L1
:Disp "MEDIAN OF L1",median(L1

                                                                                                                                                                                                                                        That's not all, however. Awesome as the median( command is, it can also take a frequency list argument, for situations when your elements occur more than once. For example:

                                                                                                                                                                                                                                        :Disp median({1,2,3},{5,4,4})

                                                                                                                                                                                                                                        is short for

                                                                                                                                                                                                                                        :median({1,1,1,1,1,2,2,2,2,3,3,3,3})

                                                                                                                                                                                                                                        The frequency list {5,4,4} means that the first element, 1, occurs 5 times, the second element, 2, occurs 4 times, and the third element, 3, occurs 4 times.

                                                                                                                                                                                                                                        Advanced Uses

                                                                                                                                                                                                                                        Frequency lists don't need to be whole numbers. Amazing as that may sound, your calculator can handle being told that one element of the list occurs 1/3 of a time, and another occurs 22.7 times. It can even handle a frequency of 0 - it will just ignore that element, as though it weren't there. One caveat, though - if all of the elements occur 0 times, there's nothing to take the median of and your calculator will throw an error.

                                                                                                                                                                                                                                        Error Conditions

                                                                                                                                                                                                                                        • ERR:DATA TYPE is thrown, among other cases, if the data list is complex, or if the frequencies are not all positive and real.
                                                                                                                                                                                                                                        • ERR:DIM MISMATCH is thrown if the frequency list and the data list have a different number of elements.
                                                                                                                                                                                                                                        • ERR:DIVIDE BY 0 is thrown if the frequency list's elements are all 0.

                                                                                                                                                                                                                                        Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Mr Dino, Timothy Foster.

                                                                                                                                                                                                                                        History

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                                                                                                                                                                                                                                        • FR: min(

                                                                                                                                                                                                                                        min(

                                                                                                                                                                                                                                        Overview

                                                                                                                                                                                                                                        Returns smaller of valueA and valueB.

                                                                                                                                                                                                                                        Availability: Token available everywhere.

                                                                                                                                                                                                                                        Syntax

                                                                                                                                                                                                                                        min(valueA,valueB)

                                                                                                                                                                                                                                        Arguments

                                                                                                                                                                                                                                        NameTypeOptional
                                                                                                                                                                                                                                        valueA
                                                                                                                                                                                                                                        valueB

                                                                                                                                                                                                                                        Location

                                                                                                                                                                                                                                        math, NUM, 6:min(

                                                                                                                                                                                                                                        Overview

                                                                                                                                                                                                                                        Returns smallest real or complex element in list.

                                                                                                                                                                                                                                        Availability: Token available everywhere.

                                                                                                                                                                                                                                        Syntax

                                                                                                                                                                                                                                        min(list)

                                                                                                                                                                                                                                        Arguments

                                                                                                                                                                                                                                        NameTypeOptional
                                                                                                                                                                                                                                        listlist

                                                                                                                                                                                                                                        Location

                                                                                                                                                                                                                                        2nd, list, MATH, 1:min(

                                                                                                                                                                                                                                        Overview

                                                                                                                                                                                                                                        Returns real or complex list of the smaller of each pair of elements in listA and listB.

                                                                                                                                                                                                                                        Availability: Token available everywhere.

                                                                                                                                                                                                                                        Syntax

                                                                                                                                                                                                                                        min(listA,listB)

                                                                                                                                                                                                                                        Arguments

                                                                                                                                                                                                                                        NameTypeOptional
                                                                                                                                                                                                                                        listAlist
                                                                                                                                                                                                                                        listBlist

                                                                                                                                                                                                                                        Location

                                                                                                                                                                                                                                        2nd, list, MATH, 1:min(

                                                                                                                                                                                                                                        Overview

                                                                                                                                                                                                                                        Returns a real or complex list of the smaller of value or each list element.

                                                                                                                                                                                                                                        Availability: Token available everywhere.

                                                                                                                                                                                                                                        Syntax

                                                                                                                                                                                                                                        min(value,list)

                                                                                                                                                                                                                                        Arguments

                                                                                                                                                                                                                                        NameTypeOptional
                                                                                                                                                                                                                                        value
                                                                                                                                                                                                                                        listlist

                                                                                                                                                                                                                                        Location

                                                                                                                                                                                                                                        2nd, list, MATH, 1:min(

                                                                                                                                                                                                                                        Description

                                                                                                                                                                                                                                        min(x,y) returns the smallest of the two numbers x and y. min(list) returns the smallest element of list. min(list1,list2) returns the pairwise minima of the two lists. min(list1,x) (equivalently, min(x,list1)) returns a list whose elements are the smaller of x or the corresponding element of the original list.

                                                                                                                                                                                                                                        min(2,3)
     2
min({2,3,4})
     2
min({1,3},{4,2})
     {1 2}
min({1,3},2)
     {1 2}

                                                                                                                                                                                                                                        Unlike relational operators, such as < and >, min( can also compare complex numbers. To do this, both arguments must be complex — either complex numbers or complex lists: min(2,𝑖) will throw a ERR:DATA TYPE error even though min(2+0𝑖,𝑖) won't. In the case of complex numbers, the number with the smallest absolute value will be returned. When the two numbers have the same absolute value, the second one will be returned: min(𝑖,-𝑖) returns -𝑖 and min(-𝑖,𝑖) returns 𝑖.

                                                                                                                                                                                                                                        Advanced Uses

                                                                                                                                                                                                                                        min( can be used in Boolean comparisons to see if every value of a list is 1 (true) — useful because commands like If or While only deal with numbers, and not lists, but comparisons like L1=L2 return a list of values. In general, the behavior you want varies, and you will use the min( or max( functions accordingly.

                                                                                                                                                                                                                                        Using min( will give you a strict test — only if every single value of a list is true will min( return true. For example, the following code will test if two lists are identical — they have the same exact elements — and print EQUAL in that case:

                                                                                                                                                                                                                                        :If dim(L1)=dim(L2
:Then
:If min(L1=L2
:Disp "EQUAL
:End

                                                                                                                                                                                                                                        The first check, to see if the sizes are identical, is necessary because otherwise comparing the lists will return a ERR:DIM MISMATCH error.

                                                                                                                                                                                                                                        Error Conditions

                                                                                                                                                                                                                                        • ERR:DATA TYPE is thrown when comparing a real and a complex number. This can be avoided by adding 0𝑖 to the real number.
                                                                                                                                                                                                                                        • ERR:DIM MISMATCH is thrown, when using min( with two lists, if they have different dimensions.

                                                                                                                                                                                                                                        Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

                                                                                                                                                                                                                                        History

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                                                                                                                                                                                                                                        • FR: μ

                                                                                                                                                                                                                                        μ

                                                                                                                                                                                                                                        Overview

                                                                                                                                                                                                                                        Availability: Token available everywhere.

                                                                                                                                                                                                                                        Syntax

                                                                                                                                                                                                                                        μ

                                                                                                                                                                                                                                        Description

                                                                                                                                                                                                                                        Examples

                                                                                                                                                                                                                                        Explanation 1

                                                                                                                                                                                                                                        code 1

                                                                                                                                                                                                                                        Explanation 2

                                                                                                                                                                                                                                        code 2

                                                                                                                                                                                                                                        Error Conditions

                                                                                                                                                                                                                                        Advanced Notes

                                                                                                                                                                                                                                        History

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                                                                                                                                                                                                                                        • FR: nDeriv(

                                                                                                                                                                                                                                        nDeriv(

                                                                                                                                                                                                                                        Overview

                                                                                                                                                                                                                                        When command is used in Classic mode, returns approximate numerical derivative of expression with respect to variable at value, with specific tolerance ε.
                                                                                                                                                                                                                                        In MathPrint mode, numeric derivative template pastes and uses default tolerance ε.

                                                                                                                                                                                                                                        Availability: Token available everywhere.

                                                                                                                                                                                                                                        Syntax

                                                                                                                                                                                                                                        nDeriv(expression,variable,value[,ε])

                                                                                                                                                                                                                                        Arguments

                                                                                                                                                                                                                                        NameTypeOptional
                                                                                                                                                                                                                                        expressionexpression
                                                                                                                                                                                                                                        variable
                                                                                                                                                                                                                                        value
                                                                                                                                                                                                                                        εYes

                                                                                                                                                                                                                                        Location

                                                                                                                                                                                                                                        math, MATH, 8:nDeriv(

                                                                                                                                                                                                                                        Description

                                                                                                                                                                                                                                        nDeriv(f(var),var,value[,h]) computes an approximation to the value of the derivative of f(var) with respect to var at var=value. h is the step size used in the approximation of the derivative. The default value of h is 0.001.

                                                                                                                                                                                                                                        nDeriv( only works for real numbers and expressions. nDeriv( can be used only once inside another instance of nDeriv(.

                                                                                                                                                                                                                                        π→X
     3.141592654
nDeriv(sin(T),T,X)
     -.9999998333
nDeriv(sin(T),T,X,(abs(X)+E⁻6)E⁻6)
     -1.000000015
nDeriv(nDeriv(cos(U),U,T),T,X)
     .999999665

                                                                                                                                                                                                                                        Advanced

                                                                                                                                                                                                                                        If the default setting for h doesn't produce a good enough result, it can be difficult to choose a correct substitute. Although larger values of h naturally produce a larger margin of error, it's not always helpful to make h very small. If the difference between f(x+h) and f(x-h) is much smaller than the actual values of f(x+h) or f(x-h), then it will only be recorded in the last few significant digits, and therefore be imprecise.

                                                                                                                                                                                                                                        A suitable compromise is to choose a tolerance h that's based on X. As suggested here, (abs(X)+]E⁻6)E⁻6 is a reasonably good value that often gives better results than the default.

                                                                                                                                                                                                                                        Formula

                                                                                                                                                                                                                                        The exact formula that the calculator uses to evaluate this function is:

                                                                                                                                                                                                                                        (1) \(\begin{align} \texttt{nDeriv}(f(t),t,x,h)=\frac{f(x+h)-f(x-h)}{2h} \end{align}\)

                                                                                                                                                                                                                                        This formula is known as the symmetric derivative, and using it generally increases the accuracy of the calculation. However, in a few instances it can give erroneous answers. One case where it gives false answers is with the function,

                                                                                                                                                                                                                                        (2) \(\begin{align} f(x) = \dfrac{1}{x^2} \bigg\vert_{x=0} \end{align}\)

                                                                                                                                                                                                                                        This derivative is undefined when calculated algebraically, but due to the method of calculation, the derivative given by nDeriv( is zero. These problems can be avoided by ensuring that a function's derivative is defined at the point of interest.

                                                                                                                                                                                                                                        Error Conditions

                                                                                                                                                                                                                                        • ERR:DOMAIN is thrown if h is 0 (since this would yield division by 0 in the formula)
                                                                                                                                                                                                                                        • ERR:ILLEGAL NEST is thrown if nDeriv( commands are nested more than one level deep. Just having one nDeriv( command inside another is okay, though.

                                                                                                                                                                                                                                        Source: parts of this page were written by the following TI|BD contributors: DarkerLine, Deoxal, GoVegan, kg583, Timothy Foster.

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                                                                                                                                                                                                                                        • FR: 𝑛Max

                                                                                                                                                                                                                                        𝑛Max

                                                                                                                                                                                                                                        Overview

                                                                                                                                                                                                                                        Availability: Token available everywhere.

                                                                                                                                                                                                                                        Syntax

                                                                                                                                                                                                                                        𝑛Max

                                                                                                                                                                                                                                        Description

                                                                                                                                                                                                                                        Examples

                                                                                                                                                                                                                                        Explanation 1

                                                                                                                                                                                                                                        code 1

                                                                                                                                                                                                                                        Explanation 2

                                                                                                                                                                                                                                        code 2

                                                                                                                                                                                                                                        Error Conditions

                                                                                                                                                                                                                                        Advanced Notes

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                                                                                                                                                                                                                                        • FR: 𝑛Min

                                                                                                                                                                                                                                        𝑛Min

                                                                                                                                                                                                                                        Overview

                                                                                                                                                                                                                                        Availability: Token available everywhere.

                                                                                                                                                                                                                                        Syntax

                                                                                                                                                                                                                                        𝑛Min

                                                                                                                                                                                                                                        Description

                                                                                                                                                                                                                                        Examples

                                                                                                                                                                                                                                        Explanation 1

                                                                                                                                                                                                                                        code 1

                                                                                                                                                                                                                                        Explanation 2

                                                                                                                                                                                                                                        code 2

                                                                                                                                                                                                                                        Error Conditions

                                                                                                                                                                                                                                        Advanced Notes

                                                                                                                                                                                                                                        History

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                                                                                                                                                                                                                                        TI-82 1.0 𝑛Start added
                                                                                                                                                                                                                                        TI-83 0.01013 Renamed 𝑛Start to 𝑛Min
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                                                                                                                                                                                                                                        • FR: n

                                                                                                                                                                                                                                        n

                                                                                                                                                                                                                                        Overview

                                                                                                                                                                                                                                        Syntax

                                                                                                                                                                                                                                        n

                                                                                                                                                                                                                                        Description

                                                                                                                                                                                                                                        Examples

                                                                                                                                                                                                                                        Explanation 1

                                                                                                                                                                                                                                        code 1

                                                                                                                                                                                                                                        Explanation 2

                                                                                                                                                                                                                                        code 2

                                                                                                                                                                                                                                        Error Conditions

                                                                                                                                                                                                                                        Advanced Notes

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                                                                                                                                                                                                                                        • FR: n

                                                                                                                                                                                                                                        n

                                                                                                                                                                                                                                        Overview

                                                                                                                                                                                                                                        Availability: Token available everywhere.

                                                                                                                                                                                                                                        Syntax

                                                                                                                                                                                                                                        n

                                                                                                                                                                                                                                        Description

                                                                                                                                                                                                                                        Examples

                                                                                                                                                                                                                                        Explanation 1

                                                                                                                                                                                                                                        code 1

                                                                                                                                                                                                                                        Explanation 2

                                                                                                                                                                                                                                        code 2

                                                                                                                                                                                                                                        Error Conditions

                                                                                                                                                                                                                                        Advanced Notes

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                                                                                                                                                                                                                                        • FR: ⁄

                                                                                                                                                                                                                                        ⁄

                                                                                                                                                                                                                                        Overview

                                                                                                                                                                                                                                        Syntax

                                                                                                                                                                                                                                        ⁄

                                                                                                                                                                                                                                        Description

                                                                                                                                                                                                                                        Examples

                                                                                                                                                                                                                                        Explanation 1

                                                                                                                                                                                                                                        code 1

                                                                                                                                                                                                                                        Explanation 2

                                                                                                                                                                                                                                        code 2

                                                                                                                                                                                                                                        Error Conditions

                                                                                                                                                                                                                                        Advanced Notes

                                                                                                                                                                                                                                        History

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                                                                                                                                                                                                                                        • FR: normalFRép(

                                                                                                                                                                                                                                        normalcdf(

                                                                                                                                                                                                                                        Overview

                                                                                                                                                                                                                                        Computes the normal distribution probability between lowerbound and upperbound for the specified μ and σ.

                                                                                                                                                                                                                                        Availability: Token available everywhere.

                                                                                                                                                                                                                                        Syntax

                                                                                                                                                                                                                                        normalcdf(lowerbound,upperbound[,μ,σ])

                                                                                                                                                                                                                                        Arguments

                                                                                                                                                                                                                                        NameTypeOptional
                                                                                                                                                                                                                                        lowerbound
                                                                                                                                                                                                                                        upperbound
                                                                                                                                                                                                                                        μYes
                                                                                                                                                                                                                                        σYes

                                                                                                                                                                                                                                        Location

                                                                                                                                                                                                                                        2nd, distr, DISTR, 2:normalcdf(

                                                                                                                                                                                                                                        Description

                                                                                                                                                                                                                                        normalcdf( is the normal (Gaussian) cumulative density function. If some random variable follows a normal distribution, you can use this command to find the probability that this variable will fall in the interval you supply.

                                                                                                                                                                                                                                        There are two ways to use normalcdf(. With two arguments (lower bound and upper bound), the calculator will assume you mean the standard normal distribution, and use that to find the probability corresponding to the interval between "lower bound" and "upper bound". You can also supply two additional arguments to use the normal distribution with a specified mean and standard deviation. For example:

                                                                                                                                                                                                                                        for the standard normal distribution
:normalcdf(-1,1

for the normal distribution with mean 10 and std. dev. 2.5
:normalcdf(5,15,10,2.5

                                                                                                                                                                                                                                        Advanced

                                                                                                                                                                                                                                        Often, you want to find a "tail probability" - a special case for which the interval has no lower or no upper bound. For example, "what is the probability x is greater than 2?". The TI-83+ has no special symbol for infinity, but you can use E99 to get a very large number that will work equally well in this case (E is the decimal exponent obtained by pressing [2nd] [EE]). Use E99 for positive infinity, and -E99 for negative infinity.

                                                                                                                                                                                                                                        The normal distribution is often used to approximate the binomial distribution when there are a lot of trials. This isn't really necessary on the TI-83+ because the binompdf( and binomcdf( commands are already very fast - however, the normal distribution can be slightly faster, and the skill can come in handy if you don't have access to a calculator but do have a table of normal distributions (yeah, right). Here is how to convert a binomial distribution to a normal one:

                                                                                                                                                                                                                                        :binompdf(N,P,X
can be
:normalcdf(X-.5,X+.5,NP,√(NP(1-P

:binomcdf(N,P,X,Y
can be
:normalcdf(X-.5,Y+.5,NP,√(NP(1-P

                                                                                                                                                                                                                                        How much faster this is will depend on N and P, since the binomial distribution takes a long time to evaluate for large values of N, but the normal distribution takes about the same time for any mean and standard deviation. Also, this is an approximation that is only valid for some binomial distributions - a common rule of thumb is NP>10.

                                                                                                                                                                                                                                        Formulas

                                                                                                                                                                                                                                        As with other continuous distributions, any probability is an integral of the probability density function. Here, too, we can define normalcdf( for the standard normal case in terms of normalpdf(:

                                                                                                                                                                                                                                        (1) \(\begin{align} \texttt{normalcdf}(a,b)=\int_a^b \texttt{normalpdf}(x) \, \mathrm{d}x=\frac1{\sqrt{2\pi\,}} \int_a^b e^{-\frac1{2}x^2} \, \mathrm{d}x \end{align}\)

                                                                                                                                                                                                                                        or in terms of the error function:

                                                                                                                                                                                                                                        (2) \(\begin{align} \texttt{normalcdf}(a,b)=\frac1{2}\left(\texttt{erf}\left(\frac{b}{\sqrt{2}}\right)-\texttt{erf}\left(\frac{a}{\sqrt{2}}\right)\right) \end{align}\)

                                                                                                                                                                                                                                        For the arbitrary mean μ and standard deviation σ, normalcdf( is defined in terms of the standard normal distribution, with the bounds of the interval standardized:

                                                                                                                                                                                                                                        (3) \(\begin{align} \texttt{normalcdf}(a,b,\mu,\sigma)=\texttt{normalcdf}\left(\frac{a-\mu}{\sigma},\frac{b-\mu}{\sigma} \right) \end{align}\)

                                                                                                                                                                                                                                        Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, thornahawk, Weregoose.

                                                                                                                                                                                                                                        History

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                                                                                                                                                                                                                                        • FR: normalFdp(

                                                                                                                                                                                                                                        normalpdf(

                                                                                                                                                                                                                                        Overview

                                                                                                                                                                                                                                        Computes the probability density function for the normal distribution at a specified x value for the specified μ and σ.

                                                                                                                                                                                                                                        Availability: Token available everywhere.

                                                                                                                                                                                                                                        Syntax

                                                                                                                                                                                                                                        normalpdf(x[,μ,σ])

                                                                                                                                                                                                                                        Arguments

                                                                                                                                                                                                                                        NameTypeOptional
                                                                                                                                                                                                                                        x
                                                                                                                                                                                                                                        μYes
                                                                                                                                                                                                                                        σYes

                                                                                                                                                                                                                                        Location

                                                                                                                                                                                                                                        2nd, distr, DISTR, 1:normalpdf(

                                                                                                                                                                                                                                        Description

                                                                                                                                                                                                                                        normalpdf( is the normal (Gaussian) probability density function.

                                                                                                                                                                                                                                        Since the normal distribution is continuous, the value of normalpdf( doesn't represent an actual probability - in fact, one of the only uses for this command is to draw a graph of the normal curve. You could also use it for various calculus purposes, such as finding inflection points.

                                                                                                                                                                                                                                        The command can be used in two ways: normalpdf(x) will evaluate the standard normal p.d.f. (with mean at 0 and a standard deviation of 1) at x, and normalpdf(x,μ,σ) will work for an arbitrary normal curve, with mean μ and standard deviation σ.

                                                                                                                                                                                                                                        Formulas

                                                                                                                                                                                                                                        For the standard normal distribution, normalpdf(x) is defined as

                                                                                                                                                                                                                                        (1) \(\begin{align} \texttt{normalpdf}(x)=\frac1{\sqrt{2\pi\,}} \, e^{-\frac1{2}x^2} \end{align}\)

                                                                                                                                                                                                                                        For other normal distributions, normalpdf( is defined in terms of the standard distribution:

                                                                                                                                                                                                                                        (2) \(\begin{align} \texttt{normalpdf}(x,\mu,\sigma)=\frac{1}{\sigma} \, \texttt{normalpdf} \left(\frac{x-\mu}{\sigma}\right) \end{align}\)

                                                                                                                                                                                                                                        Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, thornahawk.

                                                                                                                                                                                                                                        History

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                                                                                                                                                                                                                                        • FR: non(

                                                                                                                                                                                                                                        not(

                                                                                                                                                                                                                                        Overview

                                                                                                                                                                                                                                        Returns 0 if value is ≠ 0. value can be a real number, expression, or list.

                                                                                                                                                                                                                                        Availability: Token available everywhere.

                                                                                                                                                                                                                                        Syntax

                                                                                                                                                                                                                                        not(value)

                                                                                                                                                                                                                                        Arguments

                                                                                                                                                                                                                                        NameTypeOptional
                                                                                                                                                                                                                                        value

                                                                                                                                                                                                                                        Location

                                                                                                                                                                                                                                        2nd, test, LOGIC, 4:not(

                                                                                                                                                                                                                                        Description

                                                                                                                                                                                                                                        The last logical operator available on the 83 series takes only one value as input. not( comes with its own parentheses to make up for this loss. Quite simply, it negates the input: False becomes True (1) and True returns False (0). not( can be nested; one use is to make any True value into a 1.

                                                                                                                                                                                                                                        :not(0)
           1

:not(-20 and 14)

           0

:not(not(2))
           1

                                                                                                                                                                                                                                        Advanced Uses

                                                                                                                                                                                                                                        not(not(X)) will make any value X into 1 if it's not 0, and will keep it 0 if it is.

                                                                                                                                                                                                                                        Optimization

                                                                                                                                                                                                                                        not(X) and X=0 have the same truth value, but not( is shorter if the closing parenthesis is omitted:

                                                                                                                                                                                                                                        :If A=0
can be
:If not(A

                                                                                                                                                                                                                                        Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan.

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                                                                                                                                                                                                                                        • FR: vactNet(

                                                                                                                                                                                                                                        npv(

                                                                                                                                                                                                                                        Overview

                                                                                                                                                                                                                                        Computes the sum of the present values for cash inflows and outflows.

                                                                                                                                                                                                                                        Availability: Token available everywhere.

                                                                                                                                                                                                                                        Syntax

                                                                                                                                                                                                                                        npv(interest rate,CF0,CFList[,CFFreq])

                                                                                                                                                                                                                                        Arguments

                                                                                                                                                                                                                                        NameTypeOptional
                                                                                                                                                                                                                                        interest rate
                                                                                                                                                                                                                                        CF0
                                                                                                                                                                                                                                        CFList
                                                                                                                                                                                                                                        CFFreqYes

                                                                                                                                                                                                                                        Location

                                                                                                                                                                                                                                        apps, 1:Finance, CALC, 7:npv(

                                                                                                                                                                                                                                        Description

                                                                                                                                                                                                                                        The npv( command computes the net present value of money over a specified time period. If a positive value is returned after executing npv(, that means it was a positive cashflow; otherwise it was a negative cashflow. The npv( command takes four arguments, and the fourth one is optional:

                                                                                                                                                                                                                                        • interest rate — the percentage of the money that is paid for the use of that money over each individual period of time.
                                                                                                                                                                                                                                        • CF0 — the initial amount of money that you start out with; this number must be a real number, otherwise you will get a ERR:DATA TYPE error.
                                                                                                                                                                                                                                        • CFList — the list of cash flows added or subtracted after the initial money.
                                                                                                                                                                                                                                        • CFFreq — the list of frequencies of each cash flow added after the initial money; if this is left off, each cash flow in the cash flow list will just appear once by default.

                                                                                                                                                                                                                                        Sample Problem

                                                                                                                                                                                                                                        Your mom recently opened a bank account for you, with $500 as a gift to start you off. This is welcome news to you, until you find out that the bank charges 5% as the interest rate for the account. So, you get a job at Rocco's Pizzas delivering pizzas, which brings in \(1,000-\)2,000 each month. For the last five months, in particular, you have earned $1,250, $1,333, $1,575, $1,100, and $1,900. (Assume there are no other expenses, such as gas, car payment, etc.)

                                                                                                                                                                                                                                        Plugging in all of the different values into the npv( command, this is what our code looks like:

                                                                                                                                                                                                                                        :npv(5,500,{1250,1333,1575,1100,1900

                                                                                                                                                                                                                                        Optimization

                                                                                                                                                                                                                                        The npv( command's optional fourth argument should be left off if each cash flow of money in the list of cash flows just appears once.

                                                                                                                                                                                                                                        :npv(5,1550,{2E3,3E3,4E3},{1,1,1
can be
:npv(5,1550,{2E3,3E3,4E3

                                                                                                                                                                                                                                        At the same time, if there are cash flows that occur multiple times, it can be smaller to just use the frequency argument:

                                                                                                                                                                                                                                        :npv(8,0,{200,200,300,300,300
can be
:npv(8,0,{200,300},{2,3

                                                                                                                                                                                                                                        Formulas

                                                                                                                                                                                                                                        Without a frequency list, the formula for npv( is the following:

                                                                                                                                                                                                                                        (1) \(\begin{align} \texttt{npv}(i,\texttt{CF}_0,\{\texttt{CF}_j\})=\sum_{j=0}^N{\texttt{CF}_j\left(1+\frac{i}{100}\right)^{-j}} \end{align}\)

                                                                                                                                                                                                                                        When a frequency list is used, the same formula can be applied if we expand the list with frequencies into a long list without frequencies. However, it's possible to do the calculation directly. We define the cumulative frequency Sj as the sum of the first j frequencies (S0 is taken to be 0):

                                                                                                                                                                                                                                        (2) \(\begin{align} \texttt{npv}(i,\texttt{CF}_0,\{\texttt{CF}_j\},\{n_j\}) =\texttt{CF}_0+\sum_{j=1}^N{\texttt{CF}_j\left(1+\frac{i}{100}\right)^{S_{j-1}}\frac{(1-(1+\frac{i}{100})^{-n_j})}{i}} \end{align}\)

                                                                                                                                                                                                                                        Error Conditions

                                                                                                                                                                                                                                        • ERR:DATA TYPE is thrown if you try to use anything other than a real number for the interest rate.
                                                                                                                                                                                                                                        • ERR:DIM MISMATCH is thrown if the list of cash flows and the list of cash flow frequencies have different dimensions.

                                                                                                                                                                                                                                        Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583.

                                                                                                                                                                                                                                        History

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                                                                                                                                                                                                                                          • FR: n⁄d

                                                                                                                                                                                                                                          n⁄d

                                                                                                                                                                                                                                          Overview

                                                                                                                                                                                                                                          Displays results as a simple fraction.

                                                                                                                                                                                                                                          Availability: Token available everywhere.

                                                                                                                                                                                                                                          Syntax

                                                                                                                                                                                                                                          n/d

                                                                                                                                                                                                                                          Location

                                                                                                                                                                                                                                          alpha, F1, 1:n/d

                                                                                                                                                                                                                                          Description

                                                                                                                                                                                                                                          n/d is the template for entering a simple fraction.
                                                                                                                                                                                                                                          n/d is accessible by pressing ALPHA then Y= then enter.

                                                                                                                                                                                                                                          Source: parts of this page were written by the following TI|BD contributors: ccrh2009.

                                                                                                                                                                                                                                          History

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                                                                                                                                                                                                                                          • FR: n₁

                                                                                                                                                                                                                                          n₁

                                                                                                                                                                                                                                          Overview

                                                                                                                                                                                                                                          Syntax

                                                                                                                                                                                                                                          n₁

                                                                                                                                                                                                                                          Description

                                                                                                                                                                                                                                          Examples

                                                                                                                                                                                                                                          Explanation 1

                                                                                                                                                                                                                                          code 1

                                                                                                                                                                                                                                          Explanation 2

                                                                                                                                                                                                                                          code 2

                                                                                                                                                                                                                                          Error Conditions

                                                                                                                                                                                                                                          Advanced Notes

                                                                                                                                                                                                                                          History

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                                                                                                                                                                                                                                          • FR: n₂

                                                                                                                                                                                                                                          n₂

                                                                                                                                                                                                                                          Overview

                                                                                                                                                                                                                                          Syntax

                                                                                                                                                                                                                                          n₂

                                                                                                                                                                                                                                          Description

                                                                                                                                                                                                                                          Examples

                                                                                                                                                                                                                                          Explanation 1

                                                                                                                                                                                                                                          code 1

                                                                                                                                                                                                                                          Explanation 2

                                                                                                                                                                                                                                          code 2

                                                                                                                                                                                                                                          Error Conditions

                                                                                                                                                                                                                                          Advanced Notes

                                                                                                                                                                                                                                          History

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                                                                                                                                                                                                                                          • FR: o

                                                                                                                                                                                                                                          o

                                                                                                                                                                                                                                          Overview

                                                                                                                                                                                                                                          Availability: Token available everywhere.

                                                                                                                                                                                                                                          Syntax

                                                                                                                                                                                                                                          o

                                                                                                                                                                                                                                          Description

                                                                                                                                                                                                                                          Examples

                                                                                                                                                                                                                                          Explanation 1

                                                                                                                                                                                                                                          code 1

                                                                                                                                                                                                                                          Explanation 2

                                                                                                                                                                                                                                          code 2

                                                                                                                                                                                                                                          Error Conditions

                                                                                                                                                                                                                                          Advanced Notes

                                                                                                                                                                                                                                          History

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                                                                                                                                                                                                                                          • FR: p

                                                                                                                                                                                                                                          p

                                                                                                                                                                                                                                          Overview

                                                                                                                                                                                                                                          Availability: Token available everywhere.

                                                                                                                                                                                                                                          Syntax

                                                                                                                                                                                                                                          p

                                                                                                                                                                                                                                          Description

                                                                                                                                                                                                                                          Examples

                                                                                                                                                                                                                                          Explanation 1

                                                                                                                                                                                                                                          code 1

                                                                                                                                                                                                                                          Explanation 2

                                                                                                                                                                                                                                          code 2

                                                                                                                                                                                                                                          Error Conditions

                                                                                                                                                                                                                                          Advanced Notes

                                                                                                                                                                                                                                          History

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                                                                                                                                                                                                                                          • FR: ṗ

                                                                                                                                                                                                                                          ṗ

                                                                                                                                                                                                                                          Overview

                                                                                                                                                                                                                                          Syntax

                                                                                                                                                                                                                                          ṗ

                                                                                                                                                                                                                                          Description

                                                                                                                                                                                                                                          Examples

                                                                                                                                                                                                                                          Explanation 1

                                                                                                                                                                                                                                          code 1

                                                                                                                                                                                                                                          Explanation 2

                                                                                                                                                                                                                                          code 2

                                                                                                                                                                                                                                          Error Conditions

                                                                                                                                                                                                                                          Advanced Notes

                                                                                                                                                                                                                                          History

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                                                                                                                                                                                                                                          • FR: π

                                                                                                                                                                                                                                          π

                                                                                                                                                                                                                                          Overview

                                                                                                                                                                                                                                          Availability: Token available everywhere.

                                                                                                                                                                                                                                          Syntax

                                                                                                                                                                                                                                          π

                                                                                                                                                                                                                                          Description

                                                                                                                                                                                                                                          Examples

                                                                                                                                                                                                                                          Explanation 1

                                                                                                                                                                                                                                          code 1

                                                                                                                                                                                                                                          Explanation 2

                                                                                                                                                                                                                                          code 2

                                                                                                                                                                                                                                          Error Conditions

                                                                                                                                                                                                                                          Advanced Notes

                                                                                                                                                                                                                                          History

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                                                                                                                                                                                                                                            • FR: parmorceaux(

                                                                                                                                                                                                                                            piecewise(

                                                                                                                                                                                                                                            Overview

                                                                                                                                                                                                                                            New piecewise function to support entry of functions as they are seen in textbook. This command can be found in » MATH B:piecewise(

                                                                                                                                                                                                                                            Comment:CE OS 5.3+

                                                                                                                                                                                                                                            Availability: Token available everywhere.

                                                                                                                                                                                                                                            Syntax

                                                                                                                                                                                                                                            piecewise(

                                                                                                                                                                                                                                            Location

                                                                                                                                                                                                                                            math

                                                                                                                                                                                                                                            Description

                                                                                                                                                                                                                                            The piecewise( command is a new addition in the release of OS 5.3 for the TI-84 Plus CE. As implied, it allows for the graphing of piecewise functions in the Y= editor. The example code demonstrates how this works from within a program.

                                                                                                                                                                                                                                            :ClrDraw
:Input "Y1=",Str1
:Input "Y2=",Str2
:Str1→Y1
:Str2→Y2
:FnOff
:"piecewise(Y1,X≥0,Y2,X<0→Y3
:DispGraph

                                                                                                                                                                                                                                            Advanced Uses

                                                                                                                                                                                                                                            One use of the piecewise( function is to evaluate an expression for a given value of X. For example:

                                                                                                                                                                                                                                            :piecewise(X²+2,X≥0

                                                                                                                                                                                                                                            This code will return the value of the expression if X≥0. So if X=0, then the program will return a value of 2. If X=3, it will return a value of 11. If X=-5, it will return an error.

                                                                                                                                                                                                                                            Optimization

                                                                                                                                                                                                                                            This command can simplify and compact the usage of piecewise expressions in programs. If you have less than 6 conditions that will never overlap, and they all affect a single variable, you can use the piecewise( command to make your code smaller, as shown below. Beware of comparability, though.

                                                                                                                                                                                                                                            :If X<2
:Then
:4.5X→N
:Else
:8X+3→N
:End
can be
:piecewise(4.5X,X<2,8X+3,X≥2→N

                                                                                                                                                                                                                                            Error Conditions

                                                                                                                                                                                                                                            • ERR:INVALID is thrown if expressions are not defined.
                                                                                                                                                                                                                                            • ERR:DATA TYPE is thrown if a quotation mark is not placed before a piecewise command that is to be stored to an equation variable.

                                                                                                                                                                                                                                            See Also

                                                                                                                                                                                                                                            Source: parts of this page were written by the following TI|BD contributors: Battlesquid, iPhoenixOnTIBD, kg583, Myles_Zadok.

                                                                                                                                                                                                                                            History

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                                                                                                                                                                                                                                            • FR: ·

                                                                                                                                                                                                                                            ·

                                                                                                                                                                                                                                            Overview

                                                                                                                                                                                                                                            Syntax

                                                                                                                                                                                                                                            ·

                                                                                                                                                                                                                                            Description

                                                                                                                                                                                                                                            Examples

                                                                                                                                                                                                                                            Explanation 1

                                                                                                                                                                                                                                            code 1

                                                                                                                                                                                                                                            Explanation 2

                                                                                                                                                                                                                                            code 2

                                                                                                                                                                                                                                            Error Conditions

                                                                                                                                                                                                                                            Advanced Notes

                                                                                                                                                                                                                                            History

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                                                                                                                                                                                                                                            • FR: poissonFRép(

                                                                                                                                                                                                                                            poissoncdf(

                                                                                                                                                                                                                                            Overview

                                                                                                                                                                                                                                            Computes a cumulative probability at x for the discrete Poisson distribution with specified mean μ.

                                                                                                                                                                                                                                            Availability: Token available everywhere.

                                                                                                                                                                                                                                            Syntax

                                                                                                                                                                                                                                            poissoncdf(μ,x)

                                                                                                                                                                                                                                            Arguments

                                                                                                                                                                                                                                            NameTypeOptional
                                                                                                                                                                                                                                            μ
                                                                                                                                                                                                                                            x

                                                                                                                                                                                                                                            Location

                                                                                                                                                                                                                                            2nd, distr, DISTR, D:poissoncdf(

                                                                                                                                                                                                                                            Description

                                                                                                                                                                                                                                            This command is used to calculate Poisson distribution cumulative probability. In plainer language, it solves a specific type of often-encountered probability problem, that occurs under the following conditions:

                                                                                                                                                                                                                                            1. A specific event happens at a known average rate (X occurrences per time interval)
                                                                                                                                                                                                                                            2. Each occurrence is independent of the time since the last occurrence
                                                                                                                                                                                                                                            3. We're interested in the probability that the event occurs at most a specific number of times in a given time interval.

                                                                                                                                                                                                                                            The poissoncdf( command takes two arguments: The mean is the average number of times the event will happen during the time interval we're interested in. The value is the number of times we're interested in the event happening (so the output is the probability that the event happens at most value times in the interval). Note that you may need to convert the mean so that the time intervals in both cases match up. This is done by a simple proportion: if the event happens 10 times per minute, it happens 20 times per two minutes.

                                                                                                                                                                                                                                            For example, consider point on a city street where an average of 5 cars pass by each minute. What is the probability that in a given minute, no more than 3 cars will drive by?

                                                                                                                                                                                                                                            1. The event is a car passing by, which happens at an average rate of 5 occurences per time interval (a minute)
                                                                                                                                                                                                                                            2. Each occurrence is independent of the time since the last occurrence (we'll assume this is true, though traffic might imply a correlation here)
                                                                                                                                                                                                                                            3. We're interested in the probability that the event occurs at most 3 times in the time interval.

                                                                                                                                                                                                                                            The syntax in this case is:

                                                                                                                                                                                                                                            :poissoncdf(5,3

                                                                                                                                                                                                                                            This will give about .265 when you run it, so there's a .265 probability that in a given minute, no more than 3 cars will drive by.

                                                                                                                                                                                                                                            Formulas

                                                                                                                                                                                                                                            The poissoncdf( command can be seen as a sum of poissonpdf( commands:

                                                                                                                                                                                                                                            (1) \(\begin{align} \texttt{poissoncdf}(\lambda,k)=\sum_{i=0}^k \texttt{poissonpdf}(\lambda,i) = \sum_{i=0}^k \frac {e^{-\lambda} \lambda^i}{i!} \end{align}\)

                                                                                                                                                                                                                                            We can also write the poissoncdf( command in terms of the incomplete gamma function:

                                                                                                                                                                                                                                            (2) \(\begin{align} \texttt{poissoncdf}(\lambda,k)=\frac{\Gamma(k+1,\lambda)}{k!} \end{align}\)

                                                                                                                                                                                                                                            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583.

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                                                                                                                                                                                                                                            • FR: poissonFdp(

                                                                                                                                                                                                                                            poissonpdf(

                                                                                                                                                                                                                                            Overview

                                                                                                                                                                                                                                            Computes a probability at x for the discrete Poisson distribution with the specified mean μ.

                                                                                                                                                                                                                                            Availability: Token available everywhere.

                                                                                                                                                                                                                                            Syntax

                                                                                                                                                                                                                                            poissonpdf(μ,x)

                                                                                                                                                                                                                                            Arguments

                                                                                                                                                                                                                                            NameTypeOptional
                                                                                                                                                                                                                                            μ
                                                                                                                                                                                                                                            x

                                                                                                                                                                                                                                            Location

                                                                                                                                                                                                                                            2nd, distr, DISTR, C:poissonpdf(

                                                                                                                                                                                                                                            Description

                                                                                                                                                                                                                                            This command is used to calculate Poisson distribution probability. In plainer language, it solves a specific type of often-encountered probability problem, that occurs under the following conditions:

                                                                                                                                                                                                                                            1. A specific event happens at a known average rate (X occurrences per time interval)
                                                                                                                                                                                                                                            2. Each occurrence is independent of the time since the last occurrence
                                                                                                                                                                                                                                            3. We're interested in the probability that the event occurs a specific number of times in a given time.

                                                                                                                                                                                                                                            The poissonpdf( command takes two arguments: The mean is the average number of times the event will happen during the time interval we're interested in. The value is the number of times we're interested in the event happening (so the output is the probability that the event happens value times in the interval).

                                                                                                                                                                                                                                            For example, consider point on a city street where an average of 5 cars pass by each minute. What is the probability that in a given minute, 8 cars will drive by?

                                                                                                                                                                                                                                            1. The event is a car passing by, which happens at an average rate of 5 occurrences per time interval (a minute)
                                                                                                                                                                                                                                            2. Each occurrence is independent of the time since the last occurrence (we'll assume this is true, though traffic might imply a correlation here)
                                                                                                                                                                                                                                            3. We're interested in the probability that the event occurs 8 times in the time interval

                                                                                                                                                                                                                                            The syntax in this case is:

                                                                                                                                                                                                                                            :poissonpdf(5,8

                                                                                                                                                                                                                                            This will give about .065 when you run it, so there's a .065 probability that in a given minute, 8 cars will drive by.

                                                                                                                                                                                                                                            Formulas

                                                                                                                                                                                                                                            The value of poissonpdf( is given by the formula

                                                                                                                                                                                                                                            (1) \(\begin{align} \texttt{poissonpdf}(\lambda,k) = \frac{e^{-\lambda}\lambda^k}{k!} \end{align}\)

                                                                                                                                                                                                                                            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583.

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                                                                                                                                                                                                                                            • FR: prgm

                                                                                                                                                                                                                                            prgm

                                                                                                                                                                                                                                            Overview

                                                                                                                                                                                                                                            Executes the program name.

                                                                                                                                                                                                                                            Availability: Token only available from within the Basic editor.

                                                                                                                                                                                                                                            Syntax

                                                                                                                                                                                                                                            prgmname

                                                                                                                                                                                                                                            Arguments

                                                                                                                                                                                                                                            NameTypeOptional
                                                                                                                                                                                                                                            name

                                                                                                                                                                                                                                            Location

                                                                                                                                                                                                                                            prgm, CTRL, D:prgm

                                                                                                                                                                                                                                            Description

                                                                                                                                                                                                                                            The prgm command is used to execute a program from inside another program (at any time while the program is running), with the secondary program acting as a subprogram for that program. Although they are listed in the program menu and can be executed independently like any other program, subprograms are primarily designed to do a particular task for the other program.

                                                                                                                                                                                                                                            You insert the prgm command into the program where you want the subprogram to run, and then type (with the alpha-lock on) the program name. You can also go to the program menu to choose a program, pressing ENTER to paste the program name into your program.

                                                                                                                                                                                                                                            PROGRAM:MYPROG
:ClrHome
:Output(3,3,"Hello
:prgmWHATEVER

                                                                                                                                                                                                                                            When the subprogram name is encountered during a program, the program will be put on hold and program execution will transfer to the subprogram. Once the subprogram is finished, program execution will go back to the program, continuing right after the subprogram name.

                                                                                                                                                                                                                                            Although subprograms can call themselves or other subprograms, this should be done sparingly because it can cause memory leaks if done too much or if the subprogram doesn't return to the parent program.

                                                                                                                                                                                                                                            Branching is local to each program, so you can’t use Goto in one program to jump to a Lbl in another program. In addition, all variables are global, so changing a variable in one program affects the variable everywhere else.

                                                                                                                                                                                                                                            Advanced Uses

                                                                                                                                                                                                                                            Each time you call a TI-Basic program, 16 bytes are used to save your place in the original program so you can return to it correctly. This is a small enough amount that you don't have to worry about it, unless you're low on RAM or use a lot of recursion.

                                                                                                                                                                                                                                            Error Conditions

                                                                                                                                                                                                                                            See Also

                                                                                                                                                                                                                                            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Xphoenix.

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                                                                                                                                                                                                                                            • FR: prod(

                                                                                                                                                                                                                                            prod(

                                                                                                                                                                                                                                            Overview

                                                                                                                                                                                                                                            Returns product of list elements between start and end

                                                                                                                                                                                                                                            Availability: Token available everywhere.

                                                                                                                                                                                                                                            Syntax

                                                                                                                                                                                                                                            prod(list[,start,end])

                                                                                                                                                                                                                                            Arguments

                                                                                                                                                                                                                                            NameTypeOptional
                                                                                                                                                                                                                                            listlist
                                                                                                                                                                                                                                            startYes
                                                                                                                                                                                                                                            endYes

                                                                                                                                                                                                                                            Location

                                                                                                                                                                                                                                            2nd, list, MATH, 6:prod(

                                                                                                                                                                                                                                            Description

                                                                                                                                                                                                                                            The prod( command calculates the product of all or part of a list.

                                                                                                                                                                                                                                            When you use it with only one argument, the list, it multiplies all the elements of the list. You can also give it a bound of start and end and it will only multiply the elements starting and ending at those indices (inclusive).

                                                                                                                                                                                                                                            prod({1,2,3,4,5})
    120
prod({1,2,3,4,5},2,4)
    24
prod({1,2,3,4,5},3)
    60

                                                                                                                                                                                                                                            Optimization

                                                                                                                                                                                                                                            If the value of end is the last element of the list, it can be omitted:

                                                                                                                                                                                                                                            prod({1,2,3,4,5},3,5)
can be
prod({1,2,3,4,5},3)

                                                                                                                                                                                                                                            Error Conditions

                                                                                                                                                                                                                                            • ERR:DOMAIN if the starting or ending value aren't positive integers.
                                                                                                                                                                                                                                            • ERR:INVALID DIM if the starting or ending value exceed the size of the list, or are in the wrong order.

                                                                                                                                                                                                                                            Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan.

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                                                                                                                                                                                                                                            • FR: pxl-Test(

                                                                                                                                                                                                                                            pxl-Test(

                                                                                                                                                                                                                                            Overview

                                                                                                                                                                                                                                            Returns 1 if pixel (row, column) is on, 0 if it is off;

                                                                                                                                                                                                                                            Availability: Token available everywhere.

                                                                                                                                                                                                                                            Syntax

                                                                                                                                                                                                                                            pxl-Test(row,column)

                                                                                                                                                                                                                                            Arguments

                                                                                                                                                                                                                                            NameTypeOptional
                                                                                                                                                                                                                                            row
                                                                                                                                                                                                                                            column

                                                                                                                                                                                                                                            Location

                                                                                                                                                                                                                                            2nd, draw, POINTS, 7:pxl-Test(

                                                                                                                                                                                                                                            Description

                                                                                                                                                                                                                                            The pxl-Test( command is used to test a pixel at the given (Y,X) coordinates of the graph screen, to see whether it is on or off. One is returned if the pixel is on and zero is returned if the pixel is off. Please note that the coordinates are switched around so that the row comes first and then the column — it's (Y,X) instead of (X,Y). This command's coordinates are independent of the window settings.

                                                                                                                                                                                                                                            You can store the result of pxl-Test( to a variable for later use, or use the command in a conditional or loop.

                                                                                                                                                                                                                                            :Pxl-On(25,25
:If pxl-Test(25,25
:Disp "Pixel turned on!

                                                                                                                                                                                                                                            Error Conditions

                                                                                                                                                                                                                                            • ERR:DOMAIN is triggered if the coordinates are not whole numbers or not in the right range ([0..62] for row, [0..94] for column). These bounds are also affected by split screen mode (Horiz)

                                                                                                                                                                                                                                            Source: parts of this page were written by the following TI|BD contributors: Battlesquid, burr, DarkerLine, GoVegan.

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                                                                                                                                                                                                                                            • FR: p̂

                                                                                                                                                                                                                                            p̂

                                                                                                                                                                                                                                            Overview

                                                                                                                                                                                                                                            Syntax

                                                                                                                                                                                                                                            p̂

                                                                                                                                                                                                                                            Description

                                                                                                                                                                                                                                            Examples

                                                                                                                                                                                                                                            Explanation 1

                                                                                                                                                                                                                                            code 1

                                                                                                                                                                                                                                            Explanation 2

                                                                                                                                                                                                                                            code 2

                                                                                                                                                                                                                                            Error Conditions

                                                                                                                                                                                                                                            Advanced Notes

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                                                                                                                                                                                                                                            • FR: p̂₁

                                                                                                                                                                                                                                            p̂₁

                                                                                                                                                                                                                                            Overview

                                                                                                                                                                                                                                            Syntax

                                                                                                                                                                                                                                            p̂₁

                                                                                                                                                                                                                                            Description

                                                                                                                                                                                                                                            Examples

                                                                                                                                                                                                                                            Explanation 1

                                                                                                                                                                                                                                            code 1

                                                                                                                                                                                                                                            Explanation 2

                                                                                                                                                                                                                                            code 2

                                                                                                                                                                                                                                            Error Conditions

                                                                                                                                                                                                                                            Advanced Notes

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                                                                                                                                                                                                                                            • FR: p̂₂

                                                                                                                                                                                                                                            p̂₂

                                                                                                                                                                                                                                            Overview

                                                                                                                                                                                                                                            Syntax

                                                                                                                                                                                                                                            p̂₂

                                                                                                                                                                                                                                            Description

                                                                                                                                                                                                                                            Examples

                                                                                                                                                                                                                                            Explanation 1

                                                                                                                                                                                                                                            code 1

                                                                                                                                                                                                                                            Explanation 2

                                                                                                                                                                                                                                            code 2

                                                                                                                                                                                                                                            Error Conditions

                                                                                                                                                                                                                                            Advanced Notes

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                                                                                                                                                                                                                                            • FR: q

                                                                                                                                                                                                                                            q

                                                                                                                                                                                                                                            Overview

                                                                                                                                                                                                                                            Availability: Token available everywhere.

                                                                                                                                                                                                                                            Syntax

                                                                                                                                                                                                                                            q

                                                                                                                                                                                                                                            Description

                                                                                                                                                                                                                                            Examples

                                                                                                                                                                                                                                            Explanation 1

                                                                                                                                                                                                                                            code 1

                                                                                                                                                                                                                                            Explanation 2

                                                                                                                                                                                                                                            code 2

                                                                                                                                                                                                                                            Error Conditions

                                                                                                                                                                                                                                            Advanced Notes

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                                                                                                                                                                                                                                            • FR: r

                                                                                                                                                                                                                                            r

                                                                                                                                                                                                                                            Overview

                                                                                                                                                                                                                                            Availability: Token available everywhere.

                                                                                                                                                                                                                                            Syntax

                                                                                                                                                                                                                                            r

                                                                                                                                                                                                                                            Description

                                                                                                                                                                                                                                            Examples

                                                                                                                                                                                                                                            Explanation 1

                                                                                                                                                                                                                                            code 1

                                                                                                                                                                                                                                            Explanation 2

                                                                                                                                                                                                                                            code 2

                                                                                                                                                                                                                                            Error Conditions

                                                                                                                                                                                                                                            Advanced Notes

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                                                                                                                                                                                                                                            • FR: NbrAléat

                                                                                                                                                                                                                                            rand

                                                                                                                                                                                                                                            Overview

                                                                                                                                                                                                                                            Returns a random number between 0 and 1 for a specified number of trials numtrials.

                                                                                                                                                                                                                                            Availability: Token available everywhere.

                                                                                                                                                                                                                                            Syntax

                                                                                                                                                                                                                                            rand[(numtrials)]

                                                                                                                                                                                                                                            Arguments

                                                                                                                                                                                                                                            NameTypeOptional
                                                                                                                                                                                                                                            numtrialsYes

                                                                                                                                                                                                                                            Location

                                                                                                                                                                                                                                            math, PRB, 1:rand

                                                                                                                                                                                                                                            Description

                                                                                                                                                                                                                                            rand generates a uniformly-distributed pseudorandom number (this page and others will sometimes drop the pseudo- prefix for simplicity) between 0 and 1. rand(n) generates a list of n uniformly-distributed pseudorandom numbers between 0 and 1. seed→rand seeds (initializes) the built-in pseudorandom number generator. The factory default seed is 0.

                                                                                                                                                                                                                                            L'Ecuyer's algorithm is used by TI calculators to generate pseudorandom numbers.

                                                                                                                                                                                                                                            0→rand
     0
rand
     .9435974025
rand(2)
     {.908318861 .1466878292}

                                                                                                                                                                                                                                            Note: Due to specifics of the random number generating algorithm, the smallest number possible to generate is slightly greater than 0. The largest number possible is actually 1, but since returning a result of 1 would mess up the output of randBin( and randNorm(, the actual value returned in such cases is 1-1.11e-12 (which is displayed as 1, and is "equal" to 1 for the purposes of the = command). To see 1, store 196164532 to rand and then run the random number generator. If you instead try to store the “random” value directly to a list element, the value as viewed inside of the list editor will be 1-1.11e-12, displayed as 0.99999999999889.

                                                                                                                                                                                                                                            Advanced Uses

                                                                                                                                                                                                                                            To seed the random number generator, store a positive integer to rand (the command will ignore any decimals, and the sign of the number). Seeding the random number generator has several uses:

                                                                                                                                                                                                                                            When writing a program that uses random numbers, you may add a 0→rand instruction to the beginning of the program — this ensures that the program's actions will be repeatable, making it easier to fix a bug. Just don't forget to take it out when you've finished writing the program.

                                                                                                                                                                                                                                            Seeding the random number generator can also be used to create fairly secure (unbreakable without a computer) encryption. Pick a secret key, and store it to rand as a seed. Then, perform some randomly generated manipulations on the data you want to encode — for example, shifting each character of a string by a random number. Decoding the message is simple: store the secret key to rand and perform the opposite of those random operations. However, this is impossible to do if you don't know the secret key.

                                                                                                                                                                                                                                            When seeding the random number generator, as above, you make every random number generated afterwards predictable. This may be problematic even if your program doesn't need random numbers, because other programs might. To prevent this, use the following code to save and restore "randomness":

                                                                                                                                                                                                                                            :randInt(1,E9)→N

                                                                                                                                                                                                                                            (code that involves seeding the RNG here)

                                                                                                                                                                                                                                            :N→rand

                                                                                                                                                                                                                                            Since generating random numbers is a fairly time-consuming operation, the rand(# of numbers) syntax is very effective at generating a delay in your program — just add the line:

                                                                                                                                                                                                                                            :rand(N)

                                                                                                                                                                                                                                            The bigger N is, the longer the delay. In relation to the commonly used For( loop delay, the number used in the rand( delay is about 10 times smaller. However, this code has a side effect of storing a list of random numbers to Ans, which may be undesirable. To avoid this, use this somewhat longer line:

                                                                                                                                                                                                                                            :If dim(rand(N))

                                                                                                                                                                                                                                            Despite the presence of an If statement, you don't have to worry about the next line being skipped, since dim(rand(N)) will always be true.

                                                                                                                                                                                                                                            Error Conditions

                                                                                                                                                                                                                                            • ERR:DOMAIN if you try to generate a list of random numbers and the list length isn't an integer 1-999.

                                                                                                                                                                                                                                            Source: parts of this page were written by the following TI|BD contributors: builderboy, burr, CloudVariable, DarkerLine, Deoxal, GoVegan, MrTanookiMario, thornahawk, Timothy Foster, ztrumpet.

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                                                                                                                                                                                                                                            • FR: BinAléat(

                                                                                                                                                                                                                                            randBin(

                                                                                                                                                                                                                                            Overview

                                                                                                                                                                                                                                            Generates and displays a random real number from a specified Binomial distribution.

                                                                                                                                                                                                                                            Availability: Token available everywhere.

                                                                                                                                                                                                                                            Syntax

                                                                                                                                                                                                                                            randBin(numtrials,prob[,numsimulations])

                                                                                                                                                                                                                                            Arguments

                                                                                                                                                                                                                                            NameTypeOptional
                                                                                                                                                                                                                                            numtrials
                                                                                                                                                                                                                                            prob
                                                                                                                                                                                                                                            numsimulationsYes

                                                                                                                                                                                                                                            Location

                                                                                                                                                                                                                                            math, PRB, 7:randBin(

                                                                                                                                                                                                                                            Description

                                                                                                                                                                                                                                            randBin(n,p) generates a pseudorandom integer between 0 and n inclusive according to the binomial distribution B(n,p) - that is, n trials of an event with probability of success p are performed, and the number of successes is returned. randBin(n,p,simulations) performs the above calculation simulations times, and returns a list of the results. The expected (average) result is n*p.

                                                                                                                                                                                                                                            n should be an integer greater than or equal to 1, while p should be a real number between 0 and 1 inclusive.

                                                                                                                                                                                                                                            seed→rand affects the output of randBin(

                                                                                                                                                                                                                                            0→rand
     0
randBin(5,1/2
     2
randBin(5,1/2,10
     {3 3 2 4 3 2 2 2 4 3}

                                                                                                                                                                                                                                            Formulas

                                                                                                                                                                                                                                            The value of randBin( for a given seed can be expressed in terms of rand:

                                                                                                                                                                                                                                            randBin(N,P)=sum(P>rand(N

                                                                                                                                                                                                                                            This is identical to the output of randBin( in the sense that for the same seed, both expressions will generate the same random numbers.

                                                                                                                                                                                                                                            Error Conditions

                                                                                                                                                                                                                                            • ERR:DOMAIN is triggered if the probability is not on the interval from 0 to 1.

                                                                                                                                                                                                                                            Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, MrTanookiMario, nap386, Timothy Foster, Xeda Elnara.

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                                                                                                                                                                                                                                            • FR: entAléat(

                                                                                                                                                                                                                                            randInt(

                                                                                                                                                                                                                                            Overview

                                                                                                                                                                                                                                            Generates and displays a random integer within a range specified by lower and upper integer bounds for a specified number of trials numtrials.

                                                                                                                                                                                                                                            Availability: Token available everywhere.

                                                                                                                                                                                                                                            Syntax

                                                                                                                                                                                                                                            randInt( lower,upper [,numtrials])

                                                                                                                                                                                                                                            Arguments

                                                                                                                                                                                                                                            NameTypeOptional
                                                                                                                                                                                                                                            lower
                                                                                                                                                                                                                                            upper
                                                                                                                                                                                                                                            numtrialsYes

                                                                                                                                                                                                                                            Location

                                                                                                                                                                                                                                            math, PRB, 5:randInt(

                                                                                                                                                                                                                                            Description

                                                                                                                                                                                                                                            randInt(min,max) generates a uniformly-distributed pseudorandom integer between min and max inclusive. randInt(min,max,n) generates a list of n uniformly-distributed pseudorandom integers between min and max.

                                                                                                                                                                                                                                            seed→rand affects the output of randInt(.

                                                                                                                                                                                                                                            0→rand
     0
randInt(1,10)
     10
randInt(1,10,5)
     {10 2 6 5 8}

                                                                                                                                                                                                                                            Optimization

                                                                                                                                                                                                                                            When the lower bound of randInt( is 0, you can replace it with int(#rand to save space. For example:

                                                                                                                                                                                                                                            :randInt(0,12
can be
:int(13rand

                                                                                                                                                                                                                                            Similarly, if you don't want to include zero in the range, you can use a variant of 1-#int(#rand:

                                                                                                                                                                                                                                            :1-2int(2rand

                                                                                                                                                                                                                                            In this particular example, the only values that you will ever get are -1 or 1.

                                                                                                                                                                                                                                            Formulas

                                                                                                                                                                                                                                            The value of randInt( for a given seed can be expressed in terms of rand:

                                                                                                                                                                                                                                            randInt(A,B)=

                                                                                                                                                                                                                                            • when A<B, A+int((B-A+1)rand
                                                                                                                                                                                                                                            • otherwise, B+int((A-B+1)rand

                                                                                                                                                                                                                                            This is identical to the output of randInt( in the sense that for the same seed, both expressions will generate the same random numbers.

                                                                                                                                                                                                                                            Error Conditions

                                                                                                                                                                                                                                            • ERR:DOMAIN is thrown if any of the arguments is a decimal.
                                                                                                                                                                                                                                            • ERR: DATA TYPE is given if you use imaginary numbers like 6i or something like Matrices or Lists. This error is used instead of ERR:DOMAIN for "i".

                                                                                                                                                                                                                                            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, nap386, Xeda Elnara.

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                                                                                                                                                                                                                                              • FR: randIntNoRep(

                                                                                                                                                                                                                                              randIntNoRep(

                                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                                              Returns a random ordered list of integers from a lower integer to an upper integer which may include the lower integer and upper integer. If the optional argument numelements is specified, the first numelements are listed. The first numelements term in the list of random integers are displayed.

                                                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                                              randIntNoRep(lowerint,upperint [,numelements])

                                                                                                                                                                                                                                              Arguments

                                                                                                                                                                                                                                              NameTypeOptional
                                                                                                                                                                                                                                              lowerint
                                                                                                                                                                                                                                              upperint
                                                                                                                                                                                                                                              numelementsYes

                                                                                                                                                                                                                                              Location

                                                                                                                                                                                                                                              math, PRB, 8:randIntNoRep(

                                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                                              randIntNoRep( is used when you need to create a list of numbers in random order in which no integer is repeated. This command is useful for things such as simulating decks of cards. Commonly, before this command was introduced, the following code would shuffle a deck:

                                                                                                                                                                                                                                              rand(52→L₂
seq(X,X,0,51→L₁
SortA(L₂,L₁

                                                                                                                                                                                                                                              This result can now be achieved with the following code:

                                                                                                                                                                                                                                              randIntNoRep(0,51→L₁

                                                                                                                                                                                                                                              Advanced Uses

                                                                                                                                                                                                                                              seed→rand affects the output of randIntNoRep(

                                                                                                                                                                                                                                              What this does is quite simple. When you seed rand, then the next time you use randIntNoRep(, you will get a result that will be fairly random, but the same on all calculators. This allows several things to be possible, including password protection and encryption. For example, if you were to use the following code, you could encrypt and decrypt messages only if you use the same encryption value. In this example, Str1 contains the message:

                                                                                                                                                                                                                                              Decode:

                                                                                                                                                                                                                                              "ABCDEFGHIJKLMNOPQRSTUVWXYZ .!,0123456789→Str2
Input "CODE:",A
A→rand
randIntNoRep(1,length(Str2→L1
length(Str1→B
".
For(A,1,B
Ans+sub(Str2,sum(cumSum(L1=inString(Str2,sub(Str1,A,1)))),1
End
sub(Ans,2,B

                                                                                                                                                                                                                                              Encode:

                                                                                                                                                                                                                                              "ABCDEFGHIJKLMNOPQRSTUVWXYZ .!,0123456789→Str2
Input "CODE:",A
A→rand
length(Str2→C
randIntNoRep(1,Ans→L1
length(Str1→B
".
For(A,1,B
Ans+sub(Str2,L1(C+1-inString(Str2,sub(Str1,A,1))),1
End
sub(Ans,2,B

                                                                                                                                                                                                                                              The output strings are in Ans

                                                                                                                                                                                                                                              Source: parts of this page were written by the following TI|BD contributors: burr, MrTanookiMario, Timothy Foster, Xeda Elnara.

                                                                                                                                                                                                                                              History

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                                                                                                                                                                                                                                              • FR: MatAléat(

                                                                                                                                                                                                                                              randM(

                                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                                              Returns a random matrix of rows × columns.
                                                                                                                                                                                                                                              Max rows x columns = 400 matrix elements.

                                                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                                              randM(rows,columns)

                                                                                                                                                                                                                                              Arguments

                                                                                                                                                                                                                                              NameTypeOptional
                                                                                                                                                                                                                                              rowsinteger
                                                                                                                                                                                                                                              columnsinteger

                                                                                                                                                                                                                                              Location

                                                                                                                                                                                                                                              2nd, matrix, MATH, 6:randM(

                                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                                              randM(M, N) generates an M by N matrix whose entries are pseudorandom integers between -9 and 9 inclusive.

                                                                                                                                                                                                                                              seed→rand affects the output of randM(.

                                                                                                                                                                                                                                              0→rand
    0
randM(3,3)
    [[9  -3 -9]
     [4  -2 0 ]
     [-7 8  8 ]]

                                                                                                                                                                                                                                              If you actually cared about the bounds of the random numbers, this command would not be very useful, since it's hard to manipulate the matrix to yield uniformly spread random numbers in a different range.

                                                                                                                                                                                                                                              Formulas

                                                                                                                                                                                                                                              The entries of randM( are actually the outputs of successive calls to randInt(-9,9), filled in starting at the bottom right and moving left across each row from the last row to the first.

                                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                                              • ERR:INVALID DIM is thrown if the number of rows or columns of the matrix isn't an integer 1-99.

                                                                                                                                                                                                                                              Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, MrTanookiMario.

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                                                                                                                                                                                                                                              • FR: normAléat(

                                                                                                                                                                                                                                              randNorm(

                                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                                              Generates and displays a random real number from a specified Normal distribution specified by μ and σ for a specified number of trials numtrials.

                                                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                                              randNorm(μ,σ[,numtrials])

                                                                                                                                                                                                                                              Arguments

                                                                                                                                                                                                                                              NameTypeOptional
                                                                                                                                                                                                                                              μ
                                                                                                                                                                                                                                              σ
                                                                                                                                                                                                                                              numtrials

                                                                                                                                                                                                                                              Location

                                                                                                                                                                                                                                              math, PRB, 6:randNorm(

                                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                                              randNorm(µ,σ) generates a normally-distributed pseudorandom number with mean µ and standard deviation σ. The result returned will most probably be within the range µ±3_σ_. randNorm(µ,σ,n) generates a list of n normally-distributed pseudorandom numbers with mean µ and standard deviation σ.

                                                                                                                                                                                                                                              seed→rand affects the output of randNorm(.

                                                                                                                                                                                                                                              0→rand
     0
randNorm(0,1)
     -1.585709623
randNorm(0,1,3)
     {-1.330473604 1.05074514 -.0368606663}

                                                                                                                                                                                                                                              Although a theoretical normally distributed variable could take on any real value, numbers on a calculator have a limited precision, which leads to a maximum range of approximately µ±7.02_σ_ for values of randNorm(.

                                                                                                                                                                                                                                              Optimization

                                                                                                                                                                                                                                              When the mean is 0 and the standard deviation 1, invNorm(rand) and invNorm(rand(N)) save space over randNorm(0,1) and randNorm(0,1,N) respectively.

                                                                                                                                                                                                                                              Formulas

                                                                                                                                                                                                                                              The value of randNorm( for a given seed can be expressed in terms of rand:

                                                                                                                                                                                                                                              randNorm(µ,σ)=µ-σinvNorm(rand

                                                                                                                                                                                                                                              This is identical to the output of randNorm( in the sense that for the same seed, both expressions will generate the same random numbers.

                                                                                                                                                                                                                                              The following formula can be used to get a target interval where A and B are two real intervals.

                                                                                                                                                                                                                                              µ=(A+B)/2
σ=(-A+B)/6

                                                                                                                                                                                                                                              Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, MrTanookiMario, Silver Phantom, Timothy Foster, Weregoose.

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                                                                                                                                                                                                                                              TI-83 0.01013 Added
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                                                                                                                                                                                                                                              • FR: r𝑒^θ𝑖

                                                                                                                                                                                                                                              r𝑒^θ𝑖

                                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                                              Sets the mode to polar complex number mode (re``^θi).

                                                                                                                                                                                                                                              Availability: Token only available from within the Basic editor.

                                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                                              re^θi

                                                                                                                                                                                                                                              Arguments

                                                                                                                                                                                                                                              NameTypeOptional
                                                                                                                                                                                                                                              e
                                                                                                                                                                                                                                              θ
                                                                                                                                                                                                                                              i

                                                                                                                                                                                                                                              Location

                                                                                                                                                                                                                                              mode

                                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                                              The re^θ𝑖 command puts the calculator into polar complex number mode. This means that:

                                                                                                                                                                                                                                              • Taking square roots of negative numbers, and similar operations, no longer returns an error.
                                                                                                                                                                                                                                              • Complex results are displayed in the form re^(θ𝑖) (hence the name of the command)

                                                                                                                                                                                                                                              The mathematical underpinning of this complex number format is due to the fact that if (x,y) is a point in the plane using the normal coordinates, it can also be represented using coordinates (r,θ) where r is the distance from the origin and θ is the angle that the line segment to the point from the origin makes to the positive x-axis (see Polar and PolarGC for more information on polar coordinates and graphing). What does this have to do with complex numbers? Simple: if x+y𝑖 is a complex number in normal (rectangular) form, and re^(θ𝑖) is the same number in polar form, then (x,y) and (r,θ) represent the same point in the plane.

                                                                                                                                                                                                                                              Of course, that has a lot to do with how you define imaginary exponents, which isn't that obvious.

                                                                                                                                                                                                                                              An equivalent form to polar form is the form r[cos(θ)+𝑖sin(θ)].

                                                                                                                                                                                                                                              Unfortunately, the calculator seems to have some confusion about the use of degree and radian angle measures for θ in this mode (the answer is: you can only use radians — degrees make no sense with complex exponents). When calculating a value re^(θ𝑖) by using the e^( command and plugging in numbers, the calculator assumes θ is a radian angle, whether it's in Degree or Radian mode. However, when displaying a complex number as re^(θ𝑖), the calculator will display θ in radian or degree measure, whichever is enabled. This may lead to such pathological output as:

                                                                                                                                                                                                                                              Degree:r𝑒^θ𝑖
        Done
𝑒^(πi)
        1𝑒^(180i)
Ans=𝑒^(180𝑖)
        0 (false)

                                                                                                                                                                                                                                              It's recommended, then, to use Radian mode whenever you're in re^θ𝑖 mode.

                                                                                                                                                                                                                                              Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan.

                                                                                                                                                                                                                                              History

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                                                                                                                                                                                                                                              • FR: reel(

                                                                                                                                                                                                                                              real(

                                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                                              Returns the real part of a complex number or list of complex numbers.

                                                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                                              real(value)

                                                                                                                                                                                                                                              Arguments

                                                                                                                                                                                                                                              NameTypeOptional
                                                                                                                                                                                                                                              valuecomplex|complex[]

                                                                                                                                                                                                                                              Location

                                                                                                                                                                                                                                              math, CPLX, 2:real(

                                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                                              real(z) returns the real part of the complex number z. If z is represented as x+i_y_ where x and y are both real, real(z) returns x. Also works on a list of complex numbers.

                                                                                                                                                                                                                                              real(3+4i)
     3

                                                                                                                                                                                                                                              Advanced Uses

                                                                                                                                                                                                                                              The real( command is expanded by several assembly libraries (such as xLIB and Omnicalc) to call their own routines. If xLib is installed, then real( will no longer work as intended even in programs that want to use it for its intended purpose.

                                                                                                                                                                                                                                              If you actually want to take the real part of a complex number, and want the program to work with one of these assembly libraries, you could use the imag( command instead - real(Z) is equivalent to imag(Z𝑖). Alternatively, you could tell people using your program to uninstall xLIB or Omnicalc first.

                                                                                                                                                                                                                                              If a program you downloaded has an error and 2:Goto takes you to a line with real( and a bunch of arguments, this is probably because the program uses Omnicalc or xLIB which you don't have installed.

                                                                                                                                                                                                                                              See Also

                                                                                                                                                                                                                                              Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

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                                                                                                                                                                                                                                              • FR: Gauss(

                                                                                                                                                                                                                                              ref(

                                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                                              Returns the row-echelon form of a matrix.

                                                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                                              ref(matrix)

                                                                                                                                                                                                                                              Arguments

                                                                                                                                                                                                                                              NameTypeOptional
                                                                                                                                                                                                                                              matrixmatrix

                                                                                                                                                                                                                                              Location

                                                                                                                                                                                                                                              2nd, matrix, MATH, A:ref(

                                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                                              Given a matrix with at least as many columns as it has rows, the ref( command uses a technique called Gaussian elimination to put the matrix into row-echelon form.

                                                                                                                                                                                                                                              This means that the leftmost N columns (if the matrix has N rows) of the matrix are upper triangular - all entries below the main diagonal are zero. What's more, every entry on the main diagonal is either 0 or 1.

                                                                                                                                                                                                                                              [[1,2,5,0][2,2,1,2][3,4,6,2]]
    [[1 2 5 0]
     [2 2 1 2]
     [3 4 6 2]
ref(Ans)►Frac
    [[1 4/3 2   2/3]
     [0 1   9/2 -1 ]
     [0 0   0   0  ]]

                                                                                                                                                                                                                                              Advanced Uses

                                                                                                                                                                                                                                              In theory, a system of linear equations in N variables can be solved using the ref( command - an equation of the form \(a_1x_1+\dots + a_nx_n = b\) becomes a row \(a_1, \dots, a_n, b\), and is put into the matrix. If there is a sufficient number of conditions, the last row of the reduced matrix will give you the value of the last variable, and back-substitution will give you the others.

                                                                                                                                                                                                                                              In practice, it's easier to use rref( instead for the same purpose.

                                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                                              Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, kg583, Timothy Foster.

                                                                                                                                                                                                                                              History

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                                                                                                                                                                                                                                                • FR: remainder(

                                                                                                                                                                                                                                                remainder(

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Reports the remainder as a whole number from a division of two whole numbers where the divisor is not zero.

                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                remainder(dividend, divisor)

                                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                                dividend
                                                                                                                                                                                                                                                divisor

                                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                                math, NUM, 0:remainder(

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Reports the remainder as a whole number from a division of two lists where the divisor is not zero.

                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                remainder(list, divisor)

                                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                                listlist
                                                                                                                                                                                                                                                divisor

                                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                                math, NUM, 0:remainder(

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Reports the remainder as a whole number from a division of two whole numbers where the divisor is a list.

                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                remainder(dividend, list)

                                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                                dividend
                                                                                                                                                                                                                                                listlist

                                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                                math, NUM, 0:remainder(

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Reports the remainder as a whole number from a division of two lists.

                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                remainder(list, list)

                                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                                listlist
                                                                                                                                                                                                                                                listlist

                                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                                math, NUM, 0:remainder(

                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                The remainder( function divides the first number given by the second number, and returns the remainder similar to the modulus. This command is only available if you have the TI-84+/SE and the new 2.53 MP operating system on your calculator. This command can be used both on the Home screen and when programming.

                                                                                                                                                                                                                                                See the code segment below for an example:

                                                                                                                                                                                                                                                remainder(30,7)
               2

                                                                                                                                                                                                                                                This returns a value of 2 because 30 divided by 7 has a remainder of 2.

                                                                                                                                                                                                                                                The first input must be an integer in the range 0 to 1012 and the second must be an integer in the range 1 to 1012 (since division by zero is not allowed).

                                                                                                                                                                                                                                                Compatibility

                                                                                                                                                                                                                                                As said earlier, this command only works on a TI-84+ Silver Edition with the 2.53 MP OS, so this will not work on earlier OSes. To avoid non-portability, use the following code.

                                                                                                                                                                                                                                                BfPart(A/B

instead of

remainder(A,B

                                                                                                                                                                                                                                                fPart( is a command that works in more OSes and more models. They also are the same size (5 bytes), as long as B is one byte.

                                                                                                                                                                                                                                                There is one difference: remainder( is guaranteed to return the correct answer for inputs in its accepted domain, and if you enter numbers that are too large, it will throw an error. The method with fPart(, on the other hand, will work for numbers of any size that does not actually cause an overflow - but when the numbers get too large, it will give the wrong answer. Compare:

                                                                                                                                                                                                                                                remainder(18!,19
           Error
19fPart(18!/19
               0

                                                                                                                                                                                                                                                Here, the remainder( command fails because the input is out of range.. The fPart( method returns an answer, but it is wrong: 18! is not divisible by 19, because 18! is the product of the integers 1 through 18, and none of them are divisible by the prime number 19. When using fPart( as a substitute for remainder(, make sure that the inputs are within the proper range.

                                                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                                                • ERR:DIVIDE BY 0 occurs if the divisor is zero.
                                                                                                                                                                                                                                                • ERR:DOMAIN occurs if the divisor or dividend is out of range: only integers between 0 and 1E12 are allowed.
                                                                                                                                                                                                                                                • ERR:SYNTAX occurs if the divisor or dividend is a symbol, or character or non-real number
                                                                                                                                                                                                                                                • ERR:DATA TYPE occurs if the divisor or dividend is not a number, (i.e. text)

                                                                                                                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: 12Me21, DarkerLine, Deflect, kg583, Kydapoot, Michael2_3B, Silver Phantom, sonic65101, Timothy Foster, tyler999.

                                                                                                                                                                                                                                                History

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                                                                                                                                                                                                                                                • FR: ρ

                                                                                                                                                                                                                                                ρ

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                ρ

                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                Examples

                                                                                                                                                                                                                                                Explanation 1

                                                                                                                                                                                                                                                code 1

                                                                                                                                                                                                                                                Explanation 2

                                                                                                                                                                                                                                                code 2

                                                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                                                Advanced Notes

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                                                                                                                                                                                                                                                • FR: arrondi(

                                                                                                                                                                                                                                                round(

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Returns a number, expression, list, or matrix rounded to #decimals ( 9).

                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                round(value[,#decimals])

                                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                                value
                                                                                                                                                                                                                                                #decimalsYes

                                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                                math, NUM, 2:round(

                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                round(value[,#decimals]) returns value rounded to #decimals decimal places. #decimals must be < 10. The default value for #decimals is 9. Also works on complex numbers, lists and matrices.

                                                                                                                                                                                                                                                round(5.45,0)
     5
round(5.65,0)
     6
round(‾5.65,0)
     ‾6
round(π)-π
     4.102e-10
round(π,4)
     3.1416
round({1.5,2.4,3.8},0)
     {2,2,4}
round([[1.8,3.5,120.3][3,‾1,0.2]],0)
     [[2  4   120]
     [3  ‾1  0   ]]

                                                                                                                                                                                                                                                Advanced Uses

                                                                                                                                                                                                                                                Sometimes, round-off error will cause the result of an expression to be slightly off of the correct integer value — for example, a result may be 5.0000000013 instead of 5. If the error is small enough, it will not even be visible if you recall the variable on the home screen. However, this is enough to cause a ERR:DOMAIN error with commands such as sub( and Output(, which require their arguments to be integers.

                                                                                                                                                                                                                                                The easiest way to fix this problem is by wrapping the different arguments in a round( instruction. For example, instead of:

                                                                                                                                                                                                                                                Output(X,1,">")

                                                                                                                                                                                                                                                Try:

                                                                                                                                                                                                                                                Output(round(X,0),1,">")

                                                                                                                                                                                                                                                The int( command will not work here because the round-off error may be negative, such as 4.9999999986 instead of 5, in which case the number will be rounded down to 4.

                                                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                                                • ERR:DOMAIN if the number of places to round to is not an integer 0 through 9.

                                                                                                                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: burr, CloudVariable, DarkerLine, GoVegan.

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                                                                                                                                                                                                                                                • FR: *ligne(

                                                                                                                                                                                                                                                *row(

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Returns a matrix with row of matrix multiplied by value and stored in row.

                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                *row(value,matrix,row)

                                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                                *
                                                                                                                                                                                                                                                value
                                                                                                                                                                                                                                                matrixmatrix
                                                                                                                                                                                                                                                row

                                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                                2nd, matrix, MATH, E:row(

                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                Examples

                                                                                                                                                                                                                                                Explanation 1

                                                                                                                                                                                                                                                code 1

                                                                                                                                                                                                                                                Explanation 2

                                                                                                                                                                                                                                                code 2

                                                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                                                Advanced Notes

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                                                                                                                                                                                                                                                • FR: ligne+(

                                                                                                                                                                                                                                                row+(

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Returns a matrix with rowA of matrix added to rowB and stored in rowB.

                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                row+(matrix,rowA,rowB)

                                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                                matrixmatrix
                                                                                                                                                                                                                                                rowA
                                                                                                                                                                                                                                                rowB

                                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                                2nd, matrix, MATH, D:row+(

                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                The row+( command adds one row of a matrix to the second, and returns the result. It is an elementary row operation used in Gaussian Elimination.

                                                                                                                                                                                                                                                [[1,2][3,4]]
    [[1 2]
     [3 4]]
row+(Ans,1,2)
    [[1 2]
     [4 6]]

                                                                                                                                                                                                                                                Advanced Uses

                                                                                                                                                                                                                                                You can add columns instead of rows with the aid of the T (transpose) command.

                                                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                                                • ERR:INVALID DIM is thrown if one of the row arguments isn't a valid row (larger than the matrix size, or otherwise bad)

                                                                                                                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, jnesselr, Weregoose.

                                                                                                                                                                                                                                                History

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                                                                                                                                                                                                                                                • FR: *ligne+(

                                                                                                                                                                                                                                                *row+(

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Returns a matrix with rowA of matrix multiplied by value, added to rowB, and stored in rowB.

                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                *row+(value,matrix,rowA,rowB)

                                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                                *
                                                                                                                                                                                                                                                value
                                                                                                                                                                                                                                                matrixmatrix
                                                                                                                                                                                                                                                rowA
                                                                                                                                                                                                                                                rowB

                                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                                2nd, matrix, MATH, F:row+(

                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                Examples

                                                                                                                                                                                                                                                Explanation 1

                                                                                                                                                                                                                                                code 1

                                                                                                                                                                                                                                                Explanation 2

                                                                                                                                                                                                                                                code 2

                                                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                                                Advanced Notes

                                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                                Calculator OS Version Description
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                                                                                                                                                                                                                                                • FR: permutLigne(

                                                                                                                                                                                                                                                rowSwap(

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Returns a matrix with rowA of matrix swapped with rowB.

                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                rowSwap(matrix,rowA,rowB)

                                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                                matrixmatrix
                                                                                                                                                                                                                                                rowA
                                                                                                                                                                                                                                                rowB

                                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                                2nd, matrix, MATH, C:rowSwap(

                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                The rowSwap( command swaps two rows of a matrix and returns the result. It is an elementary row operation used in Gaussian Elimination.

                                                                                                                                                                                                                                                [[1,2][3,4]]
    [[1 2]
     [3 4]]
rowSwap(Ans,1,2)
    [[3 4]
     [1 2]]

                                                                                                                                                                                                                                                Advanced Uses

                                                                                                                                                                                                                                                You can swap columns instead of rows with the aid of the T (transpose) command.

                                                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                                                • ERR:INVALID DIM is thrown if one of the row arguments isn't a valid row (larger than the matrix size, or otherwise bad)

                                                                                                                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan.

                                                                                                                                                                                                                                                History

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                                                                                                                                                                                                                                                • FR: Gauss-Jordan(

                                                                                                                                                                                                                                                rref(

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Returns the reduced row-echelon form of a matrix.

                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                rref(matrix)

                                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                                matrixmatrix

                                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                                2nd, matrix, MATH, B:rref(

                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                Given a matrix with at least as many columns as rows, the rref( command puts a matrix into reduced row-echelon form using Gaussian elimination.

                                                                                                                                                                                                                                                This means that as many columns of the result as possible will contain a pivot entry of 1, with all entries in the same column, or to the left of the pivot, being 0.

                                                                                                                                                                                                                                                [[1,2,5,0][2,2,1,2][3,4,6,2]]
    [[1 2 5 0]
     [2 2 1 2]
     [3 4 7 3]]
rref(Ans)
    [[1 0 0 6   ]
     [0 1 0 -5.5]
     [0 0 1 1   ]]

                                                                                                                                                                                                                                                Advanced Uses

                                                                                                                                                                                                                                                The rref( command can be used to solve a system of linear equations. First, take each equation, in the standard form of \(a_1x_1+\dots + a_nx_n = b\), and put the coefficients into a row of the matrix.

                                                                                                                                                                                                                                                Then, use rref( on the matrix. There are three possibilities now:

                                                                                                                                                                                                                                                • If the system is solvable, the left part of the result will look like the identity matrix. Then, the final column of the matrix will contain the values of the variables.
                                                                                                                                                                                                                                                • If the system is inconsistent, and has no solution, then it will end with rows that are all 0 except for the last entry.
                                                                                                                                                                                                                                                • If the system has infinitely many solutions, it will end with rows that are all 0, including the last entry.

                                                                                                                                                                                                                                                This process can be done by a program fairly easily. However, unless you're certain that the system will always have a unique solution, you should check that the result is in the correct form, before taking the values in the last column as your solution. The Matr►list( command can be used to store this column to a list.

                                                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: Battlesquid, DarkerLine, GoVegan, kg583.

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                                                                                                                                                                                                                                                • FR: r²

                                                                                                                                                                                                                                                r²

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                r²

                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                Examples

                                                                                                                                                                                                                                                Explanation 1

                                                                                                                                                                                                                                                code 1

                                                                                                                                                                                                                                                Explanation 2

                                                                                                                                                                                                                                                code 2

                                                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                                                Advanced Notes

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                                                                                                                                                                                                                                                • FR: r₁

                                                                                                                                                                                                                                                r₁

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                r₁

                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                Examples

                                                                                                                                                                                                                                                Explanation 1

                                                                                                                                                                                                                                                code 1

                                                                                                                                                                                                                                                Explanation 2

                                                                                                                                                                                                                                                code 2

                                                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                                                Advanced Notes

                                                                                                                                                                                                                                                History

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                                                                                                                                                                                                                                                • FR: r₂

                                                                                                                                                                                                                                                r₂

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                r₂

                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                Examples

                                                                                                                                                                                                                                                Explanation 1

                                                                                                                                                                                                                                                code 1

                                                                                                                                                                                                                                                Explanation 2

                                                                                                                                                                                                                                                code 2

                                                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                                                Advanced Notes

                                                                                                                                                                                                                                                History

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                                                                                                                                                                                                                                                • FR: r₃

                                                                                                                                                                                                                                                r₃

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                r₃

                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                Examples

                                                                                                                                                                                                                                                Explanation 1

                                                                                                                                                                                                                                                code 1

                                                                                                                                                                                                                                                Explanation 2

                                                                                                                                                                                                                                                code 2

                                                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                                                Advanced Notes

                                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                                Calculator OS Version Description
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                                                                                                                                                                                                                                                • FR: r₄

                                                                                                                                                                                                                                                r₄

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                r₄

                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                Examples

                                                                                                                                                                                                                                                Explanation 1

                                                                                                                                                                                                                                                code 1

                                                                                                                                                                                                                                                Explanation 2

                                                                                                                                                                                                                                                code 2

                                                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                                                Advanced Notes

                                                                                                                                                                                                                                                History

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                                                                                                                                                                                                                                                • FR: r₅

                                                                                                                                                                                                                                                r₅

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                r₅

                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                Examples

                                                                                                                                                                                                                                                Explanation 1

                                                                                                                                                                                                                                                code 1

                                                                                                                                                                                                                                                Explanation 2

                                                                                                                                                                                                                                                code 2

                                                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                                                Advanced Notes

                                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                                Calculator OS Version Description
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                                                                                                                                                                                                                                                • FR: r₆

                                                                                                                                                                                                                                                r₆

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                r₆

                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                Examples

                                                                                                                                                                                                                                                Explanation 1

                                                                                                                                                                                                                                                code 1

                                                                                                                                                                                                                                                Explanation 2

                                                                                                                                                                                                                                                code 2

                                                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                                                Advanced Notes

                                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                                Calculator OS Version Description
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                                                                                                                                                                                                                                                • FR: r𝑒^θ𝑖

                                                                                                                                                                                                                                                r𝑒^θ𝑖

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Sets the mode to polar complex number mode (re``^θi).

                                                                                                                                                                                                                                                Availability: Token only available from within the Basic editor.

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                re^θi

                                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                                e
                                                                                                                                                                                                                                                θ
                                                                                                                                                                                                                                                i

                                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                                mode

                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                The re^θ𝑖 command puts the calculator into polar complex number mode. This means that:

                                                                                                                                                                                                                                                • Taking square roots of negative numbers, and similar operations, no longer returns an error.
                                                                                                                                                                                                                                                • Complex results are displayed in the form re^(θ𝑖) (hence the name of the command)

                                                                                                                                                                                                                                                The mathematical underpinning of this complex number format is due to the fact that if (x,y) is a point in the plane using the normal coordinates, it can also be represented using coordinates (r,θ) where r is the distance from the origin and θ is the angle that the line segment to the point from the origin makes to the positive x-axis (see Polar and PolarGC for more information on polar coordinates and graphing). What does this have to do with complex numbers? Simple: if x+y𝑖 is a complex number in normal (rectangular) form, and re^(θ𝑖) is the same number in polar form, then (x,y) and (r,θ) represent the same point in the plane.

                                                                                                                                                                                                                                                Of course, that has a lot to do with how you define imaginary exponents, which isn't that obvious.

                                                                                                                                                                                                                                                An equivalent form to polar form is the form r[cos(θ)+𝑖sin(θ)].

                                                                                                                                                                                                                                                Unfortunately, the calculator seems to have some confusion about the use of degree and radian angle measures for θ in this mode (the answer is: you can only use radians — degrees make no sense with complex exponents). When calculating a value re^(θ𝑖) by using the e^( command and plugging in numbers, the calculator assumes θ is a radian angle, whether it's in Degree or Radian mode. However, when displaying a complex number as re^(θ𝑖), the calculator will display θ in radian or degree measure, whichever is enabled. This may lead to such pathological output as:

                                                                                                                                                                                                                                                Degree:r𝑒^θ𝑖
        Done
𝑒^(πi)
        1𝑒^(180i)
Ans=𝑒^(180𝑖)
        0 (false)

                                                                                                                                                                                                                                                It's recommended, then, to use Radian mode whenever you're in re^θ𝑖 mode.

                                                                                                                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan.

                                                                                                                                                                                                                                                History

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                                                                                                                                                                                                                                                • FR: s

                                                                                                                                                                                                                                                s

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                s

                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                Examples

                                                                                                                                                                                                                                                Explanation 1

                                                                                                                                                                                                                                                code 1

                                                                                                                                                                                                                                                Explanation 2

                                                                                                                                                                                                                                                code 2

                                                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                                                Advanced Notes

                                                                                                                                                                                                                                                History

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                                                                                                                                                                                                                                                • FR: suite(

                                                                                                                                                                                                                                                seq(

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Returns list created by evaluating expression with regard to variable, from begin to end by increment.

                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                seq(expression,variable,begin,end[,increment])

                                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                                expressionexpression
                                                                                                                                                                                                                                                variable
                                                                                                                                                                                                                                                begin
                                                                                                                                                                                                                                                end
                                                                                                                                                                                                                                                incrementYes

                                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                                2nd, list, OPS, 5:seq(

                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                The seq( command is very powerful, as it is (almost) the only command that can create a whole list as output. This means that you will need make use of it almost every time that you use lists. The seq( command creates a list by evaluating a formula with one variable taking on a range of several values.

                                                                                                                                                                                                                                                It is similar in this to the For( command, but unlike For(, instead of running a block of commands, it only evaluates a formula. Like the For( command, there is an optional "step" that you can use to get every 3rd, every 5th, etc. value in the range.

                                                                                                                                                                                                                                                Some sample uses of the command:

                                                                                                                                                                                                                                                :seq(I,I,3,7
                                                                                                                                                                                                                                                • evaluates the expression 'I' with I taking on the values 3..7
                                                                                                                                                                                                                                                • returns {3,4,5,6,7}
                                                                                                                                                                                                                                                :seq(AX²,X,1,7
                                                                                                                                                                                                                                                • evaluates the expression AX² with X taking on the values 1..7
                                                                                                                                                                                                                                                • returns {A,4A,9A,16A,25A,36A,49A}, depending on the value of A
                                                                                                                                                                                                                                                :seq(Y1(T),T,1,9,2
                                                                                                                                                                                                                                                • evaluates the expression Y₁(T) with T taking on every 2nd value 1..9
                                                                                                                                                                                                                                                • returns {Y₁(1),Y₁(3),Y₁(5),Y₁(7),Y₁(9)} depending on Y₁

                                                                                                                                                                                                                                                Note: the value of the variable used in the expression does not change. If X has some value stored to it, and you do a seq( command using X, X will still hold that original value. However, if X was undefined before the command, after the command, it will be defined and have a value of 0.

                                                                                                                                                                                                                                                Advanced Uses

                                                                                                                                                                                                                                                The step argument supplied can be negative. If it is, and if the starting value is greater than the ending value, then the sequence will "go backward", evaluating the expression in the opposite order. For example:

                                                                                                                                                                                                                                                :seq(I,I,1,7
    {1,2,3,4,5,6,7}
:seq(I,I,7,1,-1
    {7,6,5,4,3,2,1}

                                                                                                                                                                                                                                                You can use seq( to get a "sublist", that is, to get a list that is only a section of another list. This is pretty much the only effective way to extract a sublist. For example, to get the 2nd through 10th elements of L₁, do the following:

                                                                                                                                                                                                                                                :seq(L1(I),I,2,10

                                                                                                                                                                                                                                                While using seq(, the calculator can still interpret keypresses and store them to getKey. One possible way you can use this feature is to make a password function that asks the user to enter in the correct password before time expires.

                                                                                                                                                                                                                                                Optimizations

                                                                                                                                                                                                                                                It's faster to do an operation on an entire list, than to do the same operation inside a seq( command. For example, take the following:

                                                                                                                                                                                                                                                :seq(Y1(T),T,1,9
can be
:Y1(seq(T,T,1,9

                                                                                                                                                                                                                                                However, not all commands that work for numbers will work for lists. A notable example is getting an element from a list: L₁({1,2,3 will not return the first, second, and third elements of L₁, so you will have to put the L₁ inside the seq( command.

                                                                                                                                                                                                                                                For this same reason, you shouldn't use a seq( command when you're really performing an operation on each element of a list. For example, if L₁ has 10 elements:

                                                                                                                                                                                                                                                :seq(L1(I)²,I,1,dim(L1
can be
:L1²

                                                                                                                                                                                                                                                When generating a list of values incremented by a number i from i to a number N, seq( is not recommended as the amount of overhead on the command considerably slows the generation of the list.
                                                                                                                                                                                                                                                In cases where such a list is to be generated, it is beneficial to generate a list of a specific length, fill that list with the incrementer, and cumulatively sum each value in the list. For example, if a list of all the numbers between 1 and 500 were desired:

                                                                                                                                                                                                                                                :500→dim(L1
:Fill(1,L1
:cumSum(L1→L1

                                                                                                                                                                                                                                                This operation can be sped up even more using binomcdf( or binompdf(.

                                                                                                                                                                                                                                                A seq( command can replace a For( command, if all you're doing inside the For( command is storing to an element of a list. This will improve on both speed and size of your program. For example:

                                                                                                                                                                                                                                                :For(I,1,10
:I²→L1(I
:End
can be
:seq(I²,I,1,10→L1

                                                                                                                                                                                                                                                The seq( command itself can often be replaced with an unusual use of the binomcdf( or binompdf( commands, improving speed and sometimes size as well. However, this optimization is fairly advanced; read the pages for those commands to learn about it.

                                                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                                                • ERR:ILLEGAL NEST is thrown if you try to use seq( inside of another seq( command.
                                                                                                                                                                                                                                                • ERR:DATA TYPE occurs when any of the inputted arguments are imaginary or complex.
                                                                                                                                                                                                                                                • ERR:INVALID DIM occurs when the generated list has a dimension larger than 999.

                                                                                                                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: alexrudd, burr, DarkerLine, GoVegan, kg583, Timothy Foster, Timtech, Zenohm.

                                                                                                                                                                                                                                                History

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                                                                                                                                                                                                                                                • FR: défDate(

                                                                                                                                                                                                                                                setDate(

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Sets the date using a year, month, day format. The year must be 4 digits; month and day can be 1 or 2 digit.

                                                                                                                                                                                                                                                Comment:EFXX tokens are TI-84+ and later only

                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                setDate(year,month,day)

                                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                                year
                                                                                                                                                                                                                                                month
                                                                                                                                                                                                                                                day

                                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                                2nd, catalog, setDate(

                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                The setDate( command sets the date of the clock on the TI-84+/SE calculators. It takes three arguments: the year, the month, and the day. All three of these must be integers; in particular, year must be four digits, and month and day can be one or two digits. They represent the associated value that goes with a respective date. For example, this would set the date to January 1, 2008:

                                                                                                                                                                                                                                                :setDate(2008,1,1

                                                                                                                                                                                                                                                Once you have set the date, you can display it in three different formats on the mode screen using the setDtFmt( command: Month/Day/Year, Day/Month/Year, or Year/Month/Day. Of course, the date will only show up if the clock is on; if you need to turn the clock on, use the ClockOn command or select 'TURN CLOCK ON' , displayed in place of the clock on the mode screen.

                                                                                                                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Jonathan King, RandomProductions, Timtech.

                                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                                TI-84+ 0.01 Added
                                                                                                                                                                                                                                                Property Value
                                                                                                                                                                                                                                                Hex Value $EF03
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                                                                                                                                                                                                                                                • FR: défFmtDt(

                                                                                                                                                                                                                                                setDtFmt(

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Sets the date format.
                                                                                                                                                                                                                                                1 = M/D/Y2 = D/M/Y3 = Y/M/D

                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                setDtFmt(integer)

                                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                                integer

                                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                                2nd, catalog, setDtFmt(

                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                The setDtFmt( command sets the date format of the clock on the TI-84+/SE calculators when displaying the date on the mode screen. There are three different formats available, and you simply use the respective value (can be either a literal number or a variable) to display the desired one: 1 (M/D/Y), 2 (D/M/Y), or 3 (Y/M/D). For example, this would set the date format to Month/Day/Year:

                                                                                                                                                                                                                                                :setDtFmt(1

                                                                                                                                                                                                                                                In order for the date format to work, you need to set the date using either the setDate( command, or by going into the set clock menu (accessible by pressing ENTER on the 'SET CLOCK' message that is displayed at the bottom of the mode screen). Of course, the date will only show up if the clock is on; if you need to turn the clock on, use the ClockOn command, or scroll down to the 'TURN CLOCK ON' message that is displayed in place of the clock on the mode screen and press ENTER twice.

                                                                                                                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, RandomProductions.

                                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                                TI-84+ 0.01 Added
                                                                                                                                                                                                                                                Property Value
                                                                                                                                                                                                                                                Hex Value $EF01
                                                                                                                                                                                                                                                Categories
                                                                                                                                                                                                                                                Localizations
                                                                                                                                                                                                                                                • FR: défHeure(

                                                                                                                                                                                                                                                setTime(

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Sets the time using an hour, minute, second format. The hour must be in 24 hour format, in which 13 = 1 p.m.

                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                setTime(hour,minute, second)

                                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                                hour
                                                                                                                                                                                                                                                minute
                                                                                                                                                                                                                                                second

                                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                                2nd, catalog, setTime(

                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                The setTime( command sets the time of the clock on the TI-84+/SE calculators. It takes three arguments: the hour, the minute, and the second. The hour must be in 24 hour format — where 13 is equal to 1 P.M. — and the minute and second need to be a valid number within the appropriate range (1-60). For example, this would set the time to 12:30:30:

                                                                                                                                                                                                                                                :setTime(12,30,30

                                                                                                                                                                                                                                                Once you have set the time, you can display it in two different formats on the mode screen using the setTmFmt( command: 12 (12 hour) or 24 (24 hour). Of course, the time will only show up if the clock is on; if you need to turn the clock on, use the ClockOn command, or scroll down to the 'TURN CLOCK ON' message that is displayed in place of the clock on the mode screen and press ENTER twice.

                                                                                                                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, RandomProductions.

                                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                                TI-84+ 0.01 Added
                                                                                                                                                                                                                                                Property Value
                                                                                                                                                                                                                                                Hex Value $EF04
                                                                                                                                                                                                                                                Categories
                                                                                                                                                                                                                                                Localizations
                                                                                                                                                                                                                                                • FR: défFmtHr(

                                                                                                                                                                                                                                                setTmFmt(

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Sets the time format.
                                                                                                                                                                                                                                                12 = 12 hour format24 = 24 hour format

                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                setTmFmt(integer)

                                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                                integer

                                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                                2nd, catalog, setTmFmt(

                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                The setTmFmt( command sets the time format of the clock on the TI-84+/SE calculators when displaying the time on the mode screen. There are two different formats available, and you simply use the respective value (can be either a literal number or a variable) to display the desired one: 12 (12 hour) or 24 (24 hour). For example, this would set the time format to 24 hour:

                                                                                                                                                                                                                                                :setTmFmt(24

                                                                                                                                                                                                                                                In order for the time format to work, you need to set the time using either the setTime( command, or by going into the set clock menu (accessible by pressing ENTER on the 'SET CLOCK' message that is displayed at the bottom of the mode screen). Of course, the time will only show up if the clock is on; if you need to turn the clock on, use the ClockOn command, or scroll down to the 'TURN CLOCK ON' message that is displayed in place of the clock on the mode screen and press ENTER twice.

                                                                                                                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, RandomProductions.

                                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                                TI-84+ 0.01 Added
                                                                                                                                                                                                                                                Property Value
                                                                                                                                                                                                                                                Hex Value $BBDD
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                                                                                                                                                                                                                                                • FR: ß

                                                                                                                                                                                                                                                ß

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                ß

                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                Examples

                                                                                                                                                                                                                                                Explanation 1

                                                                                                                                                                                                                                                code 1

                                                                                                                                                                                                                                                Explanation 2

                                                                                                                                                                                                                                                code 2

                                                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                                                Advanced Notes

                                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                                TI-83+ 1.16 Added
                                                                                                                                                                                                                                                Property Value
                                                                                                                                                                                                                                                Hex Value $BBCB
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                                                                                                                                                                                                                                                • FR: σ

                                                                                                                                                                                                                                                σ

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                σ

                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                Examples

                                                                                                                                                                                                                                                Explanation 1

                                                                                                                                                                                                                                                code 1

                                                                                                                                                                                                                                                Explanation 2

                                                                                                                                                                                                                                                code 2

                                                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                                                Advanced Notes

                                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                                TI-83+ 1.03 Added
                                                                                                                                                                                                                                                Property Value
                                                                                                                                                                                                                                                Hex Value $C2
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                                                                                                                                                                                                                                                • FR: sin(

                                                                                                                                                                                                                                                sin(

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Returns the sine of a real number, expression, or list.

                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                sin(value)

                                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                                valuereal|expression|real[]

                                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                                sin

                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                sin(θ) returns the sine of θ, which is defined as the y-value of the point of intersection of the unit circle and a line containing the origin that makes an angle θ with the positive x-axis

                                                                                                                                                                                                                                                The value returned depends on whether the calculator is in Radian or Degree mode. A full rotation around a circle is 2π radians, which is equal to 360°. The conversion from radians to degrees is angle180/π and from degrees to radians is angleπ/180. The sin( command also works on a list of real numbers.

                                                                                                                                                                                                                                                In radians:

                                                                                                                                                                                                                                                sin(π/6)
    .5

                                                                                                                                                                                                                                                In degrees:

                                                                                                                                                                                                                                                sin(30)
    .5

                                                                                                                                                                                                                                                Advanced Uses

                                                                                                                                                                                                                                                You can bypass the mode setting by using the ° (degree) and ʳ (radian) symbols. These next two commands will return the same values no matter if your calculator is in degrees or radians:

                                                                                                                                                                                                                                                sin(30°)
    .5

                                                                                                                                                                                                                                                sin(π/6ֿ¹)
    .5

                                                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                                                • ERR:DATA TYPE is thrown if you supply a matrix or a complex argument.
                                                                                                                                                                                                                                                • ERR:DOMAIN is thrown if you supply an input ≥1E12.

                                                                                                                                                                                                                                                See Also

                                                                                                                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, simplethinker, Xeda Elnara.

                                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                                TI-82 1.0 sin added
                                                                                                                                                                                                                                                TI-83 0.01013 Renamed sin to sin(
                                                                                                                                                                                                                                                Property Value
                                                                                                                                                                                                                                                Hex Value $C3
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                                                                                                                                                                                                                                                • FR: Arcsin(

                                                                                                                                                                                                                                                sin⁻¹(

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Returns the arcsine of a real number, expression, or list.

                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                sin⁻¹(value)

                                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                                ⁻¹real|expression|real[]
                                                                                                                                                                                                                                                valuereal|expression|real[]

                                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                                2nd, sin⁻¹

                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                sinֿ¹( returns the arcsine of its argument. It is the inverse of sin(, which means that sinֿ¹(z) produces an angle θ such that sin(θ)=z.

                                                                                                                                                                                                                                                Like sin(, the result of sinֿ¹( depends on whether the calculator is in Radian or Degree mode. However, unlike sine, the result is in degrees or radians, not the argument. A full rotation around a circle is 2π radians, which is equal to 360°. The conversion of θ=sinֿ¹(n) from radians to degrees is θ180/π and from degrees to radians is θπ/180. The sinֿ¹( command also works on lists.

                                                                                                                                                                                                                                                The sinֿ¹( function can be defined for all real and complex numbers; however, the function assumes real values only in the closed interval [-1,1]. Because the trigonometric functions and their inverses in the Z80 calculators are restricted only to real values, the calculator will throw ERR:DOMAIN if the argument is outside of this interval, no matter what the mode setting may be.

                                                                                                                                                                                                                                                In radians:

                                                                                                                                                                                                                                                :sinֿ¹(1)
    1.570796327

                                                                                                                                                                                                                                                In degrees:

                                                                                                                                                                                                                                                :sinֿ¹(1)
    90

                                                                                                                                                                                                                                                Advanced Uses

                                                                                                                                                                                                                                                Since the function sine itself doesn't have the restrictions that arcsine does, and since arcsine is the inverse of sine, you can use sinֿ¹(sin( to keep a variable within a certain range (most useful on the graph screen). Here is an example for a game like pong. The ball travels between -6 and 6.

                                                                                                                                                                                                                                                You could use a flag like this:

                                                                                                                                                                                                                                                :If 6=abs(X        \\ X is the position
:-D→D        \\ D is the direction
:X+D→X        \\ new position
:Pt-On(-54,X,"=")

                                                                                                                                                                                                                                                An easier way to do this, without needing a flag or even an If statement, is using sinֿ¹(sin(

                                                                                                                                                                                                                                                :X+1→X        \\ Note: the calculator is in degree mode
:Pt-On(-54,sinֿ¹(sin(15X))/15,"=")    \\ 15 is used because sinֿ¹ ranges from [-90,90]
                                        and X from [-6,6],  so 90/6=15

                                                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                                                • ERR:DATA TYPE is thrown if you input a complex value or a matrix.
                                                                                                                                                                                                                                                • ERR:DOMAIN is thrown if you supplied an argument outside the interval [-1,1]

                                                                                                                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, simplethinker, thornahawk.

                                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                                TI-82 1.0 sin⁻¹ added
                                                                                                                                                                                                                                                TI-83 0.01013 Renamed sin⁻¹ to sin⁻¹(
                                                                                                                                                                                                                                                Property Value
                                                                                                                                                                                                                                                Hex Value $C8
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                                                                                                                                                                                                                                                • FR: sh(

                                                                                                                                                                                                                                                sinh(

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Returns the hyperbolic sine of a real number, expression, or list.

                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                sinh(value)

                                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                                valuereal|expression|real[]

                                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                                2nd, catalog, sinh(

                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                Calculates the hyperbolic sine of a value. The hyperbolic trig functions sinh(, cosh(, and tanh( are an analog of normal trig functions, but for a hyperbola, rather than a circle. They can be expressed in terms of real powers of e, and don't depend on the Degree or Radian mode setting.

                                                                                                                                                                                                                                                sinh(0)
    0
sinh(1)
    1.175201194

                                                                                                                                                                                                                                                Like normal trig commands, sinh( works on lists as well, but not on complex numbers, even though the function is often extended to the complex numbers in mathematics.

                                                                                                                                                                                                                                                Formulas

                                                                                                                                                                                                                                                The definition of hyperbolic sine is:

                                                                                                                                                                                                                                                (1) \(\begin{align} \sinh{x}=\frac{e^x-e^{-x}}{2} \end{align}\)

                                                                                                                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, thornahawk, Timothy Foster.

                                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                                TI-82 1.0 sinh added
                                                                                                                                                                                                                                                TI-83 0.01013 Renamed sinh to sinh(
                                                                                                                                                                                                                                                Property Value
                                                                                                                                                                                                                                                Hex Value $C9
                                                                                                                                                                                                                                                Categories
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                                                                                                                                                                                                                                                • FR: Argsh(

                                                                                                                                                                                                                                                sinh⁻¹(

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Returns the hyperbolic arcsine of a real number, expression, or list.

                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                sinh⁻¹ (value)

                                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                                ⁻¹real|expression|real[]
                                                                                                                                                                                                                                                valuereal|expression|real[]

                                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                                2nd, catalog, sinh

                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                The sinhֿ¹( command calculates the inverse hyperbolic sine of a value. sinhֿ¹(x) is the number y such that x = sinh(y). Unlike for the standard trig functions, this uniquely determines the inverse hyperbolic sine of any real number.

                                                                                                                                                                                                                                                The sinhֿ¹( command also works for lists.

                                                                                                                                                                                                                                                sinhֿ¹(0)
    0
sinhֿ¹({1,2,3})
    {.881373587 1.443635475 1.818446459}

                                                                                                                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, thornahawk.

                                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                                TI-82 1.0 sinh⁻¹ added
                                                                                                                                                                                                                                                TI-83 0.01013 Renamed sinh⁻¹ to sinh⁻¹(
                                                                                                                                                                                                                                                Property Value
                                                                                                                                                                                                                                                Hex Value $C9
                                                                                                                                                                                                                                                Categories
                                                                                                                                                                                                                                                Localizations
                                                                                                                                                                                                                                                • FR: Argsh(

                                                                                                                                                                                                                                                sinh⁻¹(

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Returns the hyperbolic arcsine of a real number, expression, or list.

                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                sinh⁻¹ (value)

                                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                                ⁻¹real|expression|real[]
                                                                                                                                                                                                                                                valuereal|expression|real[]

                                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                                2nd, catalog, sinh

                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                The sinhֿ¹( command calculates the inverse hyperbolic sine of a value. sinhֿ¹(x) is the number y such that x = sinh(y). Unlike for the standard trig functions, this uniquely determines the inverse hyperbolic sine of any real number.

                                                                                                                                                                                                                                                The sinhֿ¹( command also works for lists.

                                                                                                                                                                                                                                                sinhֿ¹(0)
    0
sinhֿ¹({1,2,3})
    {.881373587 1.443635475 1.818446459}

                                                                                                                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, thornahawk.

                                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                                TI-82 1.0 sinh⁻¹ added
                                                                                                                                                                                                                                                TI-83 0.01013 Renamed sinh⁻¹ to sinh⁻¹(
                                                                                                                                                                                                                                                Property Value
                                                                                                                                                                                                                                                Hex Value $C3
                                                                                                                                                                                                                                                Categories
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                                                                                                                                                                                                                                                • FR: Arcsin(

                                                                                                                                                                                                                                                sin⁻¹(

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Returns the arcsine of a real number, expression, or list.

                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                sin⁻¹(value)

                                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                                ⁻¹real|expression|real[]
                                                                                                                                                                                                                                                valuereal|expression|real[]

                                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                                2nd, sin⁻¹

                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                sinֿ¹( returns the arcsine of its argument. It is the inverse of sin(, which means that sinֿ¹(z) produces an angle θ such that sin(θ)=z.

                                                                                                                                                                                                                                                Like sin(, the result of sinֿ¹( depends on whether the calculator is in Radian or Degree mode. However, unlike sine, the result is in degrees or radians, not the argument. A full rotation around a circle is 2π radians, which is equal to 360°. The conversion of θ=sinֿ¹(n) from radians to degrees is θ180/π and from degrees to radians is θπ/180. The sinֿ¹( command also works on lists.

                                                                                                                                                                                                                                                The sinֿ¹( function can be defined for all real and complex numbers; however, the function assumes real values only in the closed interval [-1,1]. Because the trigonometric functions and their inverses in the Z80 calculators are restricted only to real values, the calculator will throw ERR:DOMAIN if the argument is outside of this interval, no matter what the mode setting may be.

                                                                                                                                                                                                                                                In radians:

                                                                                                                                                                                                                                                :sinֿ¹(1)
    1.570796327

                                                                                                                                                                                                                                                In degrees:

                                                                                                                                                                                                                                                :sinֿ¹(1)
    90

                                                                                                                                                                                                                                                Advanced Uses

                                                                                                                                                                                                                                                Since the function sine itself doesn't have the restrictions that arcsine does, and since arcsine is the inverse of sine, you can use sinֿ¹(sin( to keep a variable within a certain range (most useful on the graph screen). Here is an example for a game like pong. The ball travels between -6 and 6.

                                                                                                                                                                                                                                                You could use a flag like this:

                                                                                                                                                                                                                                                :If 6=abs(X        \\ X is the position
:-D→D        \\ D is the direction
:X+D→X        \\ new position
:Pt-On(-54,X,"=")

                                                                                                                                                                                                                                                An easier way to do this, without needing a flag or even an If statement, is using sinֿ¹(sin(

                                                                                                                                                                                                                                                :X+1→X        \\ Note: the calculator is in degree mode
:Pt-On(-54,sinֿ¹(sin(15X))/15,"=")    \\ 15 is used because sinֿ¹ ranges from [-90,90]
                                        and X from [-6,6],  so 90/6=15

                                                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                                                • ERR:DATA TYPE is thrown if you input a complex value or a matrix.
                                                                                                                                                                                                                                                • ERR:DOMAIN is thrown if you supplied an argument outside the interval [-1,1]

                                                                                                                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, simplethinker, thornahawk.

                                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                                TI-82 1.0 sin⁻¹ added
                                                                                                                                                                                                                                                TI-83 0.01013 Renamed sin⁻¹ to sin⁻¹(
                                                                                                                                                                                                                                                Property Value
                                                                                                                                                                                                                                                Hex Value $BBE0
                                                                                                                                                                                                                                                Categories
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                                                                                                                                                                                                                                                • FR: ₀

                                                                                                                                                                                                                                                ₀

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                ₀

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                                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                                TI-83+ 1.16 Added
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                                                                                                                                                                                                                                                • FR: ₁
                                                                                                                                                                                                                                                ₁

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                ₁

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                                                                                                                                                                                                                                                • FR: ₁₀

                                                                                                                                                                                                                                                ₁₀

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                ₁₀

                                                                                                                                                                                                                                                Description

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                                                                                                                                                                                                                                                Advanced Notes

                                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                                TI-83+ 1.16 Added
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                                                                                                                                                                                                                                                • FR: ₂

                                                                                                                                                                                                                                                ₂

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                ₂

                                                                                                                                                                                                                                                Description

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                                                                                                                                                                                                                                                Explanation 1

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                                                                                                                                                                                                                                                Explanation 2

                                                                                                                                                                                                                                                code 2

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                                                                                                                                                                                                                                                Advanced Notes

                                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                                Calculator OS Version Description
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                                                                                                                                                                                                                                                • FR: ₃

                                                                                                                                                                                                                                                ₃

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                ₃

                                                                                                                                                                                                                                                Description

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                                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                                Calculator OS Version Description
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                                                                                                                                                                                                                                                • FR: ₄

                                                                                                                                                                                                                                                ₄

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                ₄

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                                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                                TI-83+ 1.16 Added
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                                                                                                                                                                                                                                                • FR: ₅

                                                                                                                                                                                                                                                ₅

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                ₅

                                                                                                                                                                                                                                                Description

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                                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                                TI-83+ 1.16 Added
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                                                                                                                                                                                                                                                • FR: ₆

                                                                                                                                                                                                                                                ₆

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                ₆

                                                                                                                                                                                                                                                Description

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                                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                                TI-83+ 1.16 Added
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                                                                                                                                                                                                                                                • FR: ₇

                                                                                                                                                                                                                                                ₇

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                ₇

                                                                                                                                                                                                                                                Description

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                                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                                TI-83+ 1.16 Added
                                                                                                                                                                                                                                                Property Value
                                                                                                                                                                                                                                                Hex Value $BBE8
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                                                                                                                                                                                                                                                • FR: ₈

                                                                                                                                                                                                                                                ₈

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                ₈

                                                                                                                                                                                                                                                Description

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                                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                                TI-83+ 1.16 Added
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                                                                                                                                                                                                                                                • FR: ₉

                                                                                                                                                                                                                                                ₉

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                ₉

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                                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                                TI-83+ 1.16 Added
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                                                                                                                                                                                                                                                • FR: ᴛ

                                                                                                                                                                                                                                                ᴛ

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                ᴛ

                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                Examples

                                                                                                                                                                                                                                                Explanation 1

                                                                                                                                                                                                                                                code 1

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                                                                                                                                                                                                                                                code 2

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                                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                                TI-83+ 1.16 Added
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                                                                                                                                                                                                                                                • FR: résoudre(

                                                                                                                                                                                                                                                solve(

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Solves expression for variable, given an initial guess and lower and upper bounds within which the solution is sought.

                                                                                                                                                                                                                                                Availability: Token only available from within the Basic editor.

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                solve(expression,variable,guess,{lower,upper})

                                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                                expressionexpression
                                                                                                                                                                                                                                                variable
                                                                                                                                                                                                                                                guess
                                                                                                                                                                                                                                                lower
                                                                                                                                                                                                                                                upper

                                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                                math, MATH, 0:solve(

                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                The solve( command attempts to iteratively find a real root of a given equation, given the variable to solve for, and an initial guess; i.e., given f(x), solve( will attempt to find a value of x such that f(x)=0. solve( can take a list {lower,upper} as an optional fourth argument, in which case it attempts to find a root between lower and upper inclusive (by default, lower and upper are taken to be -E99 and E99 respectively). Brent's method is used for finding the root.

                                                                                                                                                                                                                                                Unfortunately, the solve( command (as with most iterative methods) is not perfect at solving equations. solve( will in general be unable to find "multiple roots", or can only find it to an accuracy less than the usual (an example would be the root x=1 of the equation (x-1)^n=0 for n greater than 1). solve( will only return one of many possible roots to your equation if your equation has many roots to begin with. The root returned, in general, depends on the value of the guess given. The root returned is usually the root closest to the guess given for well-behaved equations; bad choices of the guess can cause solve( to either return a faraway root or not converge at all to a root.

                                                                                                                                                                                                                                                If possible, the equation should first be solved by hand - if there is a relatively simple formula for the root, that will (usually) be more efficient than using solve(. Otherwise, ensure that the solve( call actually works in all the expected cases during use.

                                                                                                                                                                                                                                                The Solver… utility (located in the same menu in the same place) is usually much easier and more intuitive to use, and is recommended instead of directly using solve( whenever applicable (e.g. the home screen). The same limitations apply to its efficiency. If you are unable to find roots using the Solver, try graphing the function and scanning for roots manually, then using 2:zero in the 2nd:CALC menu to refine your guess.

                                                                                                                                                                                                                                                Note: Solver… changes the value of the variable being solved for to the root found; solve(, on the other hand, finds the root, but does not modify the original value of the variable.

                                                                                                                                                                                                                                                Advanced Uses

                                                                                                                                                                                                                                                Reformulating an equation may be useful in certain instances. For example, the equations f(x)=0 and ef(x)=1 are equivalent. solve((X+1)2,X,0 returns ERR:NO SIGN CHG, while solve(e^((X+1)2)-1,X,0 returns -1.000000616 (pretty close to the root -1). Rearranging the equation may sometimes help as well.

                                                                                                                                                                                                                                                Specifying bounds usually helps solve( to find roots more efficiently. If bounds are readily available, they should be supplied to solve(.

                                                                                                                                                                                                                                                The error condition Bad Guess will occur if you use a string for the equation. There is a way around though. If you store the string into a function and use the function in place of the equation it will work.

                                                                                                                                                                                                                                                Str1 → Y1
solve(Y1,X,0

                                                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                                                • ERR:BAD GUESS will be thrown if guess wasn't within the lower and upper bound, or else the function is undefined at that point, or if a string is used for an equation.

                                                                                                                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, iPhoenixOnTIBD, Silver Phantom, thornahawk, Timothy Foster.

                                                                                                                                                                                                                                                History

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                                                                                                                                                                                                                                                • FR: √(

                                                                                                                                                                                                                                                √(

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                √(

                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                Takes the square root of a positive or negative number. It works exactly the same as 2×√ or ^(1/2) but is smaller and uses an ending parenthesis. If used on a list, it will return a list with the square root of each element.

                                                                                                                                                                                                                                                √(4)
        2
√(2)
        1.414213562

√({1,-1})
        {1 i}

                                                                                                                                                                                                                                                This may return a complex number or throw ERR:NONREAL ANS (depending on mode settings) if taking the square root of a negative number.

                                                                                                                                                                                                                                                Optimization

                                                                                                                                                                                                                                                Never raise something to the one-half power explicitly; use this command instead.

                                                                                                                                                                                                                                                :X^(1/2)→X
can be
:√(X→X

                                                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, thornahawk.

                                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                                TI-82 1.0 √ added
                                                                                                                                                                                                                                                TI-83 0.01013 Renamed √ to √(
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                                                                                                                                                                                                                                                • FR: □

                                                                                                                                                                                                                                                □

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                □

                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                Examples

                                                                                                                                                                                                                                                Explanation 1

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                                                                                                                                                                                                                                                Advanced Notes

                                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                                Calculator OS Version Description
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                                                                                                                                                                                                                                                • FR: √

                                                                                                                                                                                                                                                √

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                √

                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                Examples

                                                                                                                                                                                                                                                Explanation 1

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                                                                                                                                                                                                                                                code 2

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                                                                                                                                                                                                                                                Advanced Notes

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                                                                                                                                                                                                                                                TI-83+ 1.16 Added
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                                                                                                                                                                                                                                                • FR: actMintr

                                                                                                                                                                                                                                                startTmr

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Starts the clock timer. Store or note the displayed value, and use it as the argument for checkTmr( ) to check the elapsed time.

                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                startTmr

                                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                                2nd, catalog, startTmr

                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                The startTmr command is used with the built-in timer that is available on the TI-84+/SE calculators. It is used together with the checkTmr( command to determine how much time has elapsed since the timer was started. An application of these commands is timing different commands or pieces of code, as well as countdowns in games, or a time-based score (such as in Minesweeper).

                                                                                                                                                                                                                                                To use the timer, you first store startTmr to a variable (usually, a real variable) whenever you want the count to start. Now, whenever you want to check the elapsed time, you can use checkTmr( with the variable from above, giving you the number of seconds that have passed. Using checkTmr( doesn't stop the timer, you can do it as many times as you want to.

                                                                                                                                                                                                                                                In the case of Minesweeper, for example, you would store startTmr to, for example, T, after setting up and displaying the board, display the result of checkTmr(T) in the game's key-reading loop, and store checkTmr(T) to the player's score if he wins.

                                                                                                                                                                                                                                                Despite the name of the command, startTmr doesn't start the clock if it's stopped; use ClockOn instead to start the clock.

                                                                                                                                                                                                                                                Advanced Uses

                                                                                                                                                                                                                                                To time a command or routine using startTmr and checkTmr(, use the following template:

                                                                                                                                                                                                                                                :ClockOn
:startTmr→T
:Repeat checkTmr(Ans
:End
:For(n,1,(number)                    //sequence variable n
   (command(s) to be tested)
:End
:checkTmr(T+1)/(number)

                                                                                                                                                                                                                                                Making (number) higher increases accuracy, but takes longer. Also, make sure not to modify the variables n or T inside the For( loop.

                                                                                                                                                                                                                                                While this method eliminates human error from counting, it's prone to its own faults. For example, startTmr and checkTmr( always return the time rounded down to a whole second. To take this into account, replace the last line:

                                                                                                                                                                                                                                                :(checkTmr(T+{1,0})/(number)

                                                                                                                                                                                                                                                When testing code, be aware that many different things affect the time: the strength of the batteries, the amount of free RAM, and including the closing parenthesis on the For( loop. The last one, in particular, has an impact when using a single-line If statement or one of the [IS>(](IS(.html) and [DS<(](DS(.html) commands on the first line inside a For( loop.

                                                                                                                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Jonathan King, lirtosiast, Xphoenix.

                                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                                TI-84+ 0.01 Added
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                                                                                                                                                                                                                                                • FR: Ecart-type(

                                                                                                                                                                                                                                                stdDev(

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Returns the standard deviation of the elements in list with frequency freqlist.

                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                stdDev(list[,freqlist])

                                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                                listlist
                                                                                                                                                                                                                                                freqlistlistYes

                                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                                2nd, list, MATH, 7:stdDev(

                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                The stdDev( command finds the sample standard deviation of a list, a measure of the spread of a distribution. It takes a list of real numbers as a parameter. For example:

                                                                                                                                                                                                                                                :Prompt L1
:Disp "STD. DEV. OF L1",stdDev(L1

                                                                                                                                                                                                                                                Caution: the standard deviation found by this command is the sample standard deviation, not the population standard deviation, which is the one most commonly used when dealing with a sample rather than the whole population. The formula for population standard deviation is similar, but N-1 is replaced by N. There is no single command that will calculate population standard deviation for you, but 1-Var Stats will return both (sample standard deviation, the one returned by stdDev(), is Sx, while population standard deviation is σx). You can also calculate population standard deviation of L1 with the following code:

                                                                                                                                                                                                                                                :stdDev(augment(L1,{mean(L1

                                                                                                                                                                                                                                                Advanced Uses

                                                                                                                                                                                                                                                Frequency lists don't need to be whole numbers. Amazing as that may sound, your calculator can handle being told that one element of the list occurs 1/3 of a time, and another occurs 22.7 times. It can even handle a frequency of 0 - it will just ignore that element, as though it weren't there. One caveat, though - if all of the elements occur 0 times, there's no elements actually in the list and your calculator will throw an error.

                                                                                                                                                                                                                                                Formulas

                                                                                                                                                                                                                                                The formula for standard deviation used by this command is:

                                                                                                                                                                                                                                                (1) \(\begin{align} s = \sqrt{\frac{1}{N-1} \sum_{i=1}^N (x_i - \overline{x})^2} \end{align}\)

                                                                                                                                                                                                                                                This is the formula for sample standard deviation. The formula for population standard deviation, which this command does not use, varies slightly:

                                                                                                                                                                                                                                                (2) \(\begin{align} \sigma = \sqrt{\frac{1}{N} \sum_{i=1}^N (x_i - \overline{x})^2} \end{align}\)

                                                                                                                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

                                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                                TI-83 0.01013 Added
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                                                                                                                                                                                                                                                • FR: Sous-chaine(

                                                                                                                                                                                                                                                sub(

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Returns a string that is a subset of another string, from begin to length.

                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                sub(string,begin,length)

                                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                                stringstring
                                                                                                                                                                                                                                                begin
                                                                                                                                                                                                                                                lengthinteger

                                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                                2nd, catalog, sub(

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Divides a real number, expression, or list by 100.

                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                sub(value)

                                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                                valuereal|expression|real[]

                                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                                2nd, catalog, sub(

                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                The sub( command is used to get a substring, or a specific part of a string. It takes three arguments: string is the source string to get the substring from, start is the index of the token to start from, and length is the length of the substring you want. For example:

                                                                                                                                                                                                                                                :sub("TI-BASIC",4,5
    "BASIC"
:sub("TI-BASIC",5,2
    "AS"

                                                                                                                                                                                                                                                Keep in mind that you can't have an empty string, so the length argument can't be equal to 0.

                                                                                                                                                                                                                                                When the length argument is 1, sub(string,N,1 returns the Nth token in the string.

                                                                                                                                                                                                                                                Advanced Uses

                                                                                                                                                                                                                                                If only one argument is given, and it contains an expression that evaluates to a real or complex number or list of numbers, the sub( command will divide the result by 100.

                                                                                                                                                                                                                                                :sub(225
    2.25
:sub({3+5i,-4i►Frac
    {3/100+1/20i,-1/25i}

                                                                                                                                                                                                                                                Much like the use of the % symbol, this is an undocumented feature that was introduced in OS version 1.15. Thus, care should be taken when using sub( in this way, as older versions will not support it.

                                                                                                                                                                                                                                                Together with the inString( command, sub( can be used to store a "list of strings" in a string, that you can then get each individual string from. To do this, think of a delimiter, such as a comma, to separate each individual string in the "list" (the delimiter must never occur in an individual string). The code will be simpler if the delimiter also occurs at the end of the string, as in "CAT,DOG,RAT,FISH,".

                                                                                                                                                                                                                                                This routine will display each string in a "list of strings". You can adapt it to your own needs.

                                                                                                                                                                                                                                                :1→I
:inString(Str1,",→J
:While Ans
:Disp sub(Str1,I,J-I
:J+1→I
:inString(Str1,",",Ans→J
:End

                                                                                                                                                                                                                                                Alternatively, instead of using inString, you can start each individual string at the length of the longest string length, plus 1. If there are smaller strings that are not the same length, use spaces.

                                                                                                                                                                                                                                                For example, if you wanted to display the suits for a card game, do the following:

                                                                                                                                                                                                                                                :"SPADES--DIAMONDSHEARTS--CLUB----→Str1
:sub(Str1,1+8A,8

                                                                                                                                                                                                                                                (Spaces have been replaced with dashes for visual clarity.)

                                                                                                                                                                                                                                                Broken down, by manipulating A, different portions of the string can be displayed without the hassle of searching for characters. Setting A as 0 would display "SPADES—", but thanks to the spaces, the extra two characters would not be seen. A may be replaced with (A-1) if the 1st name would like to be displayed by setting A to 1.

                                                                                                                                                                                                                                                This method is more preferable when using the Home Screen, as the spaces would wipe the last end characters of any previous strings displayed.

                                                                                                                                                                                                                                                You can use this command as a number to character converter, too, as shown:

                                                                                                                                                                                                                                                //Letter Number for Q
:17→Q
//Converter:
:sub("ABCDEFGHIJKLMNOPQRSTUVWXYZ",Q,1→Str1
:Disp Str1

                                                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                                                • ERR:ARCHIVED is thrown if you try to take the substring of an archived string.
                                                                                                                                                                                                                                                • ERR:DOMAIN is thrown if the starting and/or length value is less than 1, or if it is not an integer.
                                                                                                                                                                                                                                                • ERR:INVALID DIM is thrown if the starting and/or length value is beyond the length of the string.
                                                                                                                                                                                                                                                • ERR:UNDEFINED is thrown if you try to take the substring of a non-existent string.

                                                                                                                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: 7thAce, burr, DarkerLine, GoVegan, louwenus, luby19, Michael2_3B, QubicQuantum, Toothless the Dragon, Weregoose.

                                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                                TI-83 0.01013 Added
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                                                                                                                                                                                                                                                • FR: somme(

                                                                                                                                                                                                                                                sum(

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Returns the sum of elements of list from start to end.

                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                sum(list[,start,end])

                                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                                listlist
                                                                                                                                                                                                                                                startYes
                                                                                                                                                                                                                                                endYes

                                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                                2nd, list, MATH, 5:sum(

                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                The sum( command calculates the sum of all or part of a list.

                                                                                                                                                                                                                                                When you use it with only one argument, the list, it sums up all the elements of the list. You can also give it a bound of start and end and it will only sum up the elements starting and ending at those indices (inclusive).

                                                                                                                                                                                                                                                sum({1,2,3,4,5})
    15
sum({1,2,3,4,5},2,4)
    9
sum({1,2,3,4,5},3)
    12

                                                                                                                                                                                                                                                Optimization

                                                                                                                                                                                                                                                If the value of end is the last element of the list, it can be omitted:

                                                                                                                                                                                                                                                sum({1,2,3,4,5},3,5)
can be
sum({1,2,3,4,5},3)

                                                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                                                • ERR:DOMAIN is thrown if the starting or ending value aren't positive integers.
                                                                                                                                                                                                                                                • ERR:INVALID DIM is thrown if the starting or ending value exceed the size of the list, or are in the wrong order.

                                                                                                                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

                                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                                TI-82 1.0 sum added
                                                                                                                                                                                                                                                TI-83 0.01013 Renamed sum to sum(
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                                                                                                                                                                                                                                                Hex Value $BBC4
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                                                                                                                                                                                                                                                • FR: t

                                                                                                                                                                                                                                                t

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                t

                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                Examples

                                                                                                                                                                                                                                                Explanation 1

                                                                                                                                                                                                                                                code 1

                                                                                                                                                                                                                                                Explanation 2

                                                                                                                                                                                                                                                code 2

                                                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                                                Advanced Notes

                                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                                TI-83+ 1.03 Added
                                                                                                                                                                                                                                                Property Value
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                                                                                                                                                                                                                                                • FR: tan(

                                                                                                                                                                                                                                                tan(

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Returns the tangent of a real number, expression, or list.

                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                tan(value)

                                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                                valuereal|expression|real[]

                                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                                tan

                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                tan(θ) calculates the tangent of the angle θ, which is defined by \(\tan \theta=\frac{\sin \theta}{\cos \theta}\)

                                                                                                                                                                                                                                                The value returned depends on whether the calculator is in Radian or Degree mode. A full rotation around a circle is 2π radians, which is equal to 360°. The conversion from radians to degrees is angle180/π and from degrees to radians is angleπ/180. The tan( command also works on a list of real numbers.

                                                                                                                                                                                                                                                Since tangent is defined as the quotient of sine divided by cosine, it is undefined for any angle such that cos(θ)=0.

                                                                                                                                                                                                                                                In radians:

                                                                                                                                                                                                                                                tan(π/4)
    1

                                                                                                                                                                                                                                                In degrees:

                                                                                                                                                                                                                                                tan(45)
    1

                                                                                                                                                                                                                                                Advanced Uses

                                                                                                                                                                                                                                                You can bypass the mode setting by using the ° (degree) and ʳ (radian) symbols. These next two commands will return the same values no matter if your calculator is in degrees or radians:

                                                                                                                                                                                                                                                tan(45°)
    1

                                                                                                                                                                                                                                                tan(π/4¹ )
    1

                                                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                                                • ERR:DATA TYPE is thrown if you supply a matrix or a complex argument.
                                                                                                                                                                                                                                                • ERR:DOMAIN is thrown if you supply an angle of π/2±nπ (in radians, where n is an integer) or 90±180n (in degrees, where n is an integer), or when the input is ≥1E12.

                                                                                                                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Mr Dino, simplethinker, Timothy Foster, Weregoose, Xeda Elnara.

                                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                                TI-82 1.0 tan added
                                                                                                                                                                                                                                                TI-83 0.01013 Renamed tan to tan(
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                                                                                                                                                                                                                                                • FR: Arctan(

                                                                                                                                                                                                                                                tan⁻¹(

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Returns the arctangent of a real number, expression, or list.

                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                tan⁻¹(value)

                                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                                ⁻¹real|expression|real[]
                                                                                                                                                                                                                                                valuereal|expression|real[]

                                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                                2nd, tan⁻¹

                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                tanֿ¹( returns the arctangent of its argument. It is the inverse of tan(, which means that tanֿ¹(n) produces an angle θ such that tan(θ)=n.

                                                                                                                                                                                                                                                Like tan(, the result of tanֿ¹( depends on whether the calculator is in Radian or Degree mode. However, unlike tangent, the result is in degrees or radians, not the argument. A full rotation around a circle is 2π radians, which is equal to 360°. The conversion of θ=tanֿ¹(n) from radians to degrees is θ180/π and from degrees to radians is θπ/180. The tanֿ¹( command also works on a list.

                                                                                                                                                                                                                                                tanֿ¹( will always return a value between -π/2 and π/2 (or -90° and 90°).

                                                                                                                                                                                                                                                In radians:

                                                                                                                                                                                                                                                :tanֿ¹(1)
    .7853981634

                                                                                                                                                                                                                                                In degrees:

                                                                                                                                                                                                                                                :tanֿ¹(1)
    45

                                                                                                                                                                                                                                                Optimization

                                                                                                                                                                                                                                                Expressions of the form tanֿ¹(y__/x) are usually better recast as R►Pθ(x,y); the latter will not fail even if x should happen to be equal to zero.

                                                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                                                • ERR:DATA TYPE is thrown if you input a complex value or a matrix.

                                                                                                                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, thornahawk.

                                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                                TI-82 1.0 tan⁻¹ added
                                                                                                                                                                                                                                                TI-83 0.01013 Renamed tan⁻¹ to tan⁻¹(
                                                                                                                                                                                                                                                Property Value
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                                                                                                                                                                                                                                                • FR: th(

                                                                                                                                                                                                                                                tanh(

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Returns hyperbolic tangent of a real number, expression, or list.

                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                tanh(value)

                                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                                valuereal|expression|real[]

                                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                                2nd, catalog, tanh(

                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                Calculates the hyperbolic tangent of a value. The hyperbolic trig functions sinh(, cosh(, and tanh( are an analog of normal trig functions, but for a hyperbola, rather than a circle. They can be expressed in terms of real powers of e, and don't depend on the Degree or Radian mode setting.

                                                                                                                                                                                                                                                tanh(0)
    0
tanh(1)
    .761594156

                                                                                                                                                                                                                                                Like normal trig commands, tanh( works on lists as well, but not on complex numbers, even though the function is often extended to the complex numbers in mathematics.

                                                                                                                                                                                                                                                Advanced Uses

                                                                                                                                                                                                                                                The tanh( command can be used to approximate the sign function:

                                                                                                                                                                                                                                                (1) \(\begin{align} \texttt{sgn} x=\begin{cases}-1&\text{if }x<0,\\0&\text{if }x=0,\\1&\text{if }x>0.\end{cases} \end{align}\)

                                                                                                                                                                                                                                                As the absolute value of the input becomes large, the convergence is achieved at a point closer to zero. For the function to work as intended generally, numbers having lesser orders of magnitude need to be multiplied by a factor large enough for the argument to arrive at ±16.720082053122, which is the smallest input to produce ±1 (respectively) to fourteen digits of accuracy.

                                                                                                                                                                                                                                                5/12→X
    .4166666667
tanh(E9X)
    1
tanh(-E9X)
    -1

                                                                                                                                                                                                                                                Formulas

                                                                                                                                                                                                                                                The definition of the hyperbolic tangent is:

                                                                                                                                                                                                                                                (2) \(\begin{align} \tanh{x}=\frac{e^x-e^{-x}}{e^x+e^{-x}}=\frac{e^{2x}-1}{e^{2x}+1} \end{align}\)

                                                                                                                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, Edward H, GoVegan, thornahawk, Timothy Foster, Weregoose.

                                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                                TI-82 1.0 tanh added
                                                                                                                                                                                                                                                TI-83 0.01013 Renamed tanh to tanh(
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                                                                                                                                                                                                                                                • FR: Argth(

                                                                                                                                                                                                                                                tanh⁻¹(

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Returns the hyperbolic arctangent of a real number, expression, or list.

                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                tanh⁻¹(value)

                                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                                ⁻¹real|expression|real[]
                                                                                                                                                                                                                                                valuereal|expression|real[]

                                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                                2nd, catalog, tanh

                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                The tanhֿ¹( command calculates the inverse hyperbolic tangent of a value. tanhֿ¹(x) is the number y such that x = tanh(y).

                                                                                                                                                                                                                                                tanhֿ¹(x), although it can be defined for all real and complex numbers, is real-valued only for x in the open interval (-1,1). Since Z80 calculators have their hyperbolic functions and inverses restricted to real values, ERR:DOMAIN is thrown when x is outside the interval (-1,1).

                                                                                                                                                                                                                                                The tanhֿ¹( command also works for lists.

                                                                                                                                                                                                                                                tanhֿ¹(0)
    0
tanhֿ¹({-.5,.5})
    {-.5493061443 .5493061443}

                                                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                                                • ERR:DOMAIN when taking the inverse tanh of a number not between -1 and 1.

                                                                                                                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, thornahawk.

                                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                                TI-82 1.0 tanh⁻¹ added
                                                                                                                                                                                                                                                TI-83 0.01013 Renamed tanh⁻¹ to tanh⁻¹(
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                                                                                                                                                                                                                                                • FR: Argth(

                                                                                                                                                                                                                                                tanh⁻¹(

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Returns the hyperbolic arctangent of a real number, expression, or list.

                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                tanh⁻¹(value)

                                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                                ⁻¹real|expression|real[]
                                                                                                                                                                                                                                                valuereal|expression|real[]

                                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                                2nd, catalog, tanh

                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                The tanhֿ¹( command calculates the inverse hyperbolic tangent of a value. tanhֿ¹(x) is the number y such that x = tanh(y).

                                                                                                                                                                                                                                                tanhֿ¹(x), although it can be defined for all real and complex numbers, is real-valued only for x in the open interval (-1,1). Since Z80 calculators have their hyperbolic functions and inverses restricted to real values, ERR:DOMAIN is thrown when x is outside the interval (-1,1).

                                                                                                                                                                                                                                                The tanhֿ¹( command also works for lists.

                                                                                                                                                                                                                                                tanhֿ¹(0)
    0
tanhֿ¹({-.5,.5})
    {-.5493061443 .5493061443}

                                                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                                                • ERR:DOMAIN when taking the inverse tanh of a number not between -1 and 1.

                                                                                                                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, thornahawk.

                                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                                TI-82 1.0 tanh⁻¹ added
                                                                                                                                                                                                                                                TI-83 0.01013 Renamed tanh⁻¹ to tanh⁻¹(
                                                                                                                                                                                                                                                Property Value
                                                                                                                                                                                                                                                Hex Value $C7
                                                                                                                                                                                                                                                Categories
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                                                                                                                                                                                                                                                • FR: Arctan(

                                                                                                                                                                                                                                                tan⁻¹(

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Returns the arctangent of a real number, expression, or list.

                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                tan⁻¹(value)

                                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                                ⁻¹real|expression|real[]
                                                                                                                                                                                                                                                valuereal|expression|real[]

                                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                                2nd, tan⁻¹

                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                tanֿ¹( returns the arctangent of its argument. It is the inverse of tan(, which means that tanֿ¹(n) produces an angle θ such that tan(θ)=n.

                                                                                                                                                                                                                                                Like tan(, the result of tanֿ¹( depends on whether the calculator is in Radian or Degree mode. However, unlike tangent, the result is in degrees or radians, not the argument. A full rotation around a circle is 2π radians, which is equal to 360°. The conversion of θ=tanֿ¹(n) from radians to degrees is θ180/π and from degrees to radians is θπ/180. The tanֿ¹( command also works on a list.

                                                                                                                                                                                                                                                tanֿ¹( will always return a value between -π/2 and π/2 (or -90° and 90°).

                                                                                                                                                                                                                                                In radians:

                                                                                                                                                                                                                                                :tanֿ¹(1)
    .7853981634

                                                                                                                                                                                                                                                In degrees:

                                                                                                                                                                                                                                                :tanֿ¹(1)
    45

                                                                                                                                                                                                                                                Optimization

                                                                                                                                                                                                                                                Expressions of the form tanֿ¹(y__/x) are usually better recast as R►Pθ(x,y); the latter will not fail even if x should happen to be equal to zero.

                                                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                                                • ERR:DATA TYPE is thrown if you input a complex value or a matrix.

                                                                                                                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, thornahawk.

                                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                                TI-82 1.0 tan⁻¹ added
                                                                                                                                                                                                                                                TI-83 0.01013 Renamed tan⁻¹ to tan⁻¹(
                                                                                                                                                                                                                                                Property Value
                                                                                                                                                                                                                                                Hex Value $BBCC
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                                                                                                                                                                                                                                                • FR: τ

                                                                                                                                                                                                                                                τ

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                τ

                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                Examples

                                                                                                                                                                                                                                                Explanation 1

                                                                                                                                                                                                                                                code 1

                                                                                                                                                                                                                                                Explanation 2

                                                                                                                                                                                                                                                code 2

                                                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                                                Advanced Notes

                                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                                TI-83+ 1.03 Added
                                                                                                                                                                                                                                                Property Value
                                                                                                                                                                                                                                                Hex Value $BB12
                                                                                                                                                                                                                                                Categories
                                                                                                                                                                                                                                                Localizations
                                                                                                                                                                                                                                                • FR: studentFRép(

                                                                                                                                                                                                                                                tcdf(

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Computes the Student-t distribution probability between lowerbound andupperbound for the specified degrees of freedomdf.

                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                tcdf(lowerbound,upperbound,df)

                                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                                lowerbound
                                                                                                                                                                                                                                                upperbound
                                                                                                                                                                                                                                                df

                                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                                2nd, distr, DISTR, 6:tcdf(

                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                tcdf( is the Student's t cumulative density function. If some random variable follows this distribution, you can use this command to find the probability that this variable will fall in the interval you supply.

                                                                                                                                                                                                                                                Unlike normalcdf(, this command only works for the standardized distribution with mean 0 and standard deviation 1. To use it for non-standardized values you will have to standardize them by calculating (X-μ)/σ (where μ is the mean and σ the standard deviation). Do this for both lower and upper.

                                                                                                                                                                                                                                                Advanced

                                                                                                                                                                                                                                                Often, you want to find a "tail probability" - a special case for which the interval has no lower or no upper bound (the form frequently used in one-tailed tests). For example, "what is the probability x is greater than 2?". The TI-83+ has no special symbol for infinity, but you can use E99 to get a very large number that will work equally well in this case (E is the decimal exponent obtained by pressing [2nd] [EE]). Use E99 for +∞, and -E99 for -∞.

                                                                                                                                                                                                                                                Alternatively, you can exploit the identity

                                                                                                                                                                                                                                                (1) \(\begin{align} \texttt{tcdf}(-\infty,0,\nu)=\frac1{2} \end{align}\)

                                                                                                                                                                                                                                                (similarly for the interval from 0 to ∞)

                                                                                                                                                                                                                                                and thus

                                                                                                                                                                                                                                                (2) \(\begin{align} \texttt{tcdf}(-\infty,x,\nu)=\frac1{2}+\texttt{tcdf}(0,x,\nu) \end{align}\)

                                                                                                                                                                                                                                                For the form used in two-tailed tests, the following identity may be useful:

                                                                                                                                                                                                                                                (3) \(\begin{align} \texttt{tcdf}(-x,x,\nu)=2\texttt{tcdf}(0,x,\nu) \end{align}\)

                                                                                                                                                                                                                                                Formulas

                                                                                                                                                                                                                                                As with any other continuous distribution, tcdf( can be defined in terms of the probability density function, tpdf(:

                                                                                                                                                                                                                                                (4) \(\begin{align} \texttt{tcdf}(a,b,\nu)=\int_a^b \texttt{tpdf}(t,\nu)\mathrm{d}t \end{align}\)

                                                                                                                                                                                                                                                The function can also be expressed in terms of an incomplete beta function.

                                                                                                                                                                                                                                                For one degree of freedom (ν=1), tcdf( is expressible in terms of simpler functions:

                                                                                                                                                                                                                                                (5) \(\begin{align} \texttt{tcdf}(a,b,1)=\frac1{\pi}\left(\tan^{-1}\left(b\right)-\tan^{-1}\left(a\right)\right) \end{align}\)

                                                                                                                                                                                                                                                This is the so-called Cauchy distribution.

                                                                                                                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, thornahawk.

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                                                                                                                                                                                                                                                θ

                                                                                                                                                                                                                                                Description

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                                                                                                                                                                                                                                                θMax

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                θMax

                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                Examples

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                                                                                                                                                                                                                                                θMin

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                θMin

                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                Examples

                                                                                                                                                                                                                                                Explanation 1

                                                                                                                                                                                                                                                code 1

                                                                                                                                                                                                                                                Explanation 2

                                                                                                                                                                                                                                                code 2

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                                                                                                                                                                                                                                                θstep

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                θstep

                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                Examples

                                                                                                                                                                                                                                                Explanation 1

                                                                                                                                                                                                                                                code 1

                                                                                                                                                                                                                                                Explanation 2

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                                                                                                                                                                                                                                                • FR: convHeur(

                                                                                                                                                                                                                                                timeCnv(

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Converts seconds to units of time that can be more easily understood for evaluation. The list is in {days,hours,minutes,seconds} format.

                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                timeCnv(seconds)

                                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                                seconds

                                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                                2nd, catalog, timeCnv

                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                The timeCnv( command converts seconds into the equivalent days, hours, minutes, and seconds. You just specify a number of seconds (should be a whole number, although a decimal number would work too; the calculator will simply use the integer part and discard the decimal) and the calculator will automatically break the seconds up into the standard parts of time, storing them in list format — {days,hours,minutes,seconds}. You can store this list to a variable for later use, or manipulate it the same way you do with other lists.

                                                                                                                                                                                                                                                The number of seconds you specify can be as small or large as you want, although the number must be at least zero (in which case, the time list will be all zeroes). At the same time, you will run into the standard number precision problems that plague TI-Basic when specifying an extremely large or small number. Because of this, you should try to use numbers with less than 10 digits. Here is a simple example, where the time is exactly 1 day, 1 hour, 1 minute, and 1 second:

                                                                                                                                                                                                                                                :timeCnv(90061→L1
:Disp Ans

                                                                                                                                                                                                                                                The time conversion is 60 seconds for a minute, 3600 (6060) seconds for an hour, and 86400 (6060*24) seconds for a day. Adding these three together plus the one second gives you the value that you see in the example. This is pretty basic math, so it should be easy to understand.

                                                                                                                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Thom M, Xphoenix.

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                                                                                                                                                                                                                                                >

                                                                                                                                                                                                                                                Overview

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                                                                                                                                                                                                                                                >

                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                Examples

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                                                                                                                                                                                                                                                ≥

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                ≥

                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                Examples

                                                                                                                                                                                                                                                Explanation 1

                                                                                                                                                                                                                                                code 1

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                                                                                                                                                                                                                                                • FR: ►DMS

                                                                                                                                                                                                                                                ►DMS

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Displays value in DMS format.

                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                value►DMS

                                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                                value

                                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                                2nd, angle, ANGLE, 4:DMS

                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                The ►DMS command can be used when displaying a real number on the home screen, or with the Disp and Pause commands. It will then format the number as an angle with degree, minute, and second parts.

                                                                                                                                                                                                                                                30►DMS
    30°0'0"
100/9°►DMS
    11°6'40"

                                                                                                                                                                                                                                                It will also work when displaying a number by putting it on the last line of a program by itself. It does not work with Output(, Text(, or any other more complicated display commands.

                                                                                                                                                                                                                                                Although ►DMS is meant as a way to format angles in Degree mode, it doesn't depend on the angle mode chosen, only on the number itself. Note that entering a number as degree°minute'second" will also work, in any mode, and it will not be converted to radians in Radian mode.

                                                                                                                                                                                                                                                Rounding to Nearest Second

                                                                                                                                                                                                                                                If you'd prefer to not have seconds with decimal places, you can round your answer to the nearest second with the following formula:

                                                                                                                                                                                                                                                round(Ans*3600,0)/3600►DMS

                                                                                                                                                                                                                                                Or a slightly shorter version:

                                                                                                                                                                                                                                                round(Ans36,2)/36►DMS

                                                                                                                                                                                                                                                Tip: If you find yourself needing this formula regularly, put it into a Y= graphing-function as:

                                                                                                                                                                                                                                                Y1=round(X36,2)/36

                                                                                                                                                                                                                                                And then you can call it from your home screen via:

                                                                                                                                                                                                                                                Y1(123.45678►DMS

                                                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                                                • ERR:SYNTAX is thrown if the command is used somewhere other than the allowed display commands.
                                                                                                                                                                                                                                                • ERR:DATA TYPE is thrown if the value is complex, or if given a list or matrix as argument.

                                                                                                                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583, thornahawk.

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                                                                                                                                                                                                                                                • FR: ►Dec

                                                                                                                                                                                                                                                ►Dec

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Displays a real or complex number, expression, list, or matrix in decimal format.

                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                value►Dec

                                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                                value

                                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                                math, MATH, 2:Dec

                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                This command is generally useless. Its supposed use is to convert numbers into decimal form, but any typed fractions are displayed as decimals anyway.

                                                                                                                                                                                                                                                1/3
     .3333333333
1/3►Dec
     .3333333333

                                                                                                                                                                                                                                                In 2.53 MP or higher, typed fractions are displayed in fraction form. Therefore, the ►Dec command is useful in this case.

                                                                                                                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: alexrudd, blue_bear_94, burr, CloudVariable, DarkerLine, GoVegan, Myles_Zadok, Timtech.

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                                                                                                                                                                                                                                                • FR: ►Eff(

                                                                                                                                                                                                                                                ►Eff(

                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                Computes the effective interest rate.

                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                ►Eff(nominal rate,compounding periods)

                                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                                nominal rate
                                                                                                                                                                                                                                                compounding periods

                                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                                apps, 1:Finance, CALC, C:►Eff(

                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                The ►Eff( command converts from a nominal interest rate to an effective interest rate. In other words, it converts an interest rate that does not take into account compounding periods into one that does. The two arguments are 1) the interest rate and 2) the number of compounding periods.

                                                                                                                                                                                                                                                For example, take an interest rate of 7.5% per year, compounded monthly. You can use ►Eff( to find out the actual percent of interest per year:

                                                                                                                                                                                                                                                ►Eff(7.5,12)
    7.663259886

                                                                                                                                                                                                                                                Formulas

                                                                                                                                                                                                                                                The formula for converting from a nominal rate to an effective rate is:

                                                                                                                                                                                                                                                (1) \(\begin{align} \texttt{Eff}=100\left(\left(1+\frac{\texttt{Nom}}{100 \texttt{CP}}\right)^{\texttt{CP}}-1\right) \end{align}\)

                                                                                                                                                                                                                                                Here, Eff is the effective rate, Nom is the nominal rate, and CP is the number of compounding periods.

                                                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                                                • ERR:DOMAIN is thrown if the number of compounding periods is not positive, or if the nominal rate is -100% or lower (an exception's made for the nominal rate if there is only one compounding period, since ►Eff(X,1)=X)

                                                                                                                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, jonbush, Myles_Zadok.

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                                                                                                                                                                                                                                                  • FR: ►F◄►D

                                                                                                                                                                                                                                                  ►F◄►D

                                                                                                                                                                                                                                                  Overview

                                                                                                                                                                                                                                                  Converts an answer from a fraction to a decimal or from a decimal to a fraction. Fraction and or decimal may be an approximation.

                                                                                                                                                                                                                                                  Availability: Token available everywhere.

                                                                                                                                                                                                                                                  Syntax

                                                                                                                                                                                                                                                  ►F ◄►D

                                                                                                                                                                                                                                                  Arguments

                                                                                                                                                                                                                                                  NameTypeOptional
                                                                                                                                                                                                                                                  ◄►

                                                                                                                                                                                                                                                  Location

                                                                                                                                                                                                                                                  alpha, F1, 4:

                                                                                                                                                                                                                                                  Description

                                                                                                                                                                                                                                                  The ►F◄►D command is used to convert a number from fraction form to decimal form, or vice versa. Regardless of what form the given number is, this command is meant to automatically determine the form so that it returns the other. It is in essence a combination of the ►Frac and ►Dec commands, applying ►Frac if the input is in decimal form and ►Dec if it is a fraction.

                                                                                                                                                                                                                                                  7.5►F◄ ►D
        15/2
Ans►F◄ ►D
        7.5

                                                                                                                                                                                                                                                  Source: parts of this page were written by the following TI|BD contributors: Battlesquid, burr, ccrh2009, kg583, Timothy Foster.

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                                                                                                                                                                                                                                                  • FR: ►Frac

                                                                                                                                                                                                                                                  ►Frac

                                                                                                                                                                                                                                                  Overview

                                                                                                                                                                                                                                                  Displays a real or complex number, expression, list, or matrix as a fraction simplified to its simplest terms.

                                                                                                                                                                                                                                                  Availability: Token available everywhere.

                                                                                                                                                                                                                                                  Syntax

                                                                                                                                                                                                                                                  value►Frac

                                                                                                                                                                                                                                                  Arguments

                                                                                                                                                                                                                                                  NameTypeOptional
                                                                                                                                                                                                                                                  value

                                                                                                                                                                                                                                                  Location

                                                                                                                                                                                                                                                  math, MATH, 1:Frac

                                                                                                                                                                                                                                                  Description

                                                                                                                                                                                                                                                  ►Frac attempts to display the input in fraction form. It only works on the home screen outside a program, or with the Disp and Pause commands in a program. It takes up to 12 decimal places of a non-terminating decimal to find the corresponding fraction. The decimal input is returned if ►Frac fails to find the fraction form.

                                                                                                                                                                                                                                                  For a more versatile algorithm for finding fractions, see the Decimal to Fraction routine.

                                                                                                                                                                                                                                                  .333►Frac
        .333
.333333333333►Frac
         1/3

                                                                                                                                                                                                                                                  See Also

                                                                                                                                                                                                                                                  Source: parts of this page were written by the following TI|BD contributors: alexrudd, burr, CloudVariable, DarkerLine, GoVegan, kg583, Myles_Zadok.

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                                                                                                                                                                                                                                                  • FR: ►Nom(

                                                                                                                                                                                                                                                  ►Nom(

                                                                                                                                                                                                                                                  Overview

                                                                                                                                                                                                                                                  Computes the nominal interest rate.

                                                                                                                                                                                                                                                  Availability: Token available everywhere.

                                                                                                                                                                                                                                                  Syntax

                                                                                                                                                                                                                                                  ►Nom(effective rate,compounding periods)

                                                                                                                                                                                                                                                  Arguments

                                                                                                                                                                                                                                                  NameTypeOptional
                                                                                                                                                                                                                                                  effective rate
                                                                                                                                                                                                                                                  compounding periods

                                                                                                                                                                                                                                                  Location

                                                                                                                                                                                                                                                  apps, 1:Finance, CALC, B:►Nom(

                                                                                                                                                                                                                                                  Description

                                                                                                                                                                                                                                                  The ►Nom( command converts from an effective interest rate to a nominal interest rate. In other words, it converts an interest rate that takes compounding periods into account into one that doesn't. The two arguments are 1) the interest rate and 2) the number of compounding periods.

                                                                                                                                                                                                                                                  For example, you want to know the interest rate, compounded monthly, that will yield a total increase of 10% per year:

                                                                                                                                                                                                                                                  ►Nom(10,12)
    9.568968515

                                                                                                                                                                                                                                                  Formulas

                                                                                                                                                                                                                                                  The formula for converting from an effective rate to a nominal rate is:

                                                                                                                                                                                                                                                  (1) \(\begin{align} \texttt{Nom}=100 \texttt{CP} \left(\sqrt[\texttt{CP}]{\frac{\texttt{Eff}}{100}+1}-1\right) \end{align}\)

                                                                                                                                                                                                                                                  Here, Eff is the effective rate, Nom is the nominal rate, and CP is the number of compounding periods.

                                                                                                                                                                                                                                                  Error Conditions

                                                                                                                                                                                                                                                  • ERR:DOMAIN is thrown if the number of compounding periods is not positive, or if the nominal rate is -100% or lower (an exception's made for the nominal rate if there is only one compounding period, since ►Nom(X,1)=X).

                                                                                                                                                                                                                                                  Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Xeda Elnara.

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                                                                                                                                                                                                                                                  • FR: ►Polaire

                                                                                                                                                                                                                                                  ►Polar

                                                                                                                                                                                                                                                  Overview

                                                                                                                                                                                                                                                  Displays complex value in polar format.

                                                                                                                                                                                                                                                  Availability: Token available everywhere.

                                                                                                                                                                                                                                                  Syntax

                                                                                                                                                                                                                                                  complex value ►Polar

                                                                                                                                                                                                                                                  Arguments

                                                                                                                                                                                                                                                  NameTypeOptional
                                                                                                                                                                                                                                                  complex valuecomplex

                                                                                                                                                                                                                                                  Location

                                                                                                                                                                                                                                                  math, CMPLX, 7:Polar

                                                                                                                                                                                                                                                  Description

                                                                                                                                                                                                                                                  The ►Polar command can be used when displaying a complex number on the home screen, or with the Disp and Pause commands. It will then format the number as though r𝑒^θ𝑖 mode were enabled. It also works with lists.

                                                                                                                                                                                                                                                  i
    i
i►Polar
    1𝑒^(1.570796327i)
{1,i}►Polar
    {1 1𝑒^(1.570796327i)}

                                                                                                                                                                                                                                                  It will also work when displaying a number by putting it on the last line of a program by itself. It does not work with Output(, Text(, or any other more complicated display commands.

                                                                                                                                                                                                                                                  To actually separate a number into the components of polar form, use abs( and angle(.

                                                                                                                                                                                                                                                  Error Conditions

                                                                                                                                                                                                                                                  • ERR:SYNTAX is thrown if the command is used somewhere other than the allowed display commands.
                                                                                                                                                                                                                                                  • ERR:DATA TYPE is thrown if the value is real.

                                                                                                                                                                                                                                                  Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan.

                                                                                                                                                                                                                                                  History

                                                                                                                                                                                                                                                  Calculator OS Version Description
                                                                                                                                                                                                                                                  TI-83 0.01013 Added
                                                                                                                                                                                                                                                  Property Value
                                                                                                                                                                                                                                                  Hex Value $BB2F
                                                                                                                                                                                                                                                  Categories
                                                                                                                                                                                                                                                  Localizations
                                                                                                                                                                                                                                                  • FR: ►Rect

                                                                                                                                                                                                                                                  ►Rect

                                                                                                                                                                                                                                                  Overview

                                                                                                                                                                                                                                                  Displays complex value or list in rectangular format.

                                                                                                                                                                                                                                                  Availability: Token available everywhere.

                                                                                                                                                                                                                                                  Syntax

                                                                                                                                                                                                                                                  complex value ►Rect

                                                                                                                                                                                                                                                  Arguments

                                                                                                                                                                                                                                                  NameTypeOptional
                                                                                                                                                                                                                                                  complex valuecomplex

                                                                                                                                                                                                                                                  Location

                                                                                                                                                                                                                                                  math, CMPLX, 6:Rect

                                                                                                                                                                                                                                                  Description

                                                                                                                                                                                                                                                  The ►Rect command can be used when displaying a complex number on the home screen, or with the Disp and Pause commands. It will then format the number as though a+b𝑖 mode were enabled, even when it's not. It also works with lists.

                                                                                                                                                                                                                                                  i►Polar
    1𝑒^(1.570796327i)
Ans►Rect
    i

                                                                                                                                                                                                                                                  It will also work when displaying a number by putting it on the last line of a program by itself. It does not work with Output(, Text(, or any other more complicated display commands.

                                                                                                                                                                                                                                                  To actually separate a number into the components of rectangular form, use real( and imag(.

                                                                                                                                                                                                                                                  Error Conditions

                                                                                                                                                                                                                                                  • ERR:SYNTAX is thrown if the command is used somewhere other than the allowed display commands.
                                                                                                                                                                                                                                                  • ERR:DATA TYPE is thrown if the value is real.

                                                                                                                                                                                                                                                  Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

                                                                                                                                                                                                                                                  History

                                                                                                                                                                                                                                                  Calculator OS Version Description
                                                                                                                                                                                                                                                  TI-83 0.01013 Added
                                                                                                                                                                                                                                                  Property Value
                                                                                                                                                                                                                                                  Hex Value $EF97
                                                                                                                                                                                                                                                  Categories
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                                                                                                                                                                                                                                                    • FR: versChaîne(

                                                                                                                                                                                                                                                    toString(

                                                                                                                                                                                                                                                    Overview

                                                                                                                                                                                                                                                    Converts value to a string where value can be real, complex, an evaluated expression, list, or matrix. String value displays in classic format (0) following the mode setting AUTO/DEC or in decimal format (1).

                                                                                                                                                                                                                                                    Comment:CE OS 5.2+

                                                                                                                                                                                                                                                    Availability: Token only available from within the Basic editor.

                                                                                                                                                                                                                                                    Syntax

                                                                                                                                                                                                                                                    toString((value[,format])

                                                                                                                                                                                                                                                    Arguments

                                                                                                                                                                                                                                                    NameTypeOptional
                                                                                                                                                                                                                                                    valueYes
                                                                                                                                                                                                                                                    formatYes

                                                                                                                                                                                                                                                    Location

                                                                                                                                                                                                                                                    prgm, E:toString(, C:toString(

                                                                                                                                                                                                                                                    Description

                                                                                                                                                                                                                                                    The toString( command, given any value including real numbers, complex numbers, lists, or matrices, returns the string representation of the value of the input.

                                                                                                                                                                                                                                                    toString(1337       //returns "1337"

toString({1,2,3}    //returns "{1,2,3}"

toString([[1,2][3,4]]   //returns "[[1,2][3,4]]"

toString(√-1     //returns imaginary number "i"

                                                                                                                                                                                                                                                    toString( has less limitations than the eval( command. It can handle lists, matrices, and complex numbers. Another difference from eval( is that toString( is affected by display mode changes like Fix.

                                                                                                                                                                                                                                                    toString( replaces the old number-to-string routine previously used prior to OS 5.2.

                                                                                                                                                                                                                                                    Error Conditions

                                                                                                                                                                                                                                                    • ERR:DATA TYPE is thrown when the input is a string.
                                                                                                                                                                                                                                                    • ERR:NONREAL ANSWERS is thrown when the input is a complex number and your calculator is in REAL mode.
                                                                                                                                                                                                                                                    • ERR:SYNTAX is thrown when trying to evaluate a command that doesn't return a value.

                                                                                                                                                                                                                                                    Source: parts of this page were written by the following TI|BD contributors: Battlesquid, jonbush, kg583, Michael2_3B, VoxelPrismatic.

                                                                                                                                                                                                                                                    History

                                                                                                                                                                                                                                                    Calculator OS Version Description
                                                                                                                                                                                                                                                    TI-84+CE 5.2.0 Added
                                                                                                                                                                                                                                                    Property Value
                                                                                                                                                                                                                                                    Hex Value $EF30
                                                                                                                                                                                                                                                    Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: ►n⁄d◄►Un⁄d

                                                                                                                                                                                                                                                      ►n⁄d◄►Un⁄d

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Converts the results from a fraction to mixed number or from a mixed number to a fraction, if applicable.

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      ►n/d ◄►Un/d

                                                                                                                                                                                                                                                      Arguments

                                                                                                                                                                                                                                                      NameTypeOptional
                                                                                                                                                                                                                                                      ◄►

                                                                                                                                                                                                                                                      Location

                                                                                                                                                                                                                                                      alpha, F1, 3:, n/d, Un/d

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      n/d_Un/d is the command for switching between an improper fraction and a mixed number.
                                                                                                                                                                                                                                                      It is accessible by pressing ALPHA then Y= then 3.

                                                                                                                                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: ccrh2009.

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-84+ 2.53 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $BB1C
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: StudentFdp(

                                                                                                                                                                                                                                                      tpdf(

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Computes the probability density function (pdf) for the Student-t distribution at a specified x value with specified degrees of freedom df.

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      tpdf(x,df)

                                                                                                                                                                                                                                                      Arguments

                                                                                                                                                                                                                                                      NameTypeOptional
                                                                                                                                                                                                                                                      x
                                                                                                                                                                                                                                                      df

                                                                                                                                                                                                                                                      Location

                                                                                                                                                                                                                                                      2nd, distr, DISTR, 5:tpdf(

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      tpdf( is the Student's t probability density function.

                                                                                                                                                                                                                                                      Since the t distribution is continuous, the value of tpdf( doesn't represent an actual probability — in fact, one of the few uses for this command is to draw a graph of the bell curve. You could also use it for various calculus purposes, such as finding inflection points.

                                                                                                                                                                                                                                                      The command takes two arguments: the first is the value where the PDF is to be evaluated, and the second is the number of degrees of freedom (so the calculator knows which t distribution to use). As the degrees of freedom increases without bound, tpdf( approaches normalpdf(; i.e.

                                                                                                                                                                                                                                                      (1) \(\begin{align} \lim_{\nu\rightarrow\infty}\texttt{tpdf}(x,\nu)=\texttt{normalpdf}(x) \end{align}\)

                                                                                                                                                                                                                                                      Formulas

                                                                                                                                                                                                                                                      The value of tpdf( is given by

                                                                                                                                                                                                                                                      (2) \(\begin{align} \texttt{tpdf}(t,\nu) = \frac{\Gamma((\nu+1)/2)}{\sqrt{\nu\pi}\,\Gamma(\nu/2)}\,\left(1+\frac{t^2}{\nu}\right)^{-\frac1{2}(\nu+1)} \end{align}\)

                                                                                                                                                                                                                                                      (where Γ is the gamma function), or alternatively

                                                                                                                                                                                                                                                      (3) \(\begin{align} \texttt{tpdf}(t,\nu) = \frac1{\sqrt{\nu}B(\nu/2,1/2)}\,\left(1+\frac{t^2}{\nu}\right)^{-\frac1{2}(\nu+1)} \end{align}\)

                                                                                                                                                                                                                                                      (where B is the beta function)

                                                                                                                                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583, thornahawk.

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-83 0.01013 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $BB24
                                                                                                                                                                                                                                                      Categories
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                                                                                                                                                                                                                                                      • FR: tvm_VAC

                                                                                                                                                                                                                                                      tvm_FV

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Computes the future value.

                                                                                                                                                                                                                                                      Comment:pre-CE french was vat_vacq

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      tvm_FV[(𝗡,I%,PV,PMT,P/Y,C/Y)]

                                                                                                                                                                                                                                                      Arguments

                                                                                                                                                                                                                                                      NameTypeOptional
                                                                                                                                                                                                                                                      𝗡Yes
                                                                                                                                                                                                                                                      I%Yes
                                                                                                                                                                                                                                                      PVYes
                                                                                                                                                                                                                                                      PMTYes
                                                                                                                                                                                                                                                      P/YYes
                                                                                                                                                                                                                                                      C/YYes

                                                                                                                                                                                                                                                      Location

                                                                                                                                                                                                                                                      apps, 1:Finance, CALC, 6:tvm_FV

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      The tvm__VAR_ commands use the TVM (Time Value of Money) solver to solve for the variable VAR. They're usually used in programs, since outside a program it's easier to use the interactive solver (the first option in the finance menu).

                                                                                                                                                                                                                                                      All five commands can be used by themselves, with no arguments. In that case, they will return the value of VAR solved from the current values of the other finance variables.

                                                                                                                                                                                                                                                      If you give them arguments, the values you give will replace the values of the finance variables. You can supply as many or as few arguments as needed, and the finance variables will be replaced in the order: N, I%, PV, PMT, FV, P/Y, C/Y (skipping the one you're solving for).

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      • ERR:ITERATIONS is thrown if the maximum amount of iterations was exceeded in computing I% (this usually means there is no solution)
                                                                                                                                                                                                                                                      • ERR:NO SIGN CHG is thrown if calculating I% when FV, (N*PMT), and PV all have the same sign.

                                                                                                                                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, J_Walker87.

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-83 0.01013 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $BB21
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: tvm_I%

                                                                                                                                                                                                                                                      tvm_I%

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Computes the annual interest rate.

                                                                                                                                                                                                                                                      Comment:pre-CE french was vat_I

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      tvm_I%[(𝗡,PV,PMT,FV,P/Y,C/Y)]

                                                                                                                                                                                                                                                      Arguments

                                                                                                                                                                                                                                                      NameTypeOptional
                                                                                                                                                                                                                                                      I%Yes
                                                                                                                                                                                                                                                      𝗡Yes
                                                                                                                                                                                                                                                      PVYes
                                                                                                                                                                                                                                                      PMTYes
                                                                                                                                                                                                                                                      FVYes
                                                                                                                                                                                                                                                      P/YYes
                                                                                                                                                                                                                                                      C/YYes

                                                                                                                                                                                                                                                      Location

                                                                                                                                                                                                                                                      apps, 1:Finance, CALC, 3:tvm_

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      The tvm__VAR_ commands use the TVM (Time Value of Money) solver to solve for the variable VAR. They're usually used in programs, since outside a program it's easier to use the interactive solver (the first option in the finance menu).

                                                                                                                                                                                                                                                      All five commands can be used by themselves, with no arguments. In that case, they will return the value of VAR solved from the current values of the other finance variables.

                                                                                                                                                                                                                                                      If you give them arguments, the values you give will replace the values of the finance variables. You can supply as many or as few arguments as needed, and the finance variables will be replaced in the order: N, I%, PV, PMT, FV, P/Y, C/Y (skipping the one you're solving for).

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      • ERR:ITERATIONS is thrown if the maximum amount of iterations was exceeded in computing I% (this usually means there is no solution)
                                                                                                                                                                                                                                                      • ERR:NO SIGN CHG is thrown if calculating I% when FV, (N*PMT), and PV all have the same sign.

                                                                                                                                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, J_Walker87.

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-83 0.01013 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $BB23
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: tvm_𝗡

                                                                                                                                                                                                                                                      tvm_𝗡

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Computes the number of payment periods.

                                                                                                                                                                                                                                                      Comment:pre-CE french was vat_𝗡

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      tvm_𝗡[(I%,PV,PMT,FV,P/Y,C/Y)]

                                                                                                                                                                                                                                                      Arguments

                                                                                                                                                                                                                                                      NameTypeOptional
                                                                                                                                                                                                                                                      𝗡Yes
                                                                                                                                                                                                                                                      I%Yes
                                                                                                                                                                                                                                                      PVYes
                                                                                                                                                                                                                                                      PMTYes
                                                                                                                                                                                                                                                      FVYes
                                                                                                                                                                                                                                                      P/YYes
                                                                                                                                                                                                                                                      C/YYes

                                                                                                                                                                                                                                                      Location

                                                                                                                                                                                                                                                      apps, 1:Finance, CALC, 5:tvm_

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      The tvm__VAR_ commands use the TVM (Time Value of Money) solver to solve for the variable VAR. They're usually used in programs, since outside a program it's easier to use the interactive solver (the first option in the finance menu).

                                                                                                                                                                                                                                                      All five commands can be used by themselves, with no arguments. In that case, they will return the value of VAR solved from the current values of the other finance variables.

                                                                                                                                                                                                                                                      If you give them arguments, the values you give will replace the values of the finance variables. You can supply as many or as few arguments as needed, and the finance variables will be replaced in the order: N, I%, PV, PMT, FV, P/Y, C/Y (skipping the one you're solving for).

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      • ERR:ITERATIONS is thrown if the maximum amount of iterations was exceeded in computing I% (this usually means there is no solution)
                                                                                                                                                                                                                                                      • ERR:NO SIGN CHG is thrown if calculating I% when FV, (N*PMT), and PV all have the same sign.

                                                                                                                                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, J_Walker87.

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-83 0.01013 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $BB22
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: tvm_VA

                                                                                                                                                                                                                                                      tvm_PV

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Computes the present value.

                                                                                                                                                                                                                                                      Comment:pre-CE french was vat_Vact

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      tvm_PV[(𝗡,I%,PMT,FV,P/Y,C/Y)]

                                                                                                                                                                                                                                                      Arguments

                                                                                                                                                                                                                                                      NameTypeOptional
                                                                                                                                                                                                                                                      𝗡Yes
                                                                                                                                                                                                                                                      I%Yes
                                                                                                                                                                                                                                                      PMTYes
                                                                                                                                                                                                                                                      FVYes
                                                                                                                                                                                                                                                      P/YYes
                                                                                                                                                                                                                                                      C/YYes

                                                                                                                                                                                                                                                      Location

                                                                                                                                                                                                                                                      apps, 1:Finance, CALC, 4:tvm_PV

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      The tvm__VAR_ commands use the TVM (Time Value of Money) solver to solve for the variable VAR. They're usually used in programs, since outside a program it's easier to use the interactive solver (the first option in the finance menu).

                                                                                                                                                                                                                                                      All five commands can be used by themselves, with no arguments. In that case, they will return the value of VAR solved from the current values of the other finance variables.

                                                                                                                                                                                                                                                      If you give them arguments, the values you give will replace the values of the finance variables. You can supply as many or as few arguments as needed, and the finance variables will be replaced in the order: N, I%, PV, PMT, FV, P/Y, C/Y (skipping the one you're solving for).

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      • ERR:ITERATIONS is thrown if the maximum amount of iterations was exceeded in computing I% (this usually means there is no solution)
                                                                                                                                                                                                                                                      • ERR:NO SIGN CHG is thrown if calculating I% when FV, (N*PMT), and PV all have the same sign.

                                                                                                                                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, J_Walker87.

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-83 0.01013 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $BB20
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: tvm_Pmt

                                                                                                                                                                                                                                                      tvm_Pmt

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Computes the amount of each payment.

                                                                                                                                                                                                                                                      Comment:pre-CE french was vatPmt

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      tvm_Pmt[(𝗡,I%,PV,FV,P/Y,C/Y)]

                                                                                                                                                                                                                                                      Arguments

                                                                                                                                                                                                                                                      NameTypeOptional
                                                                                                                                                                                                                                                      𝗡Yes
                                                                                                                                                                                                                                                      I%Yes
                                                                                                                                                                                                                                                      PVYes
                                                                                                                                                                                                                                                      FVYes
                                                                                                                                                                                                                                                      P/YYes
                                                                                                                                                                                                                                                      C/YYes

                                                                                                                                                                                                                                                      Location

                                                                                                                                                                                                                                                      apps, 1:Finance, CALC, 2:tvm_Pmt

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      The tvm__VAR_ commands use the TVM (Time Value of Money) solver to solve for the variable VAR. They're usually used in programs, since outside a program it's easier to use the interactive solver (the first option in the finance menu).

                                                                                                                                                                                                                                                      All five commands can be used by themselves, with no arguments. In that case, they will return the value of VAR solved from the current values of the other finance variables.

                                                                                                                                                                                                                                                      If you give them arguments, the values you give will replace the values of the finance variables. You can supply as many or as few arguments as needed, and the finance variables will be replaced in the order: N, I%, PV, PMT, FV, P/Y, C/Y (skipping the one you're solving for).

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      • ERR:ITERATIONS is thrown if the maximum amount of iterations was exceeded in computing I% (this usually means there is no solution)
                                                                                                                                                                                                                                                      • ERR:NO SIGN CHG is thrown if calculating I% when FV, (N*PMT), and PV all have the same sign.

                                                                                                                                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, J_Walker87.

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-83 0.01013 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $BB23
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: tvm_𝗡

                                                                                                                                                                                                                                                      tvm_𝗡

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Computes the number of payment periods.

                                                                                                                                                                                                                                                      Comment:pre-CE french was vat_𝗡

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      tvm_𝗡[(I%,PV,PMT,FV,P/Y,C/Y)]

                                                                                                                                                                                                                                                      Arguments

                                                                                                                                                                                                                                                      NameTypeOptional
                                                                                                                                                                                                                                                      𝗡Yes
                                                                                                                                                                                                                                                      I%Yes
                                                                                                                                                                                                                                                      PVYes
                                                                                                                                                                                                                                                      PMTYes
                                                                                                                                                                                                                                                      FVYes
                                                                                                                                                                                                                                                      P/YYes
                                                                                                                                                                                                                                                      C/YYes

                                                                                                                                                                                                                                                      Location

                                                                                                                                                                                                                                                      apps, 1:Finance, CALC, 5:tvm_

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      The tvm__VAR_ commands use the TVM (Time Value of Money) solver to solve for the variable VAR. They're usually used in programs, since outside a program it's easier to use the interactive solver (the first option in the finance menu).

                                                                                                                                                                                                                                                      All five commands can be used by themselves, with no arguments. In that case, they will return the value of VAR solved from the current values of the other finance variables.

                                                                                                                                                                                                                                                      If you give them arguments, the values you give will replace the values of the finance variables. You can supply as many or as few arguments as needed, and the finance variables will be replaced in the order: N, I%, PV, PMT, FV, P/Y, C/Y (skipping the one you're solving for).

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      • ERR:ITERATIONS is thrown if the maximum amount of iterations was exceeded in computing I% (this usually means there is no solution)
                                                                                                                                                                                                                                                      • ERR:NO SIGN CHG is thrown if calculating I% when FV, (N*PMT), and PV all have the same sign.

                                                                                                                                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, J_Walker87.

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-83 0.01013 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $EF88
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: u(𝑛)

                                                                                                                                                                                                                                                      u(𝑛)

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Comment:CE OS 5.2+

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      u(𝑛)

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-84+CE 5.2.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $EF8B
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: u(𝑛+1)

                                                                                                                                                                                                                                                      u(𝑛+1)

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Comment:CE OS 5.2+

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      u(𝑛+1)

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-84+CE 5.2.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $EF85
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: u(𝑛-1)

                                                                                                                                                                                                                                                      u(𝑛-1)

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Comment:CE OS 5.2+

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      u(𝑛-1)

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-84+CE 5.2.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $EF82
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: u(𝑛-2)

                                                                                                                                                                                                                                                      u(𝑛-2)

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Comment:CE OS 5.2+

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      u(𝑛-2)

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-84+CE 5.2.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $6304
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: u(𝑛Min)

                                                                                                                                                                                                                                                      u(𝑛Min)

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      u(𝑛Min)

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-82 1.0 UnStart added
                                                                                                                                                                                                                                                      TI-83 0.01013 Renamed UnStart to u(𝑛Min)
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $EF88
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: u(𝑛)

                                                                                                                                                                                                                                                      u(𝑛)

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Comment:CE OS 5.2+

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      u(𝑛)

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-84+CE 5.2.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $EF8B
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: u(𝑛+1)

                                                                                                                                                                                                                                                      u(𝑛+1)

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Comment:CE OS 5.2+

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      u(𝑛+1)

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-84+CE 5.2.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $EF85
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: u(𝑛-1)

                                                                                                                                                                                                                                                      u(𝑛-1)

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Comment:CE OS 5.2+

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      u(𝑛-1)

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-84+CE 5.2.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $EF82
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: u(𝑛-2)

                                                                                                                                                                                                                                                      u(𝑛-2)

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Comment:CE OS 5.2+

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      u(𝑛-2)

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-84+CE 5.2.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $6304
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: u(𝑛Min)

                                                                                                                                                                                                                                                      u(𝑛Min)

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      u(𝑛Min)

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-82 1.0 UnStart added
                                                                                                                                                                                                                                                      TI-83 0.01013 Renamed UnStart to u(𝑛Min)
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $BBC5
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: u

                                                                                                                                                                                                                                                      u

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      u

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-83+ 1.03 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $5E80
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: |u

                                                                                                                                                                                                                                                      |u

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      |u

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $BBED
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: ↑

                                                                                                                                                                                                                                                      ↑

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      ↑

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-83+ 1.16 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $6233
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: bornsup

                                                                                                                                                                                                                                                      upper

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      upper

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $7E10
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: uvAxes

                                                                                                                                                                                                                                                      uvAxes

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Sets sequence graphs to plot u(n``) on the x-axis and v(``n``) on the y-axis.

                                                                                                                                                                                                                                                      Availability: Token only available from within the Basic editor.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      uvAxes

                                                                                                                                                                                                                                                      Location

                                                                                                                                                                                                                                                      2nd, format, uv

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      When uvAxes is enabled, and the calculator is in Seq mode, the equations u and v will be graphed against each other (that is, the points (u(n),v(n)) are graphed for the values of n between n_Min and _n_Max). With this setting, sequence mode graphs are a bit like parametric mode, except the parameter _n is always an integer, and recursive definitions are possible.

                                                                                                                                                                                                                                                      The equation w is ignored when in uvAxes mode.

                                                                                                                                                                                                                                                      See "Related Commands" for other possibilities of graphing sequences.

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $7E12
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: uwAxes

                                                                                                                                                                                                                                                      uwAxes

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Sets sequence graphs to plot u(n``) on the x-axis and w(``n``) on the y-axis.

                                                                                                                                                                                                                                                      Availability: Token only available from within the Basic editor.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      uwAxes

                                                                                                                                                                                                                                                      Location

                                                                                                                                                                                                                                                      2nd, format, uw

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      When uwAxes is enabled, and the calculator is in Seq mode, the equations u and w will be graphed against each other (that is, the points (u(n),w(n)) are graphed for the values of n between n_Min and _n_Max). With this setting, sequence mode graphs are a bit like parametric mode, except the parameter _n is always an integer, and recursive definitions are possible.

                                                                                                                                                                                                                                                      The equation v is ignored when in uwAxes mode.

                                                                                                                                                                                                                                                      See "Related Commands" for other possibilities of graphing sequences.

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $EF89
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: v(𝑛)

                                                                                                                                                                                                                                                      v(𝑛)

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Comment:CE OS 5.2+

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      v(𝑛)

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-84+CE 5.2.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $EF8C
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: v(𝑛+1)

                                                                                                                                                                                                                                                      v(𝑛+1)

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Comment:CE OS 5.2+

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      v(𝑛+1)

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-84+CE 5.2.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $EF86
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: v(𝑛-1)

                                                                                                                                                                                                                                                      v(𝑛-1)

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Comment:CE OS 5.2+

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      v(𝑛-1)

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-84+CE 5.2.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $EF83
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: v(𝑛-2)

                                                                                                                                                                                                                                                      v(𝑛-2)

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Comment:CE OS 5.2+

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      v(𝑛-2)

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-84+CE 5.2.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $6305
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: v(𝑛Min)

                                                                                                                                                                                                                                                      v(𝑛Min)

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      v(𝑛Min)

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-82 1.0 VnStart added
                                                                                                                                                                                                                                                      TI-83 0.01013 Renamed VnStart to v(𝑛Min)
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $EF89
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: v(𝑛)

                                                                                                                                                                                                                                                      v(𝑛)

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Comment:CE OS 5.2+

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      v(𝑛)

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-84+CE 5.2.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $EF8C
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: v(𝑛+1)

                                                                                                                                                                                                                                                      v(𝑛+1)

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Comment:CE OS 5.2+

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      v(𝑛+1)

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-84+CE 5.2.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $EF86
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: v(𝑛-1)

                                                                                                                                                                                                                                                      v(𝑛-1)

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Comment:CE OS 5.2+

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      v(𝑛-1)

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-84+CE 5.2.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $EF83
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: v(𝑛-2)

                                                                                                                                                                                                                                                      v(𝑛-2)

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Comment:CE OS 5.2+

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      v(𝑛-2)

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-84+CE 5.2.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $6305
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: v(𝑛Min)

                                                                                                                                                                                                                                                      v(𝑛Min)

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      v(𝑛Min)

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-82 1.0 VnStart added
                                                                                                                                                                                                                                                      TI-83 0.01013 Renamed VnStart to v(𝑛Min)
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $BBC6
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: v

                                                                                                                                                                                                                                                      v

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      v

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-83+ 1.03 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $5E81
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: |v

                                                                                                                                                                                                                                                      |v

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      |v

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $BB0E
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: variance(

                                                                                                                                                                                                                                                      variance(

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Returns the variance of the elements in list with frequency freqlist.

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      variance(list[,freqlist])

                                                                                                                                                                                                                                                      Arguments

                                                                                                                                                                                                                                                      NameTypeOptional
                                                                                                                                                                                                                                                      listlist
                                                                                                                                                                                                                                                      freqlistlistYes

                                                                                                                                                                                                                                                      Location

                                                                                                                                                                                                                                                      2nd, list, MATH, 8:variance(

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      The variance( command finds the sample variance of a list, a measure of the spread of a distribution. It takes a list of real numbers as a parameter. For example:

                                                                                                                                                                                                                                                      :Prompt L1
:Disp "VARIANCE OF L1",variance(L1

                                                                                                                                                                                                                                                      Advanced Uses

                                                                                                                                                                                                                                                      Frequency lists don't need to be whole numbers; your calculator can handle being told that one element of the list occurs 1/3 of a time, and another occurs 22.7 times. It can even handle a frequency of 0 - it will just ignore that element, as though it weren't there.

                                                                                                                                                                                                                                                      Formulas

                                                                                                                                                                                                                                                      The formula for variance used by this command is:

                                                                                                                                                                                                                                                      (1) \(\begin{align} s_n^2 = \frac{1}{N-1} \sum_{i=1}^N (x_i - \overline{x})^2 \end{align}\)

                                                                                                                                                                                                                                                      This is the formula for sample variance. The formula for population variance, which this command does not use, varies slightly:

                                                                                                                                                                                                                                                      (2) \(\begin{align} \sigma^2 = \frac{1}{N} \sum_{i=1}^N (x_i - \overline{x})^2 \end{align}\)

                                                                                                                                                                                                                                                      If the population variance is required, just multiply the result of variance() by \(1-1/N\).

                                                                                                                                                                                                                                                      With frequencies wi, the formula becomes

                                                                                                                                                                                                                                                      (3) \(\begin{align} s_n^2 = \frac{\sum_{i=1}^N w_i(x_i - \overline{x})^2}{\sum_{i=1}^N (w_i)-1} \end{align}\)

                                                                                                                                                                                                                                                      where \(\overline{x}\) is the mean with frequencies included.

                                                                                                                                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583, thornahawk.

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-83 0.01013 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $7E11
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: vwAxes

                                                                                                                                                                                                                                                      vwAxes

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Sets sequence graphs to plot v(n``) on the x-axis and w(``n``) on the y-axis.

                                                                                                                                                                                                                                                      Availability: Token only available from within the Basic editor.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      vwAxes

                                                                                                                                                                                                                                                      Location

                                                                                                                                                                                                                                                      2nd, format, vw

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      When vwAxes is enabled, and the calculator is in Seq mode, the equations v and w will be graphed against each other (that is, the points (v(n),w(n)) are graphed for the values of n between n_Min and _n_Max). With this setting, sequence mode graphs are a bit like parametric mode, except the parameter _n is always an integer, and recursive definitions are possible.

                                                                                                                                                                                                                                                      The equation u is ignored when in vwAxes mode.

                                                                                                                                                                                                                                                      See "Related Commands" for other possibilities of graphing sequences.

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $EF8A
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: w(𝑛)

                                                                                                                                                                                                                                                      w(𝑛)

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Comment:CE OS 5.2+

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      w(𝑛)

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-84+CE 5.2.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $EF8D
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: w(𝑛+1)

                                                                                                                                                                                                                                                      w(𝑛+1)

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Comment:CE OS 5.2+

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      w(𝑛+1)

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-84+CE 5.2.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $EF87
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: w(𝑛-1)

                                                                                                                                                                                                                                                      w(𝑛-1)

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Comment:CE OS 5.2+

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      w(𝑛-1)

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-84+CE 5.2.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $EF84
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: w(𝑛-2)

                                                                                                                                                                                                                                                      w(𝑛-2)

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Comment:CE OS 5.2+

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      w(𝑛-2)

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-84+CE 5.2.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $6332
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: w(𝑛Min)

                                                                                                                                                                                                                                                      w(𝑛Min)

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      w(𝑛Min)

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-83 0.01013 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $EF8A
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: w(𝑛)

                                                                                                                                                                                                                                                      w(𝑛)

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Comment:CE OS 5.2+

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      w(𝑛)

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-84+CE 5.2.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $EF8D
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: w(𝑛+1)

                                                                                                                                                                                                                                                      w(𝑛+1)

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Comment:CE OS 5.2+

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      w(𝑛+1)

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-84+CE 5.2.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $EF87
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: w(𝑛-1)

                                                                                                                                                                                                                                                      w(𝑛-1)

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Comment:CE OS 5.2+

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      w(𝑛-1)

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-84+CE 5.2.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $EF84
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: w(𝑛-2)

                                                                                                                                                                                                                                                      w(𝑛-2)

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Comment:CE OS 5.2+

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      w(𝑛-2)

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-84+CE 5.2.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $6332
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: w(𝑛Min)

                                                                                                                                                                                                                                                      w(𝑛Min)

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      w(𝑛Min)

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-83 0.01013 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $BBC7
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: w

                                                                                                                                                                                                                                                      w

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      w

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-83+ 1.03 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $5E82
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: |w

                                                                                                                                                                                                                                                      |w

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      |w

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $BBC8
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: x

                                                                                                                                                                                                                                                      x

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      x

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-83+ 1.03 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $BBF0
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                                                                                                                                                                                                                                                      • FR: ×

                                                                                                                                                                                                                                                      ×

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      ×

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-83+ 1.16 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $F1
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                                                                                                                                                                                                                                                      • FR: ˣ√

                                                                                                                                                                                                                                                      ˣ√

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      ˣ√

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $FD
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                                                                                                                                                                                                                                                      • FR: Polygone

                                                                                                                                                                                                                                                      xyLine

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Used as the "type" argument in the command
                                                                                                                                                                                                                                                      Where # gives Plot1, Plot2 or Plot3.

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      Plot#(type,Xlist[,freqlist,color#])

                                                                                                                                                                                                                                                      Arguments

                                                                                                                                                                                                                                                      NameTypeOptional
                                                                                                                                                                                                                                                      typexyLine token
                                                                                                                                                                                                                                                      Xlistlist
                                                                                                                                                                                                                                                      freqlistlist
                                                                                                                                                                                                                                                      color#colorNum

                                                                                                                                                                                                                                                      Location

                                                                                                                                                                                                                                                      2nd, stat plot, TYPE

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      The commands Plot1(, Plot2(, and Plot3(, which are identical except for which stat plot (1, 2, or 3) they affect, define their corresponding stat plot. When the stat plot is defined, it is also turned on so no PlotsOn command is necessary.

                                                                                                                                                                                                                                                      The first argument of the commands is always the type of plot, and is one of Scatter, xyLine, Histogram, Boxplot, ModBoxplot, and NormProbPlot - these types are found in the TYPE submenu of the stat plot menu. The other arguments vary. For all but Histogram and Boxplot, there is a mark argument - this is a dot, a cross, or a box, symbols that can be found in the MARK submenu of the stat plot menu. On color calculators, there is an optional final argument to specify the color of the plot.

                                                                                                                                                                                                                                                      Scatter plot

                                                                                                                                                                                                                                                      Plot#(Scatter, x-list, y-list, mark) defines a scatter plot. The points defined by x-list and y-list are plotted using mark on the graph screen.

                                                                                                                                                                                                                                                      x-list and y-list must be the same length.

                                                                                                                                                                                                                                                      xyLine plot

                                                                                                                                                                                                                                                      Plot#(xyLine, x-list, y-list, mark) defines an xyLine plot. Similarly to a scatter plot, the points defined by x-list and y-list are plotted using mark on the graph screen, but with an xyLine plot they are also connected by a line, in the order that they occur in the lists.

                                                                                                                                                                                                                                                      x-list and y-list must be the same length.

                                                                                                                                                                                                                                                      Histogram plot

                                                                                                                                                                                                                                                      Plot#(Histogram, x-list, freq list) defines a Histogram plot. The x-axis is divided into intervals that are Xscl wide. A bar is drawn in in each interval whose height corresponds to the number of points in the interval. Points that are not between Xmin and Xmax are not tallied.

                                                                                                                                                                                                                                                      Xscl must not be too small - it can divide the screen into no more than 47 different bars.

                                                                                                                                                                                                                                                      Box plot

                                                                                                                                                                                                                                                      Plot#(Boxplot, x-list, freq list) defines a box plot. A rectangular box is drawn whose left edge is Q1 (the first quartile) of the data, and whose right edge is Q3 (the third quartile). A vertical segment is drawn within the box at the median, and 'whiskers' are drawn from the box to the minimum and maximum data points.

                                                                                                                                                                                                                                                      The box plot ignores the Ymax and Ymin dimensions of the screen, and any plots that aren't box plots or modified box plots. Each box plot takes approximately 1/3 of the screen in height, and if more than one are plotted, they will take up different areas of the screen.

                                                                                                                                                                                                                                                      Modified box plot

                                                                                                                                                                                                                                                      Plot#(ModBoxplot, x-list, freq list, mark) defines a modified box plot. This is almost entirely like the normal box plot, except that it also draws outliers. Whiskers are only drawn to the furthers point within 1.5 times the interquartile range (Q3-Q1) of the box. Beyond this point, data points are drawn individually, using mark.

                                                                                                                                                                                                                                                      The box plot ignores the Ymax and Ymin dimensions of the screen, and any plots that aren't box plots or modified box plots. Each box plot takes approximately 1/3 of the screen in height, and if more than one are plotted, they will take up different areas of the screen.

                                                                                                                                                                                                                                                      Normal probability plot

                                                                                                                                                                                                                                                      Plot#(NormProbPlot, data list, data axis, mark) defines a normal probability plot. The mean and standard deviation of the data are calculated. Then for each point, the number of standard deviations it is from the mean is calculated, and the point is plotted against this number using mark. data axis can be either X or Y: it determines whether the value of a point determines it's x-coordinate or y-coordinate.

                                                                                                                                                                                                                                                      The point behind this rather convoluted process is to test the extent to which the data is normally distributed. If it follows the normal distribution closely, then the result will be close to a straight line - otherwise it will be curved.

                                                                                                                                                                                                                                                      Advanced Uses

                                                                                                                                                                                                                                                      After doing a regression, a scatter plot of ʟRESID against the x-list is a useful measure of the effectiveness of the regression. If the plot appears random, this is a good sign; if there is a pattern to the plot, this means it's likely that a better regression model exists.

                                                                                                                                                                                                                                                      Optimization

                                                                                                                                                                                                                                                      The ʟ symbol at the beginning of list names can be omitted everywhere in this command.

                                                                                                                                                                                                                                                      In addition, every element except the plot type and the data list or data lists are optional, and take on the following default values:

                                                                                                                                                                                                                                                      • freq list is 1 by default, meaning that all frequencies are 1.
                                                                                                                                                                                                                                                      • mark is the box by default.
                                                                                                                                                                                                                                                      • data axis is X by default.

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      • ERR:DIM MISMATCH is thrown if the x and y lists, or the data and frequency lists, have different dimensions.
                                                                                                                                                                                                                                                      • ERR:STAT is thrown if Xscl is too small in the case of a Histogram.

                                                                                                                                                                                                                                                      All errors are thrown when plotting the stat plot, as opposed to when the command is executed, and do not provide a 2:Goto option.

                                                                                                                                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Myles_Zadok.

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $6203
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                                                                                                                                                                                                                                                      • FR: x̄

                                                                                                                                                                                                                                                      x̄

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      x̄

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-82 1.0 Added
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                                                                                                                                                                                                                                                      Hex Value $622B
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                                                                                                                                                                                                                                                      • FR: x̄₁

                                                                                                                                                                                                                                                      x̄₁

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      x̄₁

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

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                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $622E
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                                                                                                                                                                                                                                                      • FR: x̄₂

                                                                                                                                                                                                                                                      x̄₂

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      x̄₂

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $621B
                                                                                                                                                                                                                                                      Categories
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                                                                                                                                                                                                                                                      • FR: x₁

                                                                                                                                                                                                                                                      x₁

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      x₁

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

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                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $621C
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                                                                                                                                                                                                                                                      • FR: x₂

                                                                                                                                                                                                                                                      x₂

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      x₂

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $621D
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                                                                                                                                                                                                                                                      • FR: x₃

                                                                                                                                                                                                                                                      x₃

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      x₃

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $BBC9
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                                                                                                                                                                                                                                                      • FR: y

                                                                                                                                                                                                                                                      y

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      y

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-83+ 1.03 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $621E
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                                                                                                                                                                                                                                                      • FR: y₁

                                                                                                                                                                                                                                                      y₁

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      y₁

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $621F
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                                                                                                                                                                                                                                                      • FR: y₂

                                                                                                                                                                                                                                                      y₂

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      y₂

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $6220
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                                                                                                                                                                                                                                                      • FR: y₃

                                                                                                                                                                                                                                                      y₃

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      y₃

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $BBCA
                                                                                                                                                                                                                                                      Categories
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                                                                                                                                                                                                                                                      • FR: z

                                                                                                                                                                                                                                                      z

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      z

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-83+ 1.03 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $08
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                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: {

                                                                                                                                                                                                                                                      {

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      {

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $5E20
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: X₁ᴛ

                                                                                                                                                                                                                                                      X₁ᴛ

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      X₁ᴛ

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $5E22
                                                                                                                                                                                                                                                      Categories
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                                                                                                                                                                                                                                                      • FR: X₂ᴛ

                                                                                                                                                                                                                                                      X₂ᴛ

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      X₂ᴛ

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $5E24
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: X₃ᴛ

                                                                                                                                                                                                                                                      X₃ᴛ

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      X₃ᴛ

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $5E26
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: X₄ᴛ

                                                                                                                                                                                                                                                      X₄ᴛ

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      X₄ᴛ

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

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                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $5E28
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: X₅ᴛ

                                                                                                                                                                                                                                                      X₅ᴛ

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      X₅ᴛ

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $5E2A
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: X₆ᴛ

                                                                                                                                                                                                                                                      X₆ᴛ

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      X₆ᴛ

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $5E19
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: Y₀

                                                                                                                                                                                                                                                      Y₀

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      Y₀

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $5E21
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: Y₁ᴛ

                                                                                                                                                                                                                                                      Y₁ᴛ

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      Y₁ᴛ

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $5E10
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: Y₁

                                                                                                                                                                                                                                                      Y₁

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      Y₁

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $5E23
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: Y₂ᴛ

                                                                                                                                                                                                                                                      Y₂ᴛ

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      Y₂ᴛ

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $5E11
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: Y₂

                                                                                                                                                                                                                                                      Y₂

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      Y₂

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $5E25
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: Y₃ᴛ

                                                                                                                                                                                                                                                      Y₃ᴛ

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      Y₃ᴛ

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $5E12
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: Y₃

                                                                                                                                                                                                                                                      Y₃

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      Y₃

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $5E27
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: Y₄ᴛ

                                                                                                                                                                                                                                                      Y₄ᴛ

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      Y₄ᴛ

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $5E13
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: Y₄

                                                                                                                                                                                                                                                      Y₄

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      Y₄

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $5E29
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: Y₅ᴛ

                                                                                                                                                                                                                                                      Y₅ᴛ

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      Y₅ᴛ

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $5E14
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: Y₅

                                                                                                                                                                                                                                                      Y₅

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      Y₅

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $5E2B
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: Y₆ᴛ

                                                                                                                                                                                                                                                      Y₆ᴛ

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      Y₆ᴛ

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $5E15
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: Y₆

                                                                                                                                                                                                                                                      Y₆

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      Y₆

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $5E16
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: Y₇

                                                                                                                                                                                                                                                      Y₇

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      Y₇

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $5E17
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: Y₈

                                                                                                                                                                                                                                                      Y₈

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      Y₈

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $5E18
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: Y₉

                                                                                                                                                                                                                                                      Y₉

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      Y₉

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $5E40
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: r₁

                                                                                                                                                                                                                                                      r₁

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      r₁

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $5E41
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: r₂

                                                                                                                                                                                                                                                      r₂

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      r₂

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $5E42
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: r₃

                                                                                                                                                                                                                                                      r₃

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      r₃

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $5E43
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: r₄

                                                                                                                                                                                                                                                      r₄

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      r₄

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $5E44
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: r₅

                                                                                                                                                                                                                                                      r₅

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      r₅

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $5E45
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: r₆

                                                                                                                                                                                                                                                      r₆

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      r₆

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $09
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: }

                                                                                                                                                                                                                                                      }

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      }

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $BB9E
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: ¡

                                                                                                                                                                                                                                                      ¡

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      ¡

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-83+ 1.03 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $0B
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: °

                                                                                                                                                                                                                                                      °

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      °

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Normally, when the calculator is in radian mode, the trigonometric functions only return values calculated in radians. With the ° symbol you can have the angle evaluated as if in degree mode because it converts the angle into radians.

                                                                                                                                                                                                                                                      You can insert the degree symbol by pressing [2ND] [ANGLE] [ENTER].

                                                                                                                                                                                                                                                      One full rotation around a circle is 2π radians, which is equal to 360°. To convert an angle in radians to degrees you multiply by 180/π, and to convert from degrees to radians multiply by π/180.

                                                                                                                                                                                                                                                      In radian mode:

                                                                                                                                                                                                                                                      sin(45)        \\ actually calculating sin(2578.31)
    .8509035245
sin(45°)
    .7071067812

                                                                                                                                                                                                                                                      In degree mode:

                                                                                                                                                                                                                                                      sin(45)
    .7071067812
sin(45°)
    .7071067812    \\ There's no difference when in degrees

                                                                                                                                                                                                                                                      Converting Degrees, Minutes & Seconds

                                                                                                                                                                                                                                                      The degree symbol also allows you to convert degrees, minutes and seconds into decimal degrees. For example:

                                                                                                                                                                                                                                                      90°30'
       90.5
90°30'09"
       90.5025

                                                                                                                                                                                                                                                      The minute symbol is inserted by pressing [2ND] [ANGLE] [2]. The seconds symbol is inserted via [ALPHA] [+].

                                                                                                                                                                                                                                                      To convert back the other way (decimal to degrees-minutes-seconds) use the ►DMS command, accessed via [2ND] [ANGLE] [4]:

                                                                                                                                                                                                                                                      90.5025►DMS
       90°30'09"

                                                                                                                                                                                                                                                      Optimization

                                                                                                                                                                                                                                                      When you only call the trig function once in a program and want it calculated in degrees, instead of changing the mode you can just use ° to save one-byte (the newline from using the command Degree)

                                                                                                                                                                                                                                                      :Degree
:sin(X)
can be
:sin(X°)

                                                                                                                                                                                                                                                      Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, simplethinker.

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                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      Ö

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-83+ 1.03 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $BBF0
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: ×

                                                                                                                                                                                                                                                      ×

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      ×

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-83+ 1.16 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $BB8F
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: Ù

                                                                                                                                                                                                                                                      Ù

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      Ù

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-83+ 1.03 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $BB8E
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: Ú

                                                                                                                                                                                                                                                      Ú

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      Ú

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-83+ 1.03 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $BB90
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: Û

                                                                                                                                                                                                                                                      Û

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      Û

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-83+ 1.03 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $BB91
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: Ü

                                                                                                                                                                                                                                                      Ü

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      Ü

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-83+ 1.03 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $BBDD
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: ß

                                                                                                                                                                                                                                                      ß

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      ß

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-83+ 1.16 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $BB73
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: à

                                                                                                                                                                                                                                                      à

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      à

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-83+ 1.03 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $BB72
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: á

                                                                                                                                                                                                                                                      á

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      á

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-83+ 1.03 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $BB74
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: â

                                                                                                                                                                                                                                                      â

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      â

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-83+ 1.03 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $BB75
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: ä

                                                                                                                                                                                                                                                      ä

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      ä

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-83+ 1.03 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $BB97
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: ç

                                                                                                                                                                                                                                                      ç

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      ç

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-83+ 1.03 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $BB7B
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: è

                                                                                                                                                                                                                                                      è

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      è

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-83+ 1.03 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $BB7A
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: é

                                                                                                                                                                                                                                                      é

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      é

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-83+ 1.03 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $BB7C
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: ê

                                                                                                                                                                                                                                                      ê

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      ê

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-83+ 1.03 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $BB7D
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: ë

                                                                                                                                                                                                                                                      ë

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      ë

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-83+ 1.03 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $BB83
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: ì

                                                                                                                                                                                                                                                      ì

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      ì

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-83+ 1.03 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $BB82
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: í

                                                                                                                                                                                                                                                      í

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      í

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-83+ 1.03 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $BB84
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: î

                                                                                                                                                                                                                                                      î

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      î

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-83+ 1.03 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $BB85
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: ï

                                                                                                                                                                                                                                                      ï

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      ï

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-83+ 1.03 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $BB99
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: ñ

                                                                                                                                                                                                                                                      ñ

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      ñ

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-83+ 1.03 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $BB8B
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: ò

                                                                                                                                                                                                                                                      ò

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      ò

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-83+ 1.03 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $BB8A
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: ó

                                                                                                                                                                                                                                                      ó

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      ó

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-83+ 1.03 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $BB8C
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: ô

                                                                                                                                                                                                                                                      ô

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      ô

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-83+ 1.03 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $BB8D
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: ö

                                                                                                                                                                                                                                                      ö

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      ö

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-83+ 1.03 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $BB93
                                                                                                                                                                                                                                                      Categories
                                                                                                                                                                                                                                                      Localizations
                                                                                                                                                                                                                                                      • FR: ù

                                                                                                                                                                                                                                                      ù

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      ù

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-83+ 1.03 Added
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                                                                                                                                                                                                                                                      Hex Value $BB92
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                                                                                                                                                                                                                                                      • FR: ú

                                                                                                                                                                                                                                                      ú

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      ú

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-83+ 1.03 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $BB94
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                                                                                                                                                                                                                                                      • FR: û

                                                                                                                                                                                                                                                      û

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      û

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-83+ 1.03 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $BB95
                                                                                                                                                                                                                                                      Categories
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                                                                                                                                                                                                                                                      • FR: ü

                                                                                                                                                                                                                                                      ü

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Availability: Token available everywhere.

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      ü

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-83+ 1.03 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $620C
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                                                                                                                                                                                                                                                      • FR: ȳ

                                                                                                                                                                                                                                                      ȳ

                                                                                                                                                                                                                                                      Overview

                                                                                                                                                                                                                                                      Syntax

                                                                                                                                                                                                                                                      ȳ

                                                                                                                                                                                                                                                      Description

                                                                                                                                                                                                                                                      Examples

                                                                                                                                                                                                                                                      Explanation 1

                                                                                                                                                                                                                                                      code 1

                                                                                                                                                                                                                                                      Explanation 2

                                                                                                                                                                                                                                                      code 2

                                                                                                                                                                                                                                                      Error Conditions

                                                                                                                                                                                                                                                      Advanced Notes

                                                                                                                                                                                                                                                      History

                                                                                                                                                                                                                                                      Calculator OS Version Description
                                                                                                                                                                                                                                                      TI-82 1.0 Added
                                                                                                                                                                                                                                                      Property Value
                                                                                                                                                                                                                                                      Hex Value $EB
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                                                                                                                                                                                                                                                        • FR: ʟ

                                                                                                                                                                                                                                                        ʟ

                                                                                                                                                                                                                                                        Overview

                                                                                                                                                                                                                                                        Identifies the next one to five characters as a user-created list name.

                                                                                                                                                                                                                                                        Availability: Token available everywhere.

                                                                                                                                                                                                                                                        Syntax

                                                                                                                                                                                                                                                        ʟlistname

                                                                                                                                                                                                                                                        Arguments

                                                                                                                                                                                                                                                        NameTypeOptional
                                                                                                                                                                                                                                                        listnamelist

                                                                                                                                                                                                                                                        Location

                                                                                                                                                                                                                                                        2nd, list, OPS, B:

                                                                                                                                                                                                                                                        Description

                                                                                                                                                                                                                                                        The ʟ character is used at the start of the name of any custom list you create, for example:

                                                                                                                                                                                                                                                        {1,2,3}→ʟHELLO
{4,5,6}→ʟWORLD

                                                                                                                                                                                                                                                        In most cases you need to include this when accessing or manipulating a custom list (although there's a few exceptions, see the Optimization section below). You do not need this character when accessing the the default lists L₁…L₆).

                                                                                                                                                                                                                                                        The maximum length of the list name (not including the ʟ) is five letters. ʟABCDE works, but ʟABCDEF does not. List names must start with a letter A-Z but can also include numbers so ʟLIST1 and ʟLIST2 are valid list names, but ʟ123 is not.

                                                                                                                                                                                                                                                        There are two ways to insert this character:

                                                                                                                                                                                                                                                        1. Press 2nd, LIST, press right arrow to access the OPS menu, scroll to the bottom, and press ENTER to insert the ʟ character. You can then type the rest of the name of your list.
                                                                                                                                                                                                                                                        2. If your custom list already exists, you can press 2nd, LIST, select the name of your list, and press ENTER. The whole name including the ʟ character will be inserted.

                                                                                                                                                                                                                                                        Optimization

                                                                                                                                                                                                                                                        You don't actually need to include the ʟ command when storing (→) to a list.

                                                                                                                                                                                                                                                        {1,2,3}→HELLO
{4,5,6}→WORLD
{7,8,9}→X

                                                                                                                                                                                                                                                        Although the name X as used above also matches the name of a regular real variable, since the data being stored is a list, it will be saved to ʟX.

                                                                                                                                                                                                                                                        When storing to a specific list item, you MUST still include the ʟ character:

                                                                                                                                                                                                                                                        1→ʟHELLO(1)
2→ʟWORLD(2)
3→ʟX(3)

                                                                                                                                                                                                                                                        Some of the list commands also allow for leaving off the ʟ character, such as SetUpEditor. However, be careful when doing so with Input and Prompt because you might only be asking the user to input a list, but if a real value is entered, it would be saved to a real variable instead.

                                                                                                                                                                                                                                                        Error Conditions

                                                                                                                                                                                                                                                        • ERR:SYNTAX is thrown if you try to reference/create a list with more than 5 characters in its name.
                                                                                                                                                                                                                                                        • ERR:UNDEFINED is thrown if you try to use ʟ on an undefined list.

                                                                                                                                                                                                                                                        Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583, Timtech.

                                                                                                                                                                                                                                                        History

                                                                                                                                                                                                                                                        Calculator OS Version Description
                                                                                                                                                                                                                                                        TI-83 0.01013 Added
                                                                                                                                                                                                                                                        Property Value
                                                                                                                                                                                                                                                        Hex Value $0A
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                                                                                                                                                                                                                                                        • FR: ʳ

                                                                                                                                                                                                                                                        ʳ

                                                                                                                                                                                                                                                        Overview

                                                                                                                                                                                                                                                        Availability: Token available everywhere.

                                                                                                                                                                                                                                                        Syntax

                                                                                                                                                                                                                                                        ʳ

                                                                                                                                                                                                                                                        Description

                                                                                                                                                                                                                                                        Normally, when the calculator is in degree mode, the trigonometric functions only return values calculated in degrees. With the r symbol you can have the angle evaluated as if in radian mode because it converts the angle into degrees.

                                                                                                                                                                                                                                                        One full rotation around a circle is 2π radians, which is equal to 360°. To convert an angle in radians to degrees you multiply by 180/π, and to convert from degrees to radians multiply by π/180.

                                                                                                                                                                                                                                                        In degree mode:

                                                                                                                                                                                                                                                        sin(π)        \\sine of Pi degrees
    .0548036651
sin(π^^r)
    0

                                                                                                                                                                                                                                                        In radian mode:

                                                                                                                                                                                                                                                        sin(π)
    0
sin(π^^r)
    0        \\There's no difference when in radians

                                                                                                                                                                                                                                                        Optimization

                                                                                                                                                                                                                                                        When you only call the trig function once in a program and want it calculated in radians, instead of changing the mode you can just use ° to save one-byte (the newline from using the command Radian)

                                                                                                                                                                                                                                                        :Radian
:sin(X)
can be
:sin(X^^r)
                                                                                                                                                                                                                                                        • ° (degree symbol)

                                                                                                                                                                                                                                                        Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Myles_Zadok.

                                                                                                                                                                                                                                                        History

                                                                                                                                                                                                                                                        Calculator OS Version Description
                                                                                                                                                                                                                                                        TI-82 1.0 Added
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                                                                                                                                                                                                                                                        Hex Value $BBDE
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                                                                                                                                                                                                                                                        • FR: ˣ

                                                                                                                                                                                                                                                        ˣ

                                                                                                                                                                                                                                                        Overview

                                                                                                                                                                                                                                                        Syntax

                                                                                                                                                                                                                                                        ˣ

                                                                                                                                                                                                                                                        Description

                                                                                                                                                                                                                                                        Examples

                                                                                                                                                                                                                                                        Explanation 1

                                                                                                                                                                                                                                                        code 1

                                                                                                                                                                                                                                                        Explanation 2

                                                                                                                                                                                                                                                        code 2

                                                                                                                                                                                                                                                        Error Conditions

                                                                                                                                                                                                                                                        Advanced Notes

                                                                                                                                                                                                                                                        History

                                                                                                                                                                                                                                                        Calculator OS Version Description
                                                                                                                                                                                                                                                        TI-83+ 1.16 Added
                                                                                                                                                                                                                                                        Property Value
                                                                                                                                                                                                                                                        Hex Value $F1
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                                                                                                                                                                                                                                                        • FR: ˣ√

                                                                                                                                                                                                                                                        ˣ√

                                                                                                                                                                                                                                                        Overview

                                                                                                                                                                                                                                                        Availability: Token available everywhere.

                                                                                                                                                                                                                                                        Syntax

                                                                                                                                                                                                                                                        ˣ√

                                                                                                                                                                                                                                                        Description

                                                                                                                                                                                                                                                        Examples

                                                                                                                                                                                                                                                        Explanation 1

                                                                                                                                                                                                                                                        code 1

                                                                                                                                                                                                                                                        Explanation 2

                                                                                                                                                                                                                                                        code 2

                                                                                                                                                                                                                                                        Error Conditions

                                                                                                                                                                                                                                                        Advanced Notes

                                                                                                                                                                                                                                                        History

                                                                                                                                                                                                                                                        Calculator OS Version Description
                                                                                                                                                                                                                                                        TI-82 1.0 Added
                                                                                                                                                                                                                                                        Property Value
                                                                                                                                                                                                                                                        Hex Value $BBA2
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                                                                                                                                                                                                                                                        • FR: Δ

                                                                                                                                                                                                                                                        Δ

                                                                                                                                                                                                                                                        Overview

                                                                                                                                                                                                                                                        Availability: Token available everywhere.

                                                                                                                                                                                                                                                        Syntax

                                                                                                                                                                                                                                                        Δ

                                                                                                                                                                                                                                                        Description

                                                                                                                                                                                                                                                        Examples

                                                                                                                                                                                                                                                        Explanation 1

                                                                                                                                                                                                                                                        code 1

                                                                                                                                                                                                                                                        Explanation 2

                                                                                                                                                                                                                                                        code 2

                                                                                                                                                                                                                                                        Error Conditions

                                                                                                                                                                                                                                                        Advanced Notes

                                                                                                                                                                                                                                                        History

                                                                                                                                                                                                                                                        Calculator OS Version Description
                                                                                                                                                                                                                                                        TI-83+ 1.03 Added
                                                                                                                                                                                                                                                        Property Value
                                                                                                                                                                                                                                                        Hex Value $BB2C
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                                                                                                                                                                                                                                                          • FR: Δliste(

                                                                                                                                                                                                                                                          ΔList(

                                                                                                                                                                                                                                                          Overview

                                                                                                                                                                                                                                                          Returns a list containing the differences between consecutive elements in list.

                                                                                                                                                                                                                                                          Availability: Token available everywhere.

                                                                                                                                                                                                                                                          Syntax

                                                                                                                                                                                                                                                          ΔList(list)

                                                                                                                                                                                                                                                          Arguments

                                                                                                                                                                                                                                                          NameTypeOptional
                                                                                                                                                                                                                                                          Δ
                                                                                                                                                                                                                                                          listlist

                                                                                                                                                                                                                                                          Location

                                                                                                                                                                                                                                                          2nd, list, OPS, 7:List(

                                                                                                                                                                                                                                                          Description

                                                                                                                                                                                                                                                          ΔList( calculates the differences between consecutive terms of a list, and returns them in a new list.

                                                                                                                                                                                                                                                          ΔList({0,1,4,9,16,25,36})
    {1 3 5 7 9 11}

                                                                                                                                                                                                                                                          Advanced Uses

                                                                                                                                                                                                                                                          The ΔList( command is very nearly the inverse of the cumSum( command, which calculates the cumulative sums of a list. For any list, ΔList(cumSum(list)) will return the same list, but without its first element:

                                                                                                                                                                                                                                                          ΔList(cumSum({1,2,3,4,5,6,7}))
    {2 3 4 5 6 7}

                                                                                                                                                                                                                                                          Removing the first element would otherwise be a difficult procedure involving the seq( command, so this is a useful trick to know.

                                                                                                                                                                                                                                                          If a list is sorted in ascending order, min(ΔList(list)) will return 0 (false) if there are repeating values in the list, and a value corresponding to true if they are all distinct. The number of repeating elements can be determined similarly via 1+sum(0≠ΔList(list)) (again, so long as the list is sorted).

                                                                                                                                                                                                                                                          Error Conditions

                                                                                                                                                                                                                                                          Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, kg583, Timothy Foster.

                                                                                                                                                                                                                                                          History

                                                                                                                                                                                                                                                          Calculator OS Version Description
                                                                                                                                                                                                                                                          TI-83 0.01013 Added
                                                                                                                                                                                                                                                          Property Value
                                                                                                                                                                                                                                                          Hex Value $EF33
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                                                                                                                                                                                                                                                            • FR: Σ(

                                                                                                                                                                                                                                                            Σ(

                                                                                                                                                                                                                                                            Overview

                                                                                                                                                                                                                                                            Classic command as shown.
                                                                                                                                                                                                                                                            In MathPrint™ the summation entry template displays and returns the sum of elements of list from start to end,wherestart<=end.

                                                                                                                                                                                                                                                            Availability: Token available everywhere.

                                                                                                                                                                                                                                                            Syntax

                                                                                                                                                                                                                                                            Σ(expression[,start,end])

                                                                                                                                                                                                                                                            Arguments

                                                                                                                                                                                                                                                            NameTypeOptional
                                                                                                                                                                                                                                                            expressionexpression
                                                                                                                                                                                                                                                            startYes
                                                                                                                                                                                                                                                            endYes

                                                                                                                                                                                                                                                            Location

                                                                                                                                                                                                                                                            math

                                                                                                                                                                                                                                                            Description

                                                                                                                                                                                                                                                            Examples

                                                                                                                                                                                                                                                            Explanation 1

                                                                                                                                                                                                                                                            code 1

                                                                                                                                                                                                                                                            Explanation 2

                                                                                                                                                                                                                                                            code 2

                                                                                                                                                                                                                                                            Error Conditions

                                                                                                                                                                                                                                                            Advanced Notes

                                                                                                                                                                                                                                                            History

                                                                                                                                                                                                                                                            Calculator OS Version Description
                                                                                                                                                                                                                                                            TI-84+ 2.53 Added
                                                                                                                                                                                                                                                            Property Value
                                                                                                                                                                                                                                                            Hex Value $BBA9
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                                                                                                                                                                                                                                                            • FR: Σ

                                                                                                                                                                                                                                                            Σ

                                                                                                                                                                                                                                                            Overview

                                                                                                                                                                                                                                                            Availability: Token available everywhere.

                                                                                                                                                                                                                                                            Syntax

                                                                                                                                                                                                                                                            Σ

                                                                                                                                                                                                                                                            Description

                                                                                                                                                                                                                                                            Examples

                                                                                                                                                                                                                                                            Explanation 1

                                                                                                                                                                                                                                                            code 1

                                                                                                                                                                                                                                                            Explanation 2

                                                                                                                                                                                                                                                            code 2

                                                                                                                                                                                                                                                            Error Conditions

                                                                                                                                                                                                                                                            Advanced Notes

                                                                                                                                                                                                                                                            History

                                                                                                                                                                                                                                                            Calculator OS Version Description
                                                                                                                                                                                                                                                            TI-83+ 1.03 Added
                                                                                                                                                                                                                                                            Property Value
                                                                                                                                                                                                                                                            Hex Value $BB04
                                                                                                                                                                                                                                                            Categories
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                                                                                                                                                                                                                                                            • FR: ΣInt(

                                                                                                                                                                                                                                                            ΣInt(

                                                                                                                                                                                                                                                            Overview

                                                                                                                                                                                                                                                            Computes the sum, rounded to roundvalue, of the interest amount between pmt1 and pmt2 for an amortization schedule.

                                                                                                                                                                                                                                                            Availability: Token available everywhere.

                                                                                                                                                                                                                                                            Syntax

                                                                                                                                                                                                                                                            ΣInt(pmt1,pmt2[,roundvalue])

                                                                                                                                                                                                                                                            Arguments

                                                                                                                                                                                                                                                            NameTypeOptional
                                                                                                                                                                                                                                                            Σ
                                                                                                                                                                                                                                                            pmt1
                                                                                                                                                                                                                                                            pmt2Yes
                                                                                                                                                                                                                                                            roundvalueYes

                                                                                                                                                                                                                                                            Location

                                                                                                                                                                                                                                                            apps, 1:Finance, CALC, A:Int(

                                                                                                                                                                                                                                                            Description

                                                                                                                                                                                                                                                            The ΣInt( command calculates, for an amortization schedule, the interest over a range of payments: the portion of those payments that went toward paying interest. Its two required arguments are payment1 and payment2, which define the range of payments we're interested in. However, it also uses the values of the finance variables PV, PMT, and I% in its calculations.

                                                                                                                                                                                                                                                            The optional argument, roundvalue, is the number of digits to which the calculator will round all internal calculations. Since this rounding affects further steps, this isn't the same as using round( to round the result of ΣInt( to the same number of digits.

                                                                                                                                                                                                                                                            Usually, you will know the values of N, PV, and I%, but not PMT. This means you'll have to use the finance solver to solve for PMT before calculating ΣInt(; virtually always, FV will equal 0.

                                                                                                                                                                                                                                                            Sample Problem

                                                                                                                                                                                                                                                            Imagine that you have taken out a 30-year fixed-rate mortgage. The loan amount is $100000, and the annual interest rate (APR) is 8%. Payments will be made monthly. How much of the amount that was paid in the first five years went towards interest?

                                                                                                                                                                                                                                                            We know the values of N, I%, and PV, though we still need to convert them to monthly values (since payments are made monthly). N is 30*12, and I% is 8/12. PV is just 100000.

                                                                                                                                                                                                                                                            Now, we use the finance solver to solve for PMT. Since you intend to pay out the entire loan, FV is 0. Using either the interactive TVM solver, or the tvm_Pmt command, we get a value of about -$733.76 for PMT.

                                                                                                                                                                                                                                                            We are ready to use ΣInt(. We are interested in the payments made during the first five years; that is, between the 1st payment and the 5*12=60th payment. ΣInt(1,60) gives us the answer: -$39095.73 (the negative sign simply indicates the direction of cash flow)

                                                                                                                                                                                                                                                            Formulas

                                                                                                                                                                                                                                                            ΣInt( is calculated in terms of ΣPrn(, for which a recurrence exists. Since the total amount paid during an interval is known (it's the payment size, multiplied by the number of payments), we can subtract ΣPrn( from this total to get ΣInt(:

                                                                                                                                                                                                                                                            (1) \(\begin{align} \texttt{\Sigma Int}(n_1,n_2)=(n_2-n_1+1)\texttt{PMT}-\texttt{\Sigma Prn}(n_1,n_2) \end{align}\)

                                                                                                                                                                                                                                                            Error Conditions

                                                                                                                                                                                                                                                            • ERR:DOMAIN is thrown if either payment number is negative or a decimal.

                                                                                                                                                                                                                                                            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583.

                                                                                                                                                                                                                                                            History

                                                                                                                                                                                                                                                            Calculator OS Version Description
                                                                                                                                                                                                                                                            TI-83 0.01013 Added
                                                                                                                                                                                                                                                            Property Value
                                                                                                                                                                                                                                                            Hex Value $BB03
                                                                                                                                                                                                                                                            Categories
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                                                                                                                                                                                                                                                            • FR: paSomPrinc(

                                                                                                                                                                                                                                                            ΣPrn(

                                                                                                                                                                                                                                                            Overview

                                                                                                                                                                                                                                                            Computes the sum, rounded to roundvalue, of the principal amount between pmt1 and pmt2 for an amortization schedule.

                                                                                                                                                                                                                                                            Availability: Token available everywhere.

                                                                                                                                                                                                                                                            Syntax

                                                                                                                                                                                                                                                            ΣPrn(pmt1,pmt2[,roundvalue])

                                                                                                                                                                                                                                                            Arguments

                                                                                                                                                                                                                                                            NameTypeOptional
                                                                                                                                                                                                                                                            Σ
                                                                                                                                                                                                                                                            pmt1
                                                                                                                                                                                                                                                            pmt2Yes
                                                                                                                                                                                                                                                            roundvalueYes

                                                                                                                                                                                                                                                            Location

                                                                                                                                                                                                                                                            apps, 1:Finance, CALC, 0:Prn(

                                                                                                                                                                                                                                                            Description

                                                                                                                                                                                                                                                            The ΣPrn( command calculates, for an amortization schedule, the principal amount over a range of payments: the portion of those payments that went toward paying off the principal. Its two required arguments are payment1 and payment2, which define the range of payments we're interested in. However, it also uses the values of the finance variables PV, PMT, and I% in its calculations.

                                                                                                                                                                                                                                                            The optional argument, roundvalue, is the number of digits to which the calculator will round all internal calculations. Since this rounding affects further steps, this isn't the same as using round( to round the result of ΣPrn( to the same number of digits.

                                                                                                                                                                                                                                                            Usually, you will know the values of N, PV, and I%, but not PMT. This means you'll have to use the finance solver to solve for PMT before calculating ΣPrn(; virtually always, FV will equal 0.

                                                                                                                                                                                                                                                            Sample Problem

                                                                                                                                                                                                                                                            Imagine that you have taken out a 30-year fixed-rate mortgage. The loan amount is $100000, and the annual interest rate (APR) is 8%. Payments will be made monthly. How much of the principal amount was paid in the first five years?

                                                                                                                                                                                                                                                            We know the values of N, I%, and PV, though we still need to convert them to monthly values (since payments are made monthly). N is 30*12, and I% is 8/12. PV is just 100000.

                                                                                                                                                                                                                                                            Now, we use the finance solver to solve for PMT. Since you intend to pay out the entire loan, FV is 0. Using either the interactive TVM solver, or the tvm_Pmt command, we get a value of about -$733.76 for PMT.

                                                                                                                                                                                                                                                            We are ready to use ΣPrn(. We are interested in the payments made during the first five years; that is, between the 1st payment and the 5*12=60th payment. ΣPrn(1,60) gives us the answer: -$4930.14 (the negative sign simply indicates the direction of cash flow)

                                                                                                                                                                                                                                                            Formulas

                                                                                                                                                                                                                                                            The formula that the calculator uses for ΣPrn( is in terms of bal(:

                                                                                                                                                                                                                                                            (1) \(\begin{align} \texttt{\Sigma Prn}(n_1,n_2)=\texttt{bal}(n_2)-\texttt{bal}(n_1) \end{align}\)

                                                                                                                                                                                                                                                            When the roundvalue argument isn't given, we can substitute the explicit formula for bal( and simplify to get the following formula:

                                                                                                                                                                                                                                                            (2) \(\begin{align} \texttt{\Sigma Prn}(n_1,n_2)=\left(\texttt{PV}-\frac{\texttt{PMT}}{I\%/100}\right)\left[\left(1-\frac{I\%}{100}\right)^{n_1}-\left(1-\frac{I\%}{100}\right)^{n_2}\right] \end{align}\)

                                                                                                                                                                                                                                                            Error Conditions

                                                                                                                                                                                                                                                            • ERR:DOMAIN is thrown if either payment number is negative or a decimal.

                                                                                                                                                                                                                                                            Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, kg583.

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                                                                                                                                                                                                                                                            • FR: Σx²

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                                                                                                                                                                                                                                                            Hex Value $BB9F
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                                                                                                                                                                                                                                                            Calculator OS Version Description
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                                                                                                                                                                                                                                                            Calculator OS Version Description
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                                                                                                                                                                                                                                                            Hex Value $BBA1
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                                                                                                                                                                                                                                                            TI-83+ 1.03 Added
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                                                                                                                                                                                                                                                            Hex Value $BBA3
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                                                                                                                                                                                                                                                            Calculator OS Version Description
                                                                                                                                                                                                                                                            TI-83+ 1.03 Added
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                                                                                                                                                                                                                                                            Hex Value $BBA4
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                                                                                                                                                                                                                                                            Calculator OS Version Description
                                                                                                                                                                                                                                                            TI-83+ 1.03 Added
                                                                                                                                                                                                                                                            Property Value
                                                                                                                                                                                                                                                            Hex Value $5B
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                                                                                                                                                                                                                                                            History

                                                                                                                                                                                                                                                            Calculator OS Version Description
                                                                                                                                                                                                                                                            TI-82 1.0 Added
                                                                                                                                                                                                                                                            Property Value
                                                                                                                                                                                                                                                            Hex Value $6311
                                                                                                                                                                                                                                                            Categories
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                                                                                                                                                                                                                                                            Calculator OS Version Description
                                                                                                                                                                                                                                                            TI-82 1.0 Added
                                                                                                                                                                                                                                                            Property Value
                                                                                                                                                                                                                                                            Hex Value $6310
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                                                                                                                                                                                                                                                            Calculator OS Version Description
                                                                                                                                                                                                                                                            TI-82 1.0 Added
                                                                                                                                                                                                                                                            Property Value
                                                                                                                                                                                                                                                            Hex Value $6323
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                                                                                                                                                                                                                                                            Calculator OS Version Description
                                                                                                                                                                                                                                                            TI-82 1.0 Added
                                                                                                                                                                                                                                                            Property Value
                                                                                                                                                                                                                                                            Hex Value $BBA5
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                                                                                                                                                                                                                                                            Calculator OS Version Description
                                                                                                                                                                                                                                                            TI-83+ 1.03 Added
                                                                                                                                                                                                                                                            Property Value
                                                                                                                                                                                                                                                            Hex Value $BBA6
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                                                                                                                                                                                                                                                            Calculator OS Version Description
                                                                                                                                                                                                                                                            TI-83+ 1.03 Added
                                                                                                                                                                                                                                                            Property Value
                                                                                                                                                                                                                                                            Hex Value $AC
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                                                                                                                                                                                                                                                            Calculator OS Version Description
                                                                                                                                                                                                                                                            TI-82 1.0 Added
                                                                                                                                                                                                                                                            Property Value
                                                                                                                                                                                                                                                            Hex Value $BBA7
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                                                                                                                                                                                                                                                            Calculator OS Version Description
                                                                                                                                                                                                                                                            TI-83+ 1.03 Added
                                                                                                                                                                                                                                                            Property Value
                                                                                                                                                                                                                                                            Hex Value $BBA8
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                                                                                                                                                                                                                                                            Calculator OS Version Description
                                                                                                                                                                                                                                                            TI-83+ 1.03 Added
                                                                                                                                                                                                                                                            Property Value
                                                                                                                                                                                                                                                            Hex Value $BBCB
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                                                                                                                                                                                                                                                            Calculator OS Version Description
                                                                                                                                                                                                                                                            TI-83+ 1.03 Added
                                                                                                                                                                                                                                                            Property Value
                                                                                                                                                                                                                                                            Hex Value $6207
                                                                                                                                                                                                                                                            Categories
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                                                                                                                                                                                                                                                            • FR: σx

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                                                                                                                                                                                                                                                            Calculator OS Version Description
                                                                                                                                                                                                                                                            TI-82 1.0 Added
                                                                                                                                                                                                                                                            Property Value
                                                                                                                                                                                                                                                            Hex Value $6210
                                                                                                                                                                                                                                                            Categories
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                                                                                                                                                                                                                                                            • FR: σy

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                                                                                                                                                                                                                                                            Calculator OS Version Description
                                                                                                                                                                                                                                                            TI-82 1.0 Added
                                                                                                                                                                                                                                                            Property Value
                                                                                                                                                                                                                                                            Hex Value $BBCC
                                                                                                                                                                                                                                                            Categories
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                                                                                                                                                                                                                                                            • FR: τ

                                                                                                                                                                                                                                                            τ

                                                                                                                                                                                                                                                            Overview

                                                                                                                                                                                                                                                            Availability: Token available everywhere.

                                                                                                                                                                                                                                                            Syntax

                                                                                                                                                                                                                                                            τ

                                                                                                                                                                                                                                                            Description

                                                                                                                                                                                                                                                            Examples

                                                                                                                                                                                                                                                            Explanation 1

                                                                                                                                                                                                                                                            code 1

                                                                                                                                                                                                                                                            Explanation 2

                                                                                                                                                                                                                                                            code 2

                                                                                                                                                                                                                                                            Error Conditions

                                                                                                                                                                                                                                                            Advanced Notes

                                                                                                                                                                                                                                                            History

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                                                                                                                                                                                                                                                            • FR: χ

                                                                                                                                                                                                                                                            χ

                                                                                                                                                                                                                                                            Overview

                                                                                                                                                                                                                                                            Availability: Token available everywhere.

                                                                                                                                                                                                                                                            Syntax

                                                                                                                                                                                                                                                            χ

                                                                                                                                                                                                                                                            Description

                                                                                                                                                                                                                                                            Examples

                                                                                                                                                                                                                                                            Explanation 1

                                                                                                                                                                                                                                                            code 1

                                                                                                                                                                                                                                                            Explanation 2

                                                                                                                                                                                                                                                            code 2

                                                                                                                                                                                                                                                            Error Conditions

                                                                                                                                                                                                                                                            Advanced Notes

                                                                                                                                                                                                                                                            History

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                                                                                                                                                                                                                                                            • FR: χ²-Test(

                                                                                                                                                                                                                                                            χ²-Test(

                                                                                                                                                                                                                                                            Overview

                                                                                                                                                                                                                                                            Performs a chi-square test. drawflag=1 draws results; drawflag=0 calculates results.
                                                                                                                                                                                                                                                            Color#: 10 - 24 or color name pasted from [vars] COLOR.

                                                                                                                                                                                                                                                            Availability: Token only available from within the Basic editor.

                                                                                                                                                                                                                                                            Syntax

                                                                                                                                                                                                                                                            χ²-Test(observedmatrix,expectedmatrix[,drawflag,color#])

                                                                                                                                                                                                                                                            Arguments

                                                                                                                                                                                                                                                            NameTypeOptional
                                                                                                                                                                                                                                                            χ²-
                                                                                                                                                                                                                                                            observedmatrixmatrix
                                                                                                                                                                                                                                                            expectedmatrixmatrixYes
                                                                                                                                                                                                                                                            drawflagYes
                                                                                                                                                                                                                                                            color#colorNumYes

                                                                                                                                                                                                                                                            Location

                                                                                                                                                                                                                                                            stat, TESTS, C:Test(

                                                                                                                                                                                                                                                            Description

                                                                                                                                                                                                                                                            This command performs a χ² test of independence. This test is used to assess the independence of two categorical variables with known frequencies. The test is only valid for a simple random sample from the population, and only if all the frequencies are sufficiently large (greater than 5).

                                                                                                                                                                                                                                                            Note: this test is different from the χ² goodness of fit test, which the TI-83 calculators don't have a command for. For a program that will perform the χ² goodness-of-fit test, see the goodness-of-fit test routine.

                                                                                                                                                                                                                                                            To use this test, you need a matrix containing a contingency table. This is a table in which every row corresponds to a value of the first variable, and every column to a value of the second. The number in each cell represents the frequency with which the corresponding values of the two variables occur together. For example: suppose that the two variables are sex (male and female) and eye color (blue, brown, and green). The contingency table would have two rows and three columns. The cell in the first row and column would be the number of blue-eyed men in the sample, the cell in the second row and first column would be the number of blue-eyed women, and so on.

                                                                                                                                                                                                                                                            The χ²-Test( command takes two arguments: the observed matrix and expected matrix. The first of these should be the contingency table you've already completed, presumably in the Matrix editor. The expected matrix does not need to already exist: the χ²-Test( command will calculate and store the expected frequencies (under the assumption that the variables are independent) to this matrix.

                                                                                                                                                                                                                                                            The command is primarily for use in a program. Although you can access the χ²-Test( command on the home screen, via the catalog, there's no need: you can use the χ²-Test… interactive solver found in the menu instead.

                                                                                                                                                                                                                                                            In either case, it's important to understand the output of χ²-Test(. Here are the meanings of each line:

                                                                                                                                                                                                                                                            • χ² is the test statistic, calculated from the differences between the observed and the expected matrices.
                                                                                                                                                                                                                                                            • p is the probability associated with the test statistic. We use p to test the null hypothesis that the two variables are independent. If p is low (usually, if it's <0.05) this means there's little chance that two independent variables would have a contingency table so different from the expected, and we reject the null hypothesis (so we'd conclude that the two variables are not independent).
                                                                                                                                                                                                                                                            • df is the degrees of freedom, defined as (# of rows - 1)*(# of columns - 1), important for calculating p.

                                                                                                                                                                                                                                                            Sample Problem

                                                                                                                                                                                                                                                            You want to compare the effectiveness of three treatments in curing a terminal disease. You have obtained data for 100 patients who had the disease, which contained information on the treatment used, and whether the patient lived or died. You put this information in a contingency table:

                                                                                                                                                                                                                                                            Lived

                                                                                                                                                                                                                                                            Died

                                                                                                                                                                                                                                                            Treatment A

                                                                                                                                                                                                                                                            40

                                                                                                                                                                                                                                                            10

                                                                                                                                                                                                                                                            Treatment B

                                                                                                                                                                                                                                                            27

                                                                                                                                                                                                                                                            6

                                                                                                                                                                                                                                                            Treatment C

                                                                                                                                                                                                                                                            11

                                                                                                                                                                                                                                                            6

                                                                                                                                                                                                                                                            To perform the test, you store this information to a matrix such as [A], either through the matrix editor or by hand:

                                                                                                                                                                                                                                                            :[[40,10],[27,6],[11,6→[A]

                                                                                                                                                                                                                                                            You submit this matrix as the first argument, and some other matrix (such as [B]) for the second:

                                                                                                                                                                                                                                                            :χ²-Test([A],[B]

                                                                                                                                                                                                                                                            The output looks something like this:

                                                                                                                                                                                                                                                            χ²-Test
 χ²=2.14776311
 p=.3416796916
 df=2

                                                                                                                                                                                                                                                            The most important part of this output is the line p=.3416796916 - the probability of getting such results under the hypothesis that the treatments and survival rate are independent. This value is greater than .05, so the data is not significant on a 5% level. There is not enough evidence to reject the null hypothesis, so treatment and survival rate may very well be independent. In non-mathematical language, this means that there's no reason to believe the treatments vary in effectiveness.

                                                                                                                                                                                                                                                            Advanced Uses

                                                                                                                                                                                                                                                            The final argument of χ²-Test(, draw?, will display the results in a graphical manner if you put in "1" for it. The calculator will draw the χ² distribution with the correct degrees of freedom, and shade the area of the graph beyond the χ² statistic. In addition, the same values as usually will be calculated and displayed. You would make your conclusions in the same way as for the regular output.

                                                                                                                                                                                                                                                            See Also

                                                                                                                                                                                                                                                            Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, Myles_Zadok.

                                                                                                                                                                                                                                                            History

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                                                                                                                                                                                                                                                            • FR: χ²

                                                                                                                                                                                                                                                            χ²

                                                                                                                                                                                                                                                            Overview

                                                                                                                                                                                                                                                            Syntax

                                                                                                                                                                                                                                                            χ²

                                                                                                                                                                                                                                                            Description

                                                                                                                                                                                                                                                            Examples

                                                                                                                                                                                                                                                            Explanation 1

                                                                                                                                                                                                                                                            code 1

                                                                                                                                                                                                                                                            Explanation 2

                                                                                                                                                                                                                                                            code 2

                                                                                                                                                                                                                                                            Error Conditions

                                                                                                                                                                                                                                                            Advanced Notes

                                                                                                                                                                                                                                                            History

                                                                                                                                                                                                                                                            Calculator OS Version Description
                                                                                                                                                                                                                                                            TI-82 1.0 Added
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                                                                                                                                                                                                                                                              • FR: χ²GOF-Test(

                                                                                                                                                                                                                                                              χ²GOF-Test(

                                                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                                                              Performs a test to confirm that sample data is from a population that conforms to a specified distribution.
                                                                                                                                                                                                                                                              Color#: 10 - 24 or color name pasted from [vars] COLOR.

                                                                                                                                                                                                                                                              Availability: Token only available from within the Basic editor.

                                                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                                                              χ²GOF-Test(observedlist,expectedlist,df [,drawflag,color#])

                                                                                                                                                                                                                                                              Arguments

                                                                                                                                                                                                                                                              NameTypeOptional
                                                                                                                                                                                                                                                              χ²
                                                                                                                                                                                                                                                              -
                                                                                                                                                                                                                                                              observedlistlist
                                                                                                                                                                                                                                                              expectedlistlist
                                                                                                                                                                                                                                                              df
                                                                                                                                                                                                                                                              drawflagYes
                                                                                                                                                                                                                                                              color#colorNumYes

                                                                                                                                                                                                                                                              Location

                                                                                                                                                                                                                                                              stat, TESTS, D:, GOF, Test(

                                                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                                                              The χ²GOF-Test( command performs a χ² goodness-of-fit test. Given an expected ideal distribution of a variable across several categories, and a sample from this variable, it tests the hypothesis that the variable actually fits the ideal distribution. As a special case, you could take the ideal distribution to be evenly divided across all categories. Then, the goodness-of-fit test will test the hypothesis that the variable is independent of the category.

                                                                                                                                                                                                                                                              The command takes three arguments:

                                                                                                                                                                                                                                                              • An observed list with an element for each category: the element records the number of times this category appeared in the sample.
                                                                                                                                                                                                                                                              • An expected list with an element for each category: the element records the frequency with which the category was expected to appear.
                                                                                                                                                                                                                                                              • The degrees of freedom — usually taken to be one less than the number of categories.

                                                                                                                                                                                                                                                              The output is two-fold:

                                                                                                                                                                                                                                                              • The test statistic, χ². If the null hypothesis (that the variable fits the distribution) is true, this should be close to 1.
                                                                                                                                                                                                                                                              • The probability, p, of the observed distribution assuming the null hypothesis. If this value is low (usually, if it's lower than .05, or lower than .01) this is sufficient evidence to reject the null hypothesis, and conclude that the variable fits a different distribution.

                                                                                                                                                                                                                                                              Sample Problem

                                                                                                                                                                                                                                                              Working as a sales clerk, you're wondering if the number of customers depends on the day of week. You've taken a count of the number of customers every day for a week: 17 on Monday, 21 on Tuesday, 18 on Wednesday, 10 on Thursday, 24 on Friday, 28 on Saturday, and 24 on Sunday. Store this observed count: {17,21,18,10,24,28,24} to L1.

                                                                                                                                                                                                                                                              There were a total of sum(L1)=142 customers. So the expected number of customers on each day was 142/7. Store all the expected counts: {142/7,142/7,142/7,142/7,142/7,142/7,142/7} to L2 (as a shortcut, you can store 142/7{1,1,1,1,1,1,1}).

                                                                                                                                                                                                                                                              Since there are 7 days, there are 6 (one less) degrees of freedom. So the resulting command is χ²GOF-Test(L1,L2,6).

                                                                                                                                                                                                                                                              The output will give a χ² of 10.32394366, and a p value of 0.1116563376. This is higher than 5%, so the test is not significant on a 95 percent level. It's perfectly possible, in other words, that the number of customers is independent of the day of week.

                                                                                                                                                                                                                                                              (Note that in this case, if you suspected the number of customers to be higher on weekends, you could use a more sensitive test for only two categories: 2-SampTTest)

                                                                                                                                                                                                                                                              Advanced Uses

                                                                                                                                                                                                                                                              The χ²GOF-Test( command is only on TI-84 Plus and newer calculator models. However, it's possible to use the χ²cdf( command to simulate it on the other calculators: see the χ² Goodness-of-fit Test routine.

                                                                                                                                                                                                                                                              Formulas

                                                                                                                                                                                                                                                              The formula for calculating the test statistic is as follows (Oi is the observed count of the ith category, and Ei is the expected count):

                                                                                                                                                                                                                                                              (1) \(\begin{align} \chi_{n-1}^2 = \sum_{i=1}^n \frac{(O_i-E_i)^2}{E_i} \end{align}\)

                                                                                                                                                                                                                                                              The p-value, then, is the probability that the χ² statistic would be this high, using the χ²cdf( command with the appropriate value for degrees of freedom.

                                                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                                                              • ERR:DIM MISMATCH is thrown if the two lists are of different length.
                                                                                                                                                                                                                                                              • ERR:DOMAIN is thrown if they only have one element, or if df is not a positive integer.

                                                                                                                                                                                                                                                              See Also

                                                                                                                                                                                                                                                              Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Myles_Zadok.

                                                                                                                                                                                                                                                              History

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                                                                                                                                                                                                                                                              • FR: X²FRép(

                                                                                                                                                                                                                                                              χ²cdf(

                                                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                                                              Computes the χ²distribution probability between lowerbound andupperbound for the specified degrees of freedom df.

                                                                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                                                              χ²cdf(lowerbound,upperbound,df)

                                                                                                                                                                                                                                                              Arguments

                                                                                                                                                                                                                                                              NameTypeOptional
                                                                                                                                                                                                                                                              χ²
                                                                                                                                                                                                                                                              lowerbound
                                                                                                                                                                                                                                                              upperbound
                                                                                                                                                                                                                                                              df

                                                                                                                                                                                                                                                              Location

                                                                                                                                                                                                                                                              2nd, distr, DISTR, 8:cdf(

                                                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                                                              χ²cdf( is the χ² cumulative density function. If some random variable follows a χ² distribution, you can use this command to find the probability that this variable will fall in the interval you supply.

                                                                                                                                                                                                                                                              The command takes three arguments. lower and upper define the interval in which you're interested. df specifies the degrees of freedom (choosing one of a family of χ² distributions).

                                                                                                                                                                                                                                                              Advanced Uses

                                                                                                                                                                                                                                                              Often, you want to find a "tail probability" - a special case for which the interval has no lower or no upper bound. For example, "what is the probability x is greater than 2?". The TI-83+ has no special symbol for infinity, but you can use E99 to get a very large number that will work equally well in this case (E is the decimal exponent obtained by pressing [2nd] [EE]). Use E99 for positive infinity, and -E99 for negative infinity.

                                                                                                                                                                                                                                                              The χ²cdf( command is crucial to performing a χ² goodness of fit test, which the early TI-83 series calculators do not have a command for (the χ²-Test( command performs the χ² test of independence, which is not the same thing, although the manual always just refers to it as the "χ² Test"). This test is used to test if an observed frequency distribution differs from the expected, and can be used, for example, to tell if a coin or die is fair.

                                                                                                                                                                                                                                                              The Goodness-of-Fit Test routine on the routines page will perform a χ² goodness of fit test for you. Or, if you have a TI-84+/SE with OS version 2.30 or higher, you can use the χ²GOF-Test( command.

                                                                                                                                                                                                                                                              Formulas

                                                                                                                                                                                                                                                              As with other continuous distributions, we can define χ²cdf( in forms of the probability density function:

                                                                                                                                                                                                                                                              (1) \(\begin{align} \texttt{\chi^2cdf}(a,b,k) = \int_a^b \texttt{\chi^2pdf}(x,k)\,dx \end{align}\)

                                                                                                                                                                                                                                                              See Also

                                                                                                                                                                                                                                                              Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583.

                                                                                                                                                                                                                                                              History

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                                                                                                                                                                                                                                                              • FR: Χ²Fdp(

                                                                                                                                                                                                                                                              χ²pdf(

                                                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                                                              Computes the probability density function (pdf) for the χ² distribution at a specified x value for the specified degrees of freedom df.

                                                                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                                                              χ²pdf(x,df)

                                                                                                                                                                                                                                                              Arguments

                                                                                                                                                                                                                                                              NameTypeOptional
                                                                                                                                                                                                                                                              χ²
                                                                                                                                                                                                                                                              x
                                                                                                                                                                                                                                                              df

                                                                                                                                                                                                                                                              Location

                                                                                                                                                                                                                                                              2nd, distr, DISTR, 7:pdf(

                                                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                                                              χ²pdf( is the χ² probability density function.

                                                                                                                                                                                                                                                              Since the χ² distribution is continuous, the value of χ²pdf( doesn't represent an actual probability — in fact, one of the only uses for this command is to draw a graph of the χ² curve. You could also use it for various calculus purposes, such as finding inflection points.

                                                                                                                                                                                                                                                              The command takes two arguments: the value at which to evaluate the p.d.f., and df, the number of 'degrees of freedom'.

                                                                                                                                                                                                                                                              Formulas

                                                                                                                                                                                                                                                              The value of χ²pdf( is given by

                                                                                                                                                                                                                                                              (1) \(\begin{align} \texttt{\chi^2pdf}(x,k)=\frac{(1/2)^{k/2}}{(k/2-1)!}\,x^{k/2-1}e^{-x/2} \end{align}\)

                                                                                                                                                                                                                                                              Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583.

                                                                                                                                                                                                                                                              History

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                                                                                                                                                                                                                                                              • FR: ᴇ

                                                                                                                                                                                                                                                              ᴇ

                                                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                                                              Returns value times 10 to the exponent.

                                                                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                                                              Exponent:valueᴇexponent

                                                                                                                                                                                                                                                              Arguments

                                                                                                                                                                                                                                                              NameTypeOptional
                                                                                                                                                                                                                                                              Exponent:
                                                                                                                                                                                                                                                              value
                                                                                                                                                                                                                                                              ᴇ
                                                                                                                                                                                                                                                              exponent

                                                                                                                                                                                                                                                              Location

                                                                                                                                                                                                                                                              2nd, ᴇᴇ

                                                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                                                              Returns list elements times 10 to the exponent.

                                                                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                                                              Exponent:listᴇexponent

                                                                                                                                                                                                                                                              Arguments

                                                                                                                                                                                                                                                              NameTypeOptional
                                                                                                                                                                                                                                                              Exponent:
                                                                                                                                                                                                                                                              listlist
                                                                                                                                                                                                                                                              ᴇ
                                                                                                                                                                                                                                                              exponent

                                                                                                                                                                                                                                                              Location

                                                                                                                                                                                                                                                              2nd, ᴇᴇ

                                                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                                                              Returns matrix elements times 10 to the exponent.

                                                                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                                                              Exponent:matrixᴇexponent

                                                                                                                                                                                                                                                              Arguments

                                                                                                                                                                                                                                                              NameTypeOptional
                                                                                                                                                                                                                                                              Exponent:
                                                                                                                                                                                                                                                              matrixmatrix
                                                                                                                                                                                                                                                              ᴇ
                                                                                                                                                                                                                                                              exponent

                                                                                                                                                                                                                                                              Location

                                                                                                                                                                                                                                                              2nd, ᴇᴇ

                                                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                                                                              code 1

                                                                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                                                                              code 2

                                                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                                                              History

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                                                                                                                                                                                                                                                              • FR: ᴛ

                                                                                                                                                                                                                                                              ᴛ

                                                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                                                              ᴛ

                                                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                                                                              code 1

                                                                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                                                                              code 2

                                                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                                                              History

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                                                                                                                                                                                                                                                              • FR: ᵀ

                                                                                                                                                                                                                                                              ᵀ

                                                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                                                              ᵀ

                                                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                                                              T.GIF

                                                                                                                                                                                                                                                              Command Summary

                                                                                                                                                                                                                                                              This command calculates the transpose of a matrix.

                                                                                                                                                                                                                                                              Command Syntax

                                                                                                                                                                                                                                                              matrixT

                                                                                                                                                                                                                                                              Menu Location

                                                                                                                                                                                                                                                              Press:

                                                                                                                                                                                                                                                              1. MATRX (on the 83) or 2nd MATRX (83+ or higher) to access the Matrix menu.
                                                                                                                                                                                                                                                              2. LEFT to access the MATH submenu
                                                                                                                                                                                                                                                              3. 2 to select T, or use arrows

                                                                                                                                                                                                                                                              Calculator Compatibility

                                                                                                                                                                                                                                                              TI-83/84/+/SE

                                                                                                                                                                                                                                                              Token Size

                                                                                                                                                                                                                                                              1 byte

                                                                                                                                                                                                                                                              The T command is used to calculate the transpose of a matrix: it flips a matrix along its main diagonal. This means that the (i,j)th element becomes the (j,i)th element, and vice versa. As a result, the transpose of an M by N matrix is an N by M matrix.

                                                                                                                                                                                                                                                              [[1,2,3][4,5,6]]
                                                                                                                                                                                                                                                              ………… [[1 2 3]
                                                                                                                                                                                                                                                              …………. [4 5 6]]
                                                                                                                                                                                                                                                              AnsT
                                                                                                                                                                                                                                                              ………… [[1 4]
                                                                                                                                                                                                                                                              …………. [2 5]
                                                                                                                                                                                                                                                              …………. [3 6]]

                                                                                                                                                                                                                                                              Advanced Uses

                                                                                                                                                                                                                                                              In addition to its many uses in linear algebra, the T operation is useful to programmers: with operations such as Matr►list( and augment(, which normally deal with columns, T allows you to use rows instead. See the "Related Commands" section for the commands that this is useful for.

                                                                                                                                                                                                                                                              Source: parts of this page were written by the following TI|BD contributors: DarkerLine, Timothy Foster.

                                                                                                                                                                                                                                                              History

                                                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                                                              TI-82 1.0 Added
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                                                                                                                                                                                                                                                              Hex Value $EF2F
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                                                                                                                                                                                                                                                              • FR: ᵤ

                                                                                                                                                                                                                                                              ᵤ

                                                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                                                              ᵤ

                                                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                                                              Examples

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                                                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                                                              Advanced Notes

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                                                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                                                              TI-84+ 2.53 Added
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                                                                                                                                                                                                                                                              • FR: ṗ

                                                                                                                                                                                                                                                              ṗ

                                                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                                                              ṗ

                                                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                                                              Examples

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                                                                                                                                                                                                                                                              Calculator OS Version Description
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                                                                                                                                                                                                                                                              • FR: ‛

                                                                                                                                                                                                                                                              ‛

                                                                                                                                                                                                                                                              Overview

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                                                                                                                                                                                                                                                              ‛

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                                                                                                                                                                                                                                                              Examples

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                                                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                                                              TI-83+ 1.15 Added
                                                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                                                              Hex Value $BBDB
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                                                                                                                                                                                                                                                              • FR: …

                                                                                                                                                                                                                                                              …

                                                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                                                              Comment:DB-F5: 83+ 1.16 or later

                                                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                                                              …

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                                                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                                                              History

                                                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                                                              TI-83+ 1.16 Added
                                                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                                                              Hex Value $EF2E
                                                                                                                                                                                                                                                              Categories
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                                                                                                                                                                                                                                                              • FR: ⁄

                                                                                                                                                                                                                                                              ⁄

                                                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                                                              ⁄

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                                                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                                                              History

                                                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                                                              TI-84+ 2.53 Added
                                                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                                                              Hex Value $B0
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                                                                                                                                                                                                                                                              • FR: ⁻

                                                                                                                                                                                                                                                              ⁻

                                                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                                                              ⁻

                                                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                                                              Explanation 1

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                                                                                                                                                                                                                                                              Explanation 2

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                                                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                                                              History

                                                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                                                              TI-82 1.0 Added
                                                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                                                              Hex Value $0C
                                                                                                                                                                                                                                                              Categories
                                                                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                                                                              • FR: ⁻¹
                                                                                                                                                                                                                                                              ⁻¹

                                                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                                                              ⁻¹

                                                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                                                              The ֿ¹ command returns the reciprocal of a number, equivalent to dividing 1 by the number (although reciprocals are sometimes more convenient to type). It also works for lists, by calculating the reciprocal of each element.

                                                                                                                                                                                                                                                              The ֿ¹ command can also be used on matrices, but it is the matrix inverse that is computed, not the reciprocal of each element. If [A] is an N by N (square) matrix, then [A]ֿ¹ is the N by N matrix such that [A][A]ֿ¹=[A]ֿ¹[A] is the identity matrix. ֿ¹ does not work on non-square matrices.

                                                                                                                                                                                                                                                              4ֿ¹
        .25
{1,2,3}ֿ¹
        {1 .5 .3333333333}
[[3,2][4,3]]ֿ¹
        [[3  -2]
         [-4 3 ]]

                                                                                                                                                                                                                                                              Much like the number 0 does not have a reciprocal, some square matrices do not have inverses (they are called singular matrices) and you'll get an error when you try to invert them.

                                                                                                                                                                                                                                                              Optimization

                                                                                                                                                                                                                                                              Writing Aֿ¹B instead of B/A is sometimes beneficial when B is a complicated expression, because it allows you to take off closing parentheses of B. For example:

                                                                                                                                                                                                                                                              :(P+√(P²-4Q))/2
can be
:2ֿ¹(P+√(P²-4Q

                                                                                                                                                                                                                                                              This may be slower than dividing. There are also situations in which this optimization might lose precision, especially when the number being divided is large:

                                                                                                                                                                                                                                                              7fPart(4292/7
        1
7fPart(7ֿ¹4292
        .9999999999

                                                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                                                              Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, thornahawk, ztrumpet.

                                                                                                                                                                                                                                                              History

                                                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                                                              TI-82 1.0 Added
                                                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                                                              Hex Value $BBE0
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                                                                                                                                                                                                                                                              • FR: ₀

                                                                                                                                                                                                                                                              ₀

                                                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                                                              ₀

                                                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                                                              Explanation 1

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                                                                                                                                                                                                                                                              Explanation 2

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                                                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                                                              Advanced Notes

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                                                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                                                              TI-83+ 1.16 Added
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                                                                                                                                                                                                                                                              Hex Value $BBE1
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                                                                                                                                                                                                                                                              • FR: ₁
                                                                                                                                                                                                                                                              ₁

                                                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                                                              ₁

                                                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                                                              Explanation 1

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                                                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                                                              History

                                                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                                                              TI-83+ 1.16 Added
                                                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                                                              Hex Value $BBEA
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                                                                                                                                                                                                                                                              • FR: ₁₀

                                                                                                                                                                                                                                                              ₁₀

                                                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                                                              ₁₀

                                                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                                                              Explanation 1

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                                                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                                                              History

                                                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                                                              TI-83+ 1.16 Added
                                                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                                                              Hex Value $C1
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                                                                                                                                                                                                                                                              • FR: ₁₀^(

                                                                                                                                                                                                                                                              ₁₀^(

                                                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                                                              ₁₀^(

                                                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                                                              Explanation 1

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                                                                                                                                                                                                                                                              Error Conditions

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                                                                                                                                                                                                                                                              History

                                                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                                                              TI-82 1.0 ₁₀^ added
                                                                                                                                                                                                                                                              TI-83 0.01013 Renamed ₁₀^ to ₁₀^(
                                                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                                                              Hex Value $BBE2
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                                                                                                                                                                                                                                                              • FR: ₂

                                                                                                                                                                                                                                                              ₂

                                                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                                                              ₂

                                                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                                                              Examples

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                                                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                                                              History

                                                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                                                              TI-83+ 1.16 Added
                                                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                                                              Hex Value $BBE3
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                                                                                                                                                                                                                                                              • FR: ₃

                                                                                                                                                                                                                                                              ₃

                                                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                                                              ₃

                                                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                                                              Explanation 1

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                                                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                                                              History

                                                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                                                              TI-83+ 1.16 Added
                                                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                                                              Hex Value $BBE4
                                                                                                                                                                                                                                                              Categories
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                                                                                                                                                                                                                                                              • FR: ₄

                                                                                                                                                                                                                                                              ₄

                                                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                                                              ₄

                                                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                                                              Examples

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                                                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                                                              History

                                                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                                                              TI-83+ 1.16 Added
                                                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                                                              Hex Value $BBE5
                                                                                                                                                                                                                                                              Categories
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                                                                                                                                                                                                                                                              • FR: ₅

                                                                                                                                                                                                                                                              ₅

                                                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                                                              ₅

                                                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                                                              Explanation 1

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                                                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                                                              History

                                                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                                                              TI-83+ 1.16 Added
                                                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                                                              Hex Value $BBE6
                                                                                                                                                                                                                                                              Categories
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                                                                                                                                                                                                                                                              • FR: ₆

                                                                                                                                                                                                                                                              ₆

                                                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                                                              ₆

                                                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                                                              Explanation 1

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                                                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                                                              History

                                                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                                                              TI-83+ 1.16 Added
                                                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                                                              Hex Value $BBE7
                                                                                                                                                                                                                                                              Categories
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                                                                                                                                                                                                                                                              • FR: ₇

                                                                                                                                                                                                                                                              ₇

                                                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                                                              ₇

                                                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                                                              Explanation 1

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                                                                                                                                                                                                                                                              code 2

                                                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                                                              History

                                                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                                                              TI-83+ 1.16 Added
                                                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                                                              Hex Value $BBE8
                                                                                                                                                                                                                                                              Categories
                                                                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                                                                              • FR: ₈

                                                                                                                                                                                                                                                              ₈

                                                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                                                              ₈

                                                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                                                                              code 1

                                                                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                                                                              code 2

                                                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                                                              History

                                                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                                                              TI-83+ 1.16 Added
                                                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                                                              Hex Value $BBE9
                                                                                                                                                                                                                                                              Categories
                                                                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                                                                              • FR: ₉

                                                                                                                                                                                                                                                              ₉

                                                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                                                              ₉

                                                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                                                              Explanation 1

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                                                                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                                                                              code 2

                                                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                                                              History

                                                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                                                              TI-83+ 1.16 Added
                                                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                                                              Hex Value $BBED
                                                                                                                                                                                                                                                              Categories
                                                                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                                                                              • FR: ↑

                                                                                                                                                                                                                                                              ↑

                                                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                                                              ↑

                                                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                                                                              code 1

                                                                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                                                                              code 2

                                                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                                                              History

                                                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                                                              TI-83+ 1.16 Added
                                                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                                                              Hex Value $04
                                                                                                                                                                                                                                                              Categories
                                                                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                                                                              • FR: →

                                                                                                                                                                                                                                                              →

                                                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                                                              Stores value in variable.

                                                                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                                                              Store: value→variable

                                                                                                                                                                                                                                                              Arguments

                                                                                                                                                                                                                                                              NameTypeOptional
                                                                                                                                                                                                                                                              Store:
                                                                                                                                                                                                                                                              value
                                                                                                                                                                                                                                                              variable

                                                                                                                                                                                                                                                              Location

                                                                                                                                                                                                                                                              sto→

                                                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                                                              The → (store) command will store a number, variable, or expression to a variable, using the respective value(s) of the variable(s) at the time. When storing a value in a variable, you have the value on the left side of → and the variable that it will be stored to on the right side.

                                                                                                                                                                                                                                                              :1→X
           1

:{1.3,5.7,9.11→ABC
           {1.3 5.7 9.11}

:"HELLO WORLD→Str1
           "HELLO WORLD"

                                                                                                                                                                                                                                                              Advanced

                                                                                                                                                                                                                                                              It's not easy to put a → symbol into a string, since "→→Str1 would produce a syntax error (and in general, when the calculator 'sees' a → symbol, it assumes that the string is over, and interprets the symbol literally).

                                                                                                                                                                                                                                                              However, you can use Equ►String( (outside a program) to get the → or " symbols in a string:

                                                                                                                                                                                                                                                              1. Type them on the home screen and press [ENTER]
                                                                                                                                                                                                                                                              2. Select 1:Quit when the ERR:SYNTAX comes up.
                                                                                                                                                                                                                                                              3. Press [Y=] to go to the equation editor.
                                                                                                                                                                                                                                                              4. Press [2nd] [ENTRY] to recall the symbols to Y1
                                                                                                                                                                                                                                                              5. Now, use Equ►String(Y1,Str1) to store the symbols to a string.

                                                                                                                                                                                                                                                              Optimization

                                                                                                                                                                                                                                                              You can remove closing parentheses, braces, brackets, and quotes that are before a → command.

                                                                                                                                                                                                                                                              Here are a series of examples of using the → command. The first line of each example uses more bytes than necessary. The line following strips out the unnecessary characters and uses less bytes.

                                                                                                                                                                                                                                                              Real Variables
                                                                                                                                                                                                                                                              1/(2*(3/4))→X
1/(2(3/4→X
                                                                                                                                                                                                                                                              Strings
                                                                                                                                                                                                                                                              "Hello"→Str1
"Hello→Str1
                                                                                                                                                                                                                                                              Lists
                                                                                                                                                                                                                                                              {1,2,3,2(X+1)}→L₁
{1,2,3,2(X+1→L₁

                                                                                                                                                                                                                                                              5→L₁(1)
5→L₁(1

                                                                                                                                                                                                                                                              {4,5,6}→ʟLISTX
{4,5,6→LISTX

                                                                                                                                                                                                                                                              Tip: You can remove the ʟ character when storing an entire list to a custom named list, but you must keep the ʟ character present when storing to a specific item, such as 3→ʟLISTX(1

                                                                                                                                                                                                                                                              Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, patriotsfan.

                                                                                                                                                                                                                                                              History

                                                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                                                              TI-82 1.0 Added
                                                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                                                              Hex Value $BBEE
                                                                                                                                                                                                                                                              Categories
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                                                                                                                                                                                                                                                              • FR: ↓

                                                                                                                                                                                                                                                              ↓

                                                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                                                              ↓

                                                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                                                                              code 1

                                                                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                                                                              code 2

                                                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                                                              History

                                                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                                                              TI-83+ 1.16 Added
                                                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                                                              Hex Value $6321
                                                                                                                                                                                                                                                              Categories
                                                                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                                                                              • FR: ∆Tbl

                                                                                                                                                                                                                                                              ∆Tbl

                                                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                                                              ∆Tbl

                                                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                                                                              code 1

                                                                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                                                                              code 2

                                                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                                                              History

                                                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                                                              TI-82 1.0 Added
                                                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                                                              Hex Value $6326
                                                                                                                                                                                                                                                              Categories
                                                                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                                                                              • FR: ∆X

                                                                                                                                                                                                                                                              ∆X

                                                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                                                              ∆X

                                                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                                                                              code 1

                                                                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                                                                              code 2

                                                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                                                              History

                                                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                                                              TI-82 1.0 Added
                                                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                                                              Hex Value $6327
                                                                                                                                                                                                                                                              Categories
                                                                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                                                                              • FR: ∆Y

                                                                                                                                                                                                                                                              ∆Y

                                                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                                                              ∆Y

                                                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                                                                              code 1

                                                                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                                                                              code 2

                                                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                                                              History

                                                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                                                              TI-82 1.0 Added
                                                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                                                              Hex Value $BC
                                                                                                                                                                                                                                                              Categories
                                                                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                                                                              • FR: √(

                                                                                                                                                                                                                                                              √(

                                                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                                                              √(

                                                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                                                              Takes the square root of a positive or negative number. It works exactly the same as 2×√ or ^(1/2) but is smaller and uses an ending parenthesis. If used on a list, it will return a list with the square root of each element.

                                                                                                                                                                                                                                                              √(4)
        2
√(2)
        1.414213562

√({1,-1})
        {1 i}

                                                                                                                                                                                                                                                              This may return a complex number or throw ERR:NONREAL ANS (depending on mode settings) if taking the square root of a negative number.

                                                                                                                                                                                                                                                              Optimization

                                                                                                                                                                                                                                                              Never raise something to the one-half power explicitly; use this command instead.

                                                                                                                                                                                                                                                              :X^(1/2)→X
can be
:√(X→X

                                                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                                                              Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, thornahawk.

                                                                                                                                                                                                                                                              History

                                                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                                                              TI-82 1.0 √ added
                                                                                                                                                                                                                                                              TI-83 0.01013 Renamed √ to √(
                                                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                                                              Hex Value $BBF4
                                                                                                                                                                                                                                                              Categories
                                                                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                                                                              • FR: √

                                                                                                                                                                                                                                                              √

                                                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                                                              √

                                                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                                                                              code 1

                                                                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                                                                              code 2

                                                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                                                              History

                                                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                                                              TI-83+ 1.16 Added
                                                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                                                              Hex Value $BBDC
                                                                                                                                                                                                                                                              Categories
                                                                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                                                                              • FR: ∠

                                                                                                                                                                                                                                                              ∠

                                                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                                                              ∠

                                                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                                                                              code 1

                                                                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                                                                              code 2

                                                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                                                              History

                                                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                                                              TI-83+ 1.16 Added
                                                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                                                              Hex Value $BBF1
                                                                                                                                                                                                                                                              Categories
                                                                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                                                                              • FR: ∫

                                                                                                                                                                                                                                                              ∫

                                                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                                                              ∫

                                                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                                                                              code 1

                                                                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                                                                              code 2

                                                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                                                              History

                                                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                                                              TI-83+ 1.16 Added
                                                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                                                              Hex Value $6F
                                                                                                                                                                                                                                                              Categories
                                                                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                                                                              • FR: ≠

                                                                                                                                                                                                                                                              ≠

                                                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                                                              ≠

                                                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                                                                              code 1

                                                                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                                                                              code 2

                                                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                                                              History

                                                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                                                              TI-82 1.0 Added
                                                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                                                              Hex Value $6D
                                                                                                                                                                                                                                                              Categories
                                                                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                                                                              • FR: ≤

                                                                                                                                                                                                                                                              ≤

                                                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                                                              ≤

                                                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                                                                              code 1

                                                                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                                                                              code 2

                                                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                                                              History

                                                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                                                              TI-82 1.0 Added
                                                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                                                              Hex Value $6E
                                                                                                                                                                                                                                                              Categories
                                                                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                                                                              • FR: ≥

                                                                                                                                                                                                                                                              ≥

                                                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                                                              Availability: Token available everywhere.

                                                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                                                              ≥

                                                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                                                                              code 1

                                                                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                                                                              code 2

                                                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                                                              History

                                                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                                                              TI-82 1.0 Added
                                                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                                                              Hex Value $BBF5
                                                                                                                                                                                                                                                              Categories
                                                                                                                                                                                                                                                              Localizations
                                                                                                                                                                                                                                                              • FR: ⌸

                                                                                                                                                                                                                                                              ⌸

                                                                                                                                                                                                                                                              Overview

                                                                                                                                                                                                                                                              Comment:inverted equal

                                                                                                                                                                                                                                                              Syntax

                                                                                                                                                                                                                                                              ⌸

                                                                                                                                                                                                                                                              Description

                                                                                                                                                                                                                                                              Examples

                                                                                                                                                                                                                                                              Explanation 1

                                                                                                                                                                                                                                                              code 1

                                                                                                                                                                                                                                                              Explanation 2

                                                                                                                                                                                                                                                              code 2

                                                                                                                                                                                                                                                              Error Conditions

                                                                                                                                                                                                                                                              Advanced Notes

                                                                                                                                                                                                                                                              History

                                                                                                                                                                                                                                                              Calculator OS Version Description
                                                                                                                                                                                                                                                              TI-83+ 1.16 Added
                                                                                                                                                                                                                                                              Property Value
                                                                                                                                                                                                                                                              Hex Value $3F
                                                                                                                                                                                                                                                              Categories
                                                                                                                                                                                                                                                              Localizations

                                                                                                                                                                                                                                                                ⏎ (newline)

                                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                                Examples

                                                                                                                                                                                                                                                                Explanation 1

                                                                                                                                                                                                                                                                code 1

                                                                                                                                                                                                                                                                Explanation 2

                                                                                                                                                                                                                                                                code 2

                                                                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                                                                Advanced Notes

                                                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                                                TI-82 1.0 Added
                                                                                                                                                                                                                                                                Property Value
                                                                                                                                                                                                                                                                Hex Value $7F
                                                                                                                                                                                                                                                                Categories
                                                                                                                                                                                                                                                                Localizations
                                                                                                                                                                                                                                                                • FR: □

                                                                                                                                                                                                                                                                □

                                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                                □

                                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                                Examples

                                                                                                                                                                                                                                                                Explanation 1

                                                                                                                                                                                                                                                                code 1

                                                                                                                                                                                                                                                                Explanation 2

                                                                                                                                                                                                                                                                code 2

                                                                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                                                                Advanced Notes

                                                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                                                TI-82 1.0 Added
                                                                                                                                                                                                                                                                Property Value
                                                                                                                                                                                                                                                                Hex Value $BBEC
                                                                                                                                                                                                                                                                Categories
                                                                                                                                                                                                                                                                Localizations
                                                                                                                                                                                                                                                                • FR: ►

                                                                                                                                                                                                                                                                ►

                                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                                ►

                                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                                Examples

                                                                                                                                                                                                                                                                Explanation 1

                                                                                                                                                                                                                                                                code 1

                                                                                                                                                                                                                                                                Explanation 2

                                                                                                                                                                                                                                                                code 2

                                                                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                                                                Advanced Notes

                                                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                                                TI-83+ 1.16 Added
                                                                                                                                                                                                                                                                Property Value
                                                                                                                                                                                                                                                                Hex Value $01
                                                                                                                                                                                                                                                                Categories
                                                                                                                                                                                                                                                                Localizations
                                                                                                                                                                                                                                                                • FR: ►DMS

                                                                                                                                                                                                                                                                ►DMS

                                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                                Displays value in DMS format.

                                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                                value►DMS

                                                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                                                value

                                                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                                                2nd, angle, ANGLE, 4:DMS

                                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                                The ►DMS command can be used when displaying a real number on the home screen, or with the Disp and Pause commands. It will then format the number as an angle with degree, minute, and second parts.

                                                                                                                                                                                                                                                                30►DMS
    30°0'0"
100/9°►DMS
    11°6'40"

                                                                                                                                                                                                                                                                It will also work when displaying a number by putting it on the last line of a program by itself. It does not work with Output(, Text(, or any other more complicated display commands.

                                                                                                                                                                                                                                                                Although ►DMS is meant as a way to format angles in Degree mode, it doesn't depend on the angle mode chosen, only on the number itself. Note that entering a number as degree°minute'second" will also work, in any mode, and it will not be converted to radians in Radian mode.

                                                                                                                                                                                                                                                                Rounding to Nearest Second

                                                                                                                                                                                                                                                                If you'd prefer to not have seconds with decimal places, you can round your answer to the nearest second with the following formula:

                                                                                                                                                                                                                                                                round(Ans*3600,0)/3600►DMS

                                                                                                                                                                                                                                                                Or a slightly shorter version:

                                                                                                                                                                                                                                                                round(Ans36,2)/36►DMS

                                                                                                                                                                                                                                                                Tip: If you find yourself needing this formula regularly, put it into a Y= graphing-function as:

                                                                                                                                                                                                                                                                Y1=round(X36,2)/36

                                                                                                                                                                                                                                                                And then you can call it from your home screen via:

                                                                                                                                                                                                                                                                Y1(123.45678►DMS

                                                                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                                                                • ERR:SYNTAX is thrown if the command is used somewhere other than the allowed display commands.
                                                                                                                                                                                                                                                                • ERR:DATA TYPE is thrown if the value is complex, or if given a list or matrix as argument.

                                                                                                                                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583, thornahawk.

                                                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                                                TI-82 1.0 Added
                                                                                                                                                                                                                                                                Property Value
                                                                                                                                                                                                                                                                Hex Value $02
                                                                                                                                                                                                                                                                Categories
                                                                                                                                                                                                                                                                Localizations
                                                                                                                                                                                                                                                                • FR: ►Dec

                                                                                                                                                                                                                                                                ►Dec

                                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                                Displays a real or complex number, expression, list, or matrix in decimal format.

                                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                                value►Dec

                                                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                                                value

                                                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                                                math, MATH, 2:Dec

                                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                                This command is generally useless. Its supposed use is to convert numbers into decimal form, but any typed fractions are displayed as decimals anyway.

                                                                                                                                                                                                                                                                1/3
     .3333333333
1/3►Dec
     .3333333333

                                                                                                                                                                                                                                                                In 2.53 MP or higher, typed fractions are displayed in fraction form. Therefore, the ►Dec command is useful in this case.

                                                                                                                                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: alexrudd, blue_bear_94, burr, CloudVariable, DarkerLine, GoVegan, Myles_Zadok, Timtech.

                                                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                                                TI-82 1.0 Added
                                                                                                                                                                                                                                                                Property Value
                                                                                                                                                                                                                                                                Hex Value $BB06
                                                                                                                                                                                                                                                                Categories
                                                                                                                                                                                                                                                                Localizations
                                                                                                                                                                                                                                                                • FR: ►Eff(

                                                                                                                                                                                                                                                                ►Eff(

                                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                                Computes the effective interest rate.

                                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                                ►Eff(nominal rate,compounding periods)

                                                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                                                nominal rate
                                                                                                                                                                                                                                                                compounding periods

                                                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                                                apps, 1:Finance, CALC, C:►Eff(

                                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                                The ►Eff( command converts from a nominal interest rate to an effective interest rate. In other words, it converts an interest rate that does not take into account compounding periods into one that does. The two arguments are 1) the interest rate and 2) the number of compounding periods.

                                                                                                                                                                                                                                                                For example, take an interest rate of 7.5% per year, compounded monthly. You can use ►Eff( to find out the actual percent of interest per year:

                                                                                                                                                                                                                                                                ►Eff(7.5,12)
    7.663259886

                                                                                                                                                                                                                                                                Formulas

                                                                                                                                                                                                                                                                The formula for converting from a nominal rate to an effective rate is:

                                                                                                                                                                                                                                                                (1) \(\begin{align} \texttt{Eff}=100\left(\left(1+\frac{\texttt{Nom}}{100 \texttt{CP}}\right)^{\texttt{CP}}-1\right) \end{align}\)

                                                                                                                                                                                                                                                                Here, Eff is the effective rate, Nom is the nominal rate, and CP is the number of compounding periods.

                                                                                                                                                                                                                                                                Error Conditions

                                                                                                                                                                                                                                                                • ERR:DOMAIN is thrown if the number of compounding periods is not positive, or if the nominal rate is -100% or lower (an exception's made for the nominal rate if there is only one compounding period, since ►Eff(X,1)=X)

                                                                                                                                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, jonbush, Myles_Zadok.

                                                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                                                TI-83 0.01013 Added
                                                                                                                                                                                                                                                                Property Value
                                                                                                                                                                                                                                                                Hex Value $03
                                                                                                                                                                                                                                                                Categories
                                                                                                                                                                                                                                                                Localizations
                                                                                                                                                                                                                                                                • FR: ►Frac

                                                                                                                                                                                                                                                                ►Frac

                                                                                                                                                                                                                                                                Overview

                                                                                                                                                                                                                                                                Displays a real or complex number, expression, list, or matrix as a fraction simplified to its simplest terms.

                                                                                                                                                                                                                                                                Availability: Token available everywhere.

                                                                                                                                                                                                                                                                Syntax

                                                                                                                                                                                                                                                                value►Frac

                                                                                                                                                                                                                                                                Arguments

                                                                                                                                                                                                                                                                NameTypeOptional
                                                                                                                                                                                                                                                                value

                                                                                                                                                                                                                                                                Location

                                                                                                                                                                                                                                                                math, MATH, 1:Frac

                                                                                                                                                                                                                                                                Description

                                                                                                                                                                                                                                                                ►Frac attempts to display the input in fraction form. It only works on the home screen outside a program, or with the Disp and Pause commands in a program. It takes up to 12 decimal places of a non-terminating decimal to find the corresponding fraction. The decimal input is returned if ►Frac fails to find the fraction form.

                                                                                                                                                                                                                                                                For a more versatile algorithm for finding fractions, see the Decimal to Fraction routine.

                                                                                                                                                                                                                                                                .333►Frac
        .333
.333333333333►Frac
         1/3

                                                                                                                                                                                                                                                                See Also

                                                                                                                                                                                                                                                                Source: parts of this page were written by the following TI|BD contributors: alexrudd, burr, CloudVariable, DarkerLine, GoVegan, kg583, Myles_Zadok.

                                                                                                                                                                                                                                                                History

                                                                                                                                                                                                                                                                Calculator OS Version Description
                                                                                                                                                                                                                                                                TI-82 1.0 Added
                                                                                                                                                                                                                                                                Property Value
                                                                                                                                                                                                                                                                Hex Value $EF31
                                                                                                                                                                                                                                                                Categories
                                                                                                                                                                                                                                                                  Localizations
                                                                                                                                                                                                                                                                  • FR: ►F◄►D

                                                                                                                                                                                                                                                                  ►F◄►D

                                                                                                                                                                                                                                                                  Overview

                                                                                                                                                                                                                                                                  Converts an answer from a fraction to a decimal or from a decimal to a fraction. Fraction and or decimal may be an approximation.

                                                                                                                                                                                                                                                                  Availability: Token available everywhere.

                                                                                                                                                                                                                                                                  Syntax

                                                                                                                                                                                                                                                                  ►F ◄►D

                                                                                                                                                                                                                                                                  Arguments

                                                                                                                                                                                                                                                                  NameTypeOptional
                                                                                                                                                                                                                                                                  ◄►

                                                                                                                                                                                                                                                                  Location

                                                                                                                                                                                                                                                                  alpha, F1, 4:

                                                                                                                                                                                                                                                                  Description

                                                                                                                                                                                                                                                                  The ►F◄►D command is used to convert a number from fraction form to decimal form, or vice versa. Regardless of what form the given number is, this command is meant to automatically determine the form so that it returns the other. It is in essence a combination of the ►Frac and ►Dec commands, applying ►Frac if the input is in decimal form and ►Dec if it is a fraction.

                                                                                                                                                                                                                                                                  7.5►F◄ ►D
        15/2
Ans►F◄ ►D
        7.5

                                                                                                                                                                                                                                                                  Source: parts of this page were written by the following TI|BD contributors: Battlesquid, burr, ccrh2009, kg583, Timothy Foster.

                                                                                                                                                                                                                                                                  History

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                                                                                                                                                                                                                                                                  • FR: ►Nom(

                                                                                                                                                                                                                                                                  ►Nom(

                                                                                                                                                                                                                                                                  Overview

                                                                                                                                                                                                                                                                  Computes the nominal interest rate.

                                                                                                                                                                                                                                                                  Availability: Token available everywhere.

                                                                                                                                                                                                                                                                  Syntax

                                                                                                                                                                                                                                                                  ►Nom(effective rate,compounding periods)

                                                                                                                                                                                                                                                                  Arguments

                                                                                                                                                                                                                                                                  NameTypeOptional
                                                                                                                                                                                                                                                                  effective rate
                                                                                                                                                                                                                                                                  compounding periods

                                                                                                                                                                                                                                                                  Location

                                                                                                                                                                                                                                                                  apps, 1:Finance, CALC, B:►Nom(

                                                                                                                                                                                                                                                                  Description

                                                                                                                                                                                                                                                                  The ►Nom( command converts from an effective interest rate to a nominal interest rate. In other words, it converts an interest rate that takes compounding periods into account into one that doesn't. The two arguments are 1) the interest rate and 2) the number of compounding periods.

                                                                                                                                                                                                                                                                  For example, you want to know the interest rate, compounded monthly, that will yield a total increase of 10% per year:

                                                                                                                                                                                                                                                                  ►Nom(10,12)
    9.568968515

                                                                                                                                                                                                                                                                  Formulas

                                                                                                                                                                                                                                                                  The formula for converting from an effective rate to a nominal rate is:

                                                                                                                                                                                                                                                                  (1) \(\begin{align} \texttt{Nom}=100 \texttt{CP} \left(\sqrt[\texttt{CP}]{\frac{\texttt{Eff}}{100}+1}-1\right) \end{align}\)

                                                                                                                                                                                                                                                                  Here, Eff is the effective rate, Nom is the nominal rate, and CP is the number of compounding periods.

                                                                                                                                                                                                                                                                  Error Conditions

                                                                                                                                                                                                                                                                  • ERR:DOMAIN is thrown if the number of compounding periods is not positive, or if the nominal rate is -100% or lower (an exception's made for the nominal rate if there is only one compounding period, since ►Nom(X,1)=X).

                                                                                                                                                                                                                                                                  Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Xeda Elnara.

                                                                                                                                                                                                                                                                  History

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                                                                                                                                                                                                                                                                  TI-83 0.01013 Added
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                                                                                                                                                                                                                                                                  • FR: ►Polaire

                                                                                                                                                                                                                                                                  ►Polar

                                                                                                                                                                                                                                                                  Overview

                                                                                                                                                                                                                                                                  Displays complex value in polar format.

                                                                                                                                                                                                                                                                  Availability: Token available everywhere.

                                                                                                                                                                                                                                                                  Syntax

                                                                                                                                                                                                                                                                  complex value ►Polar

                                                                                                                                                                                                                                                                  Arguments

                                                                                                                                                                                                                                                                  NameTypeOptional
                                                                                                                                                                                                                                                                  complex valuecomplex

                                                                                                                                                                                                                                                                  Location

                                                                                                                                                                                                                                                                  math, CMPLX, 7:Polar

                                                                                                                                                                                                                                                                  Description

                                                                                                                                                                                                                                                                  The ►Polar command can be used when displaying a complex number on the home screen, or with the Disp and Pause commands. It will then format the number as though r𝑒^θ𝑖 mode were enabled. It also works with lists.

                                                                                                                                                                                                                                                                  i
    i
i►Polar
    1𝑒^(1.570796327i)
{1,i}►Polar
    {1 1𝑒^(1.570796327i)}

                                                                                                                                                                                                                                                                  It will also work when displaying a number by putting it on the last line of a program by itself. It does not work with Output(, Text(, or any other more complicated display commands.

                                                                                                                                                                                                                                                                  To actually separate a number into the components of polar form, use abs( and angle(.

                                                                                                                                                                                                                                                                  Error Conditions

                                                                                                                                                                                                                                                                  • ERR:SYNTAX is thrown if the command is used somewhere other than the allowed display commands.
                                                                                                                                                                                                                                                                  • ERR:DATA TYPE is thrown if the value is real.

                                                                                                                                                                                                                                                                  Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan.

                                                                                                                                                                                                                                                                  History

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                                                                                                                                                                                                                                                                  • FR: ►Rect

                                                                                                                                                                                                                                                                  ►Rect

                                                                                                                                                                                                                                                                  Overview

                                                                                                                                                                                                                                                                  Displays complex value or list in rectangular format.

                                                                                                                                                                                                                                                                  Availability: Token available everywhere.

                                                                                                                                                                                                                                                                  Syntax

                                                                                                                                                                                                                                                                  complex value ►Rect

                                                                                                                                                                                                                                                                  Arguments

                                                                                                                                                                                                                                                                  NameTypeOptional
                                                                                                                                                                                                                                                                  complex valuecomplex

                                                                                                                                                                                                                                                                  Location

                                                                                                                                                                                                                                                                  math, CMPLX, 6:Rect

                                                                                                                                                                                                                                                                  Description

                                                                                                                                                                                                                                                                  The ►Rect command can be used when displaying a complex number on the home screen, or with the Disp and Pause commands. It will then format the number as though a+b𝑖 mode were enabled, even when it's not. It also works with lists.

                                                                                                                                                                                                                                                                  i►Polar
    1𝑒^(1.570796327i)
Ans►Rect
    i

                                                                                                                                                                                                                                                                  It will also work when displaying a number by putting it on the last line of a program by itself. It does not work with Output(, Text(, or any other more complicated display commands.

                                                                                                                                                                                                                                                                  To actually separate a number into the components of rectangular form, use real( and imag(.

                                                                                                                                                                                                                                                                  Error Conditions

                                                                                                                                                                                                                                                                  • ERR:SYNTAX is thrown if the command is used somewhere other than the allowed display commands.
                                                                                                                                                                                                                                                                  • ERR:DATA TYPE is thrown if the value is real.

                                                                                                                                                                                                                                                                  Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan.

                                                                                                                                                                                                                                                                  History

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                                                                                                                                                                                                                                                                  TI-83 0.01013 Added
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                                                                                                                                                                                                                                                                    • FR: ►n⁄d◄►Un⁄d

                                                                                                                                                                                                                                                                    ►n⁄d◄►Un⁄d

                                                                                                                                                                                                                                                                    Overview

                                                                                                                                                                                                                                                                    Converts the results from a fraction to mixed number or from a mixed number to a fraction, if applicable.

                                                                                                                                                                                                                                                                    Availability: Token available everywhere.

                                                                                                                                                                                                                                                                    Syntax

                                                                                                                                                                                                                                                                    ►n/d ◄►Un/d

                                                                                                                                                                                                                                                                    Arguments

                                                                                                                                                                                                                                                                    NameTypeOptional
                                                                                                                                                                                                                                                                    ◄►

                                                                                                                                                                                                                                                                    Location

                                                                                                                                                                                                                                                                    alpha, F1, 3:, n/d, Un/d

                                                                                                                                                                                                                                                                    Description

                                                                                                                                                                                                                                                                    n/d_Un/d is the command for switching between an improper fraction and a mixed number.
                                                                                                                                                                                                                                                                    It is accessible by pressing ALPHA then Y= then 3.

                                                                                                                                                                                                                                                                    Source: parts of this page were written by the following TI|BD contributors: ccrh2009.

                                                                                                                                                                                                                                                                    History

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                                                                                                                                                                                                                                                                    • FR: ◄

                                                                                                                                                                                                                                                                    ◄

                                                                                                                                                                                                                                                                    Overview

                                                                                                                                                                                                                                                                    Syntax

                                                                                                                                                                                                                                                                    ◄

                                                                                                                                                                                                                                                                    Description

                                                                                                                                                                                                                                                                    Examples

                                                                                                                                                                                                                                                                    Explanation 1

                                                                                                                                                                                                                                                                    code 1

                                                                                                                                                                                                                                                                    Explanation 2

                                                                                                                                                                                                                                                                    code 2

                                                                                                                                                                                                                                                                    Error Conditions

                                                                                                                                                                                                                                                                    Advanced Notes

                                                                                                                                                                                                                                                                    History

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                                                                                                                                                                                                                                                                    • FR: ⬚

                                                                                                                                                                                                                                                                    ⬚

                                                                                                                                                                                                                                                                    Overview

                                                                                                                                                                                                                                                                    Syntax

                                                                                                                                                                                                                                                                    ⬚

                                                                                                                                                                                                                                                                    Description

                                                                                                                                                                                                                                                                    Examples

                                                                                                                                                                                                                                                                    Explanation 1

                                                                                                                                                                                                                                                                    code 1

                                                                                                                                                                                                                                                                    Explanation 2

                                                                                                                                                                                                                                                                    code 2

                                                                                                                                                                                                                                                                    Error Conditions

                                                                                                                                                                                                                                                                    Advanced Notes

                                                                                                                                                                                                                                                                    History

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                                                                                                                                                                                                                                                                    • FR: ﹢

                                                                                                                                                                                                                                                                    ﹢

                                                                                                                                                                                                                                                                    Overview

                                                                                                                                                                                                                                                                    Availability: Token available everywhere.

                                                                                                                                                                                                                                                                    Syntax

                                                                                                                                                                                                                                                                    ﹢

                                                                                                                                                                                                                                                                    Description

                                                                                                                                                                                                                                                                    Examples

                                                                                                                                                                                                                                                                    Explanation 1

                                                                                                                                                                                                                                                                    code 1

                                                                                                                                                                                                                                                                    Explanation 2

                                                                                                                                                                                                                                                                    code 2

                                                                                                                                                                                                                                                                    Error Conditions

                                                                                                                                                                                                                                                                    Advanced Notes

                                                                                                                                                                                                                                                                    History

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                                                                                                                                                                                                                                                                    • FR: 𝐅

                                                                                                                                                                                                                                                                    𝐅

                                                                                                                                                                                                                                                                    Overview

                                                                                                                                                                                                                                                                    Syntax

                                                                                                                                                                                                                                                                    𝐅

                                                                                                                                                                                                                                                                    Description

                                                                                                                                                                                                                                                                    Examples

                                                                                                                                                                                                                                                                    Explanation 1

                                                                                                                                                                                                                                                                    code 1

                                                                                                                                                                                                                                                                    Explanation 2

                                                                                                                                                                                                                                                                    code 2

                                                                                                                                                                                                                                                                    Error Conditions

                                                                                                                                                                                                                                                                    Advanced Notes

                                                                                                                                                                                                                                                                    History

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                                                                                                                                                                                                                                                                    TI-83+ 1.03 Added
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                                                                                                                                                                                                                                                                    • FR: 𝐅FRép(

                                                                                                                                                                                                                                                                    𝐅cdf(

                                                                                                                                                                                                                                                                    Overview

                                                                                                                                                                                                                                                                    Computes the 𝐅 distribution probability between lowerboundand upperbound for the specified numerator df (degrees of freedom) and denominator df.

                                                                                                                                                                                                                                                                    Availability: Token available everywhere.

                                                                                                                                                                                                                                                                    Syntax

                                                                                                                                                                                                                                                                    𝐅cdf(lowerbound,upperbound,numerator df,denominator df)

                                                                                                                                                                                                                                                                    Arguments

                                                                                                                                                                                                                                                                    NameTypeOptional
                                                                                                                                                                                                                                                                    𝐅
                                                                                                                                                                                                                                                                    lowerbound
                                                                                                                                                                                                                                                                    upperbound
                                                                                                                                                                                                                                                                    numerator df
                                                                                                                                                                                                                                                                    denominator df

                                                                                                                                                                                                                                                                    Location

                                                                                                                                                                                                                                                                    2nd, distr, DISTR, 0:cdf(

                                                                                                                                                                                                                                                                    Description

                                                                                                                                                                                                                                                                    Examples

                                                                                                                                                                                                                                                                    Explanation 1

                                                                                                                                                                                                                                                                    code 1

                                                                                                                                                                                                                                                                    Explanation 2

                                                                                                                                                                                                                                                                    code 2

                                                                                                                                                                                                                                                                    Error Conditions

                                                                                                                                                                                                                                                                    Advanced Notes

                                                                                                                                                                                                                                                                    History

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                                                                                                                                                                                                                                                                    TI-83 0.01013 Added
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                                                                                                                                                                                                                                                                    • FR: 𝐅fdp(

                                                                                                                                                                                                                                                                    𝐅pdf(

                                                                                                                                                                                                                                                                    Overview

                                                                                                                                                                                                                                                                    Computes the 𝐅 distribution probability between lowerboundand upperbound for the specified numerator df (degrees of freedom) and denominator df.

                                                                                                                                                                                                                                                                    Availability: Token available everywhere.

                                                                                                                                                                                                                                                                    Syntax

                                                                                                                                                                                                                                                                    𝐅pdf(x,numerator df,denominator df)

                                                                                                                                                                                                                                                                    Arguments

                                                                                                                                                                                                                                                                    NameTypeOptional
                                                                                                                                                                                                                                                                    𝐅
                                                                                                                                                                                                                                                                    x
                                                                                                                                                                                                                                                                    numerator df
                                                                                                                                                                                                                                                                    denominator df

                                                                                                                                                                                                                                                                    Location

                                                                                                                                                                                                                                                                    2nd, distr, DISTR, 9:pdf(

                                                                                                                                                                                                                                                                    Description

                                                                                                                                                                                                                                                                    Fpdf( is the F-distribution probability density function.

                                                                                                                                                                                                                                                                    Since the F-distribution is continuous, the value of Fpdf( doesn't represent an actual probability - in fact, one of the only uses for this command is to draw a graph of the distribution. You could also use it for various calculus purposes, such as finding inflection points.

                                                                                                                                                                                                                                                                    The command takes 3 arguments: x is the point at which to evaluate the function (when graphing, use X for this argument), numerator df and denominator df are the numerator degrees of freedom and denominator degrees of freedom respectively (these specify a single Fpdf( curve out of an infinite family).

                                                                                                                                                                                                                                                                    The F-distribution is used mainly in significance tests of variance.

                                                                                                                                                                                                                                                                    Formulas

                                                                                                                                                                                                                                                                    The value of the Fpdf( is given by

                                                                                                                                                                                                                                                                    (1) \(\begin{align} \texttt{Fpdf}(x,d_1,d_2) = \frac{\left( \frac{d_1x}{d_1x+d_2} \right)^{d_1/2} \left(1-\frac{d_1x}{d_1x+d_2}\right)^{d_2/2}}{x \texttt{B}(d_1/2,d_2/2)} \end{align}\)

                                                                                                                                                                                                                                                                    where B(x,y) is the Beta function.

                                                                                                                                                                                                                                                                    Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583.

                                                                                                                                                                                                                                                                    History

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                                                                                                                                                                                                                                                                    TI-83 0.01013 Added
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                                                                                                                                                                                                                                                                    • FR: 𝑒

                                                                                                                                                                                                                                                                    𝑒

                                                                                                                                                                                                                                                                    Overview

                                                                                                                                                                                                                                                                    Returns decimal approximation of the constant 𝑒.

                                                                                                                                                                                                                                                                    Availability: Token available everywhere.

                                                                                                                                                                                                                                                                    Syntax

                                                                                                                                                                                                                                                                    𝑒

                                                                                                                                                                                                                                                                    Location

                                                                                                                                                                                                                                                                    2nd, e

                                                                                                                                                                                                                                                                    Description

                                                                                                                                                                                                                                                                    e is a constant on the TI-83 series calculators. The constant holds the approximate value of Euler's number, fairly important in calculus and other higher-level mathematics.

                                                                                                                                                                                                                                                                    The approximate value, to as many digits as stored in the calculator, is 2.718281828459…

                                                                                                                                                                                                                                                                    The main use of e is as the base of the exponential function 𝑒^( (which is also a separate function on the calculator), and its inverse, the natural logarithm ln(. From these functions, others such as the trigonometric functions (e.g. sin() and the hyperbolic functions (e.g. sinh() can be defined. In r𝑒^θ𝑖 mode, e is used in an alternate form of expressing complex numbers.

                                                                                                                                                                                                                                                                    Important as the number e is, nine times out of ten you won't need the constant itself when using your calculator, but rather the 𝑒^( and ln( functions.

                                                                                                                                                                                                                                                                    Source: parts of this page were written by the following TI|BD contributors: alexrudd, burr, DarkerLine, GoVegan, Myles_Zadok, simplethinker, Timothy Foster.

                                                                                                                                                                                                                                                                    History

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                                                                                                                                                                                                                                                                    • FR: 𝑒^(

                                                                                                                                                                                                                                                                    𝑒^(

                                                                                                                                                                                                                                                                    Overview

                                                                                                                                                                                                                                                                    Returns e raised to power.

                                                                                                                                                                                                                                                                    Availability: Token available everywhere.

                                                                                                                                                                                                                                                                    Syntax

                                                                                                                                                                                                                                                                    𝑒^(power)

                                                                                                                                                                                                                                                                    Arguments

                                                                                                                                                                                                                                                                    NameTypeOptional
                                                                                                                                                                                                                                                                    power

                                                                                                                                                                                                                                                                    Location

                                                                                                                                                                                                                                                                    2nd, eˣ

                                                                                                                                                                                                                                                                    Overview

                                                                                                                                                                                                                                                                    Returns a list of e raised to a list of powers.

                                                                                                                                                                                                                                                                    Availability: Token available everywhere.

                                                                                                                                                                                                                                                                    Syntax

                                                                                                                                                                                                                                                                    𝑒^(list)

                                                                                                                                                                                                                                                                    Arguments

                                                                                                                                                                                                                                                                    NameTypeOptional
                                                                                                                                                                                                                                                                    listlist

                                                                                                                                                                                                                                                                    Location

                                                                                                                                                                                                                                                                    2nd, eˣ

                                                                                                                                                                                                                                                                    Description

                                                                                                                                                                                                                                                                    The e^( command raises the constant e to a power. Since it's possible to just type out e, ^, and (, the reason for having a separate function isn't immediately obvious but in fact most of the time you need to use e, it's to raise it to a power.

                                                                                                                                                                                                                                                                    The trigonometric and hyperbolic functions can be expressed, and in fact are usually defined, in terms of e^(.

                                                                                                                                                                                                                                                                    e^( accepts numbers and lists (but unfortunately not matrices) as arguments. It also works, and is often used for, complex numbers (in fact, one of the standard forms of complex numbers on TI-83 series calculators is r𝑒^θ𝑖, which uses the e^( function)

                                                                                                                                                                                                                                                                    e^(2)
        7.389056099
𝑒^(πi)
        -1
𝑒^({-1,0,1})
        {.3678794412 1 2.718281828}

                                                                                                                                                                                                                                                                    Formulas

                                                                                                                                                                                                                                                                    The e^( is usually defined by an infinite series:

                                                                                                                                                                                                                                                                    (1) \(\begin{align} e^x=\sum_{n=0}^\infty{\frac{x^n}{n!}} \end{align}\)

                                                                                                                                                                                                                                                                    This is then used to define exponentiation in general (for all real and even complex numbers), rather than using some sort of definition of exponents that involves multiplying a number by itself many times (which only works for integers).

                                                                                                                                                                                                                                                                    Source: parts of this page were written by the following TI|BD contributors: DarkerLine, GoVegan, Myles_Zadok, Timothy Foster.

                                                                                                                                                                                                                                                                    History

                                                                                                                                                                                                                                                                    Calculator OS Version Description
                                                                                                                                                                                                                                                                    TI-82 1.0 𝑒^ added
                                                                                                                                                                                                                                                                    TI-83 0.01013 Renamed 𝑒^ to 𝑒^(
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                                                                                                                                                                                                                                                                    • FR: 𝑖

                                                                                                                                                                                                                                                                    𝑖

                                                                                                                                                                                                                                                                    Overview

                                                                                                                                                                                                                                                                    Returns the complex number i.

                                                                                                                                                                                                                                                                    Comment:Complex i

                                                                                                                                                                                                                                                                    Availability: Token available everywhere.

                                                                                                                                                                                                                                                                    Syntax

                                                                                                                                                                                                                                                                    i

                                                                                                                                                                                                                                                                    Location

                                                                                                                                                                                                                                                                    2nd, 𝑖

                                                                                                                                                                                                                                                                    Description

                                                                                                                                                                                                                                                                    The 𝑖 symbol is short for √(-1), and is used for complex numbers in algebra and complex analysis. On the calculator, entering 𝑖 will not cause an error, even in Real mode, but operations that result in a complex number (such as taking the square root of a negative number) will. If you're dealing with complex numbers, then, it's best to switch to a+b𝑖 or r𝑒^θ𝑖 mode.

                                                                                                                                                                                                                                                                    Advanced Uses

                                                                                                                                                                                                                                                                    By using 𝑖 in a calculation, the calculator switches to complex number mode to do it, even if in Real mode. So √(-1) will throw an ERR:NONREAL ANS, but √(0𝑖-1) will not (even though it's the same number). This can be used to force calculations to be done using complex numbers regardless of the mode setting — usually by adding or subtracting 0𝑖, although more clever ways can be found.

                                                                                                                                                                                                                                                                    A good example of this technique is our Quadratic Formula routine.

                                                                                                                                                                                                                                                                    See Also

                                                                                                                                                                                                                                                                    Source: parts of this page were written by the following TI|BD contributors: burr, CloudVariable, DarkerLine, GoVegan.

                                                                                                                                                                                                                                                                    History

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                                                                                                                                                                                                                                                                    TI-82 1.0 Added
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                                                                                                                                                                                                                                                                    • FR: 𝑛

                                                                                                                                                                                                                                                                    𝑛

                                                                                                                                                                                                                                                                    Overview

                                                                                                                                                                                                                                                                    Availability: Token available everywhere.

                                                                                                                                                                                                                                                                    Syntax

                                                                                                                                                                                                                                                                    𝑛

                                                                                                                                                                                                                                                                    Description

                                                                                                                                                                                                                                                                    Examples

                                                                                                                                                                                                                                                                    Explanation 1

                                                                                                                                                                                                                                                                    code 1

                                                                                                                                                                                                                                                                    Explanation 2

                                                                                                                                                                                                                                                                    code 2

                                                                                                                                                                                                                                                                    Error Conditions

                                                                                                                                                                                                                                                                    Advanced Notes

                                                                                                                                                                                                                                                                    History

                                                                                                                                                                                                                                                                    Calculator OS Version Description
                                                                                                                                                                                                                                                                    TI-82 1.0 Added
                                                                                                                                                                                                                                                                    Property Value
                                                                                                                                                                                                                                                                    Hex Value $631D
                                                                                                                                                                                                                                                                    Categories
                                                                                                                                                                                                                                                                    Localizations
                                                                                                                                                                                                                                                                    • FR: 𝑛Max

                                                                                                                                                                                                                                                                    𝑛Max

                                                                                                                                                                                                                                                                    Overview

                                                                                                                                                                                                                                                                    Availability: Token available everywhere.

                                                                                                                                                                                                                                                                    Syntax

                                                                                                                                                                                                                                                                    𝑛Max

                                                                                                                                                                                                                                                                    Description

                                                                                                                                                                                                                                                                    Examples

                                                                                                                                                                                                                                                                    Explanation 1

                                                                                                                                                                                                                                                                    code 1

                                                                                                                                                                                                                                                                    Explanation 2

                                                                                                                                                                                                                                                                    code 2

                                                                                                                                                                                                                                                                    Error Conditions

                                                                                                                                                                                                                                                                    Advanced Notes

                                                                                                                                                                                                                                                                    History

                                                                                                                                                                                                                                                                    Calculator OS Version Description
                                                                                                                                                                                                                                                                    TI-82 1.0 Added
                                                                                                                                                                                                                                                                    Property Value
                                                                                                                                                                                                                                                                    Hex Value $631F
                                                                                                                                                                                                                                                                    Categories
                                                                                                                                                                                                                                                                    Localizations
                                                                                                                                                                                                                                                                    • FR: 𝑛Min

                                                                                                                                                                                                                                                                    𝑛Min

                                                                                                                                                                                                                                                                    Overview

                                                                                                                                                                                                                                                                    Availability: Token available everywhere.

                                                                                                                                                                                                                                                                    Syntax

                                                                                                                                                                                                                                                                    𝑛Min

                                                                                                                                                                                                                                                                    Description

                                                                                                                                                                                                                                                                    Examples

                                                                                                                                                                                                                                                                    Explanation 1

                                                                                                                                                                                                                                                                    code 1

                                                                                                                                                                                                                                                                    Explanation 2

                                                                                                                                                                                                                                                                    code 2

                                                                                                                                                                                                                                                                    Error Conditions

                                                                                                                                                                                                                                                                    Advanced Notes

                                                                                                                                                                                                                                                                    History

                                                                                                                                                                                                                                                                    Calculator OS Version Description
                                                                                                                                                                                                                                                                    TI-82 1.0 𝑛Start added
                                                                                                                                                                                                                                                                    TI-83 0.01013 Renamed 𝑛Start to 𝑛Min
                                                                                                                                                                                                                                                                    Property Value
                                                                                                                                                                                                                                                                    Hex Value $632B
                                                                                                                                                                                                                                                                    Categories
                                                                                                                                                                                                                                                                    Localizations
                                                                                                                                                                                                                                                                    • FR: 𝗡

                                                                                                                                                                                                                                                                    𝗡

                                                                                                                                                                                                                                                                    Overview

                                                                                                                                                                                                                                                                    Syntax

                                                                                                                                                                                                                                                                    𝗡

                                                                                                                                                                                                                                                                    Description

                                                                                                                                                                                                                                                                    Examples

                                                                                                                                                                                                                                                                    Explanation 1

                                                                                                                                                                                                                                                                    code 1

                                                                                                                                                                                                                                                                    Explanation 2

                                                                                                                                                                                                                                                                    code 2

                                                                                                                                                                                                                                                                    Error Conditions

                                                                                                                                                                                                                                                                    Advanced Notes

                                                                                                                                                                                                                                                                    History

                                                                                                                                                                                                                                                                    Calculator OS Version Description
                                                                                                                                                                                                                                                                    TI-83 0.01013 Added
                                                                                                                                                                                                                                                                    Property Value
                                                                                                                                                                                                                                                                    Hex Value $BBF2
                                                                                                                                                                                                                                                                    Categories
                                                                                                                                                                                                                                                                    Localizations
                                                                                                                                                                                                                                                                    • FR: 🡅

                                                                                                                                                                                                                                                                    🡅

                                                                                                                                                                                                                                                                    Overview

                                                                                                                                                                                                                                                                    Syntax

                                                                                                                                                                                                                                                                    🡅

                                                                                                                                                                                                                                                                    Description

                                                                                                                                                                                                                                                                    Examples

                                                                                                                                                                                                                                                                    Explanation 1

                                                                                                                                                                                                                                                                    code 1

                                                                                                                                                                                                                                                                    Explanation 2

                                                                                                                                                                                                                                                                    code 2

                                                                                                                                                                                                                                                                    Error Conditions

                                                                                                                                                                                                                                                                    Advanced Notes

                                                                                                                                                                                                                                                                    History

                                                                                                                                                                                                                                                                    Calculator OS Version Description
                                                                                                                                                                                                                                                                    TI-83+ 1.16 Added
                                                                                                                                                                                                                                                                    Property Value
                                                                                                                                                                                                                                                                    Hex Value $BBF3
                                                                                                                                                                                                                                                                    Categories
                                                                                                                                                                                                                                                                    Localizations
                                                                                                                                                                                                                                                                    • FR: 🡇

                                                                                                                                                                                                                                                                    🡇

                                                                                                                                                                                                                                                                    Overview

                                                                                                                                                                                                                                                                    Syntax

                                                                                                                                                                                                                                                                    🡇

                                                                                                                                                                                                                                                                    Description

                                                                                                                                                                                                                                                                    Examples

                                                                                                                                                                                                                                                                    Explanation 1

                                                                                                                                                                                                                                                                    code 1

                                                                                                                                                                                                                                                                    Explanation 2

                                                                                                                                                                                                                                                                    code 2

                                                                                                                                                                                                                                                                    Error Conditions

                                                                                                                                                                                                                                                                    Advanced Notes

                                                                                                                                                                                                                                                                    History

                                                                                                                                                                                                                                                                    Calculator OS Version Description
                                                                                                                                                                                                                                                                    TI-83+ 1.16 Added

                                                                                                                                                                                                                                                                    Ended: Tokens